microsoft/FStarDataSet · Datasets at Hugging Face

FStar.HyperStack.ST.ST

val read_sub_buffer (#a: Type0) (#rrel #rel: srel a) (b: mbuffer a rrel rel) (idx len: U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len)

val read_sub_buffer (#a: Type0) (#rrel #rel: srel a) (b: mbuffer a rrel rel) (idx len: U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) let read_sub_buffer (#a: Type0) (#rrel #rel: srel a) (b: mbuffer a rrel rel) (idx len: U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) =

true

null

false

let open HST in let s = !(Buffer?.content b) in let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in Seq.slice s (U32.v idx) (U32.v idx + U32.v len)

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "FStar.Seq.Base.slice", "FStar.UInt32.v", "Prims.op_Addition", "FStar.Seq.Base.seq", "LowStar.Monotonic.Buffer.__proj__Buffer__item__idx", "LowStar.Monotonic.Buffer.__proj__Buffer__item__max_length", "FStar.Seq.Properties.lseq", "FStar.HyperStack.ST.op_Bang", "LowStar.Monotonic.Buffer.srel_to_lsrel", "LowStar.Monotonic.Buffer.__proj__Buffer__item__content", "FStar.Monotonic.HyperStack.mem", "Prims.l_and", "LowStar.Monotonic.Buffer.live", "Prims.b2t", "Prims.op_GreaterThan", "Prims.op_LessThanOrEqual", "LowStar.Monotonic.Buffer.length", "Prims.eq2", "LowStar.Monotonic.Buffer.as_seq" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val read_sub_buffer (#a: Type0) (#rrel #rel: srel a) (b: mbuffer a rrel rel) (idx len: U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len))

[]

LowStar.Monotonic.Buffer.read_sub_buffer

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

b: LowStar.Monotonic.Buffer.mbuffer a rrel rel -> idx: FStar.UInt32.t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.ST (FStar.Seq.Base.seq a)

{ "end_col": 51, "end_line": 1499, "start_col": 4, "start_line": 1495 }

FStar.HyperStack.ST.ST

val mgcmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ recallable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false

val mgcmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ recallable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len))) let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len =

true

null

false

alloc_heap_common r len (read_sub_buffer src id_src len) false

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.Monotonic.HyperHeap.rid", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.alloc_heap_common", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.UInt32.v", "FStar.Seq.Base.seq", "Prims.eq2", "Prims.int", "Prims.l_or", "Prims.b2t", "Prims.op_GreaterThanOrEqual", "FStar.UInt.size", "FStar.Seq.Base.length", "LowStar.Monotonic.Buffer.read_sub_buffer", "Prims.l_and", "LowStar.Monotonic.Buffer.frameOf", "LowStar.Monotonic.Buffer.recallable" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val mgcmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ recallable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)))

[]

LowStar.Monotonic.Buffer.mgcmalloc_and_blit

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

r: FStar.Monotonic.HyperHeap.rid -> src: LowStar.Monotonic.Buffer.mbuffer a rrel1 rel1 -> id_src: FStar.UInt32.t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.ST (b: LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len) {LowStar.Monotonic.Buffer.frameOf b == r /\ LowStar.Monotonic.Buffer.recallable b})

{ "end_col": 64, "end_line": 1502, "start_col": 2, "start_line": 1502 }

FStar.HyperStack.ST.StackInline

val malloca (#a:Type0) (#rrel:srel a) (init:a) (len:U32.t) :HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> alloca_pre len)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init) /\ frameOf b == HS.get_tip h0))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len)

val malloca (#a:Type0) (#rrel:srel a) (init:a) (len:U32.t) :HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> alloca_pre len)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init) /\ frameOf b == HS.get_tip h0)) let malloca #a #rrel init len =

true

null

false

lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len)

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.UInt32.v", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.salloc", "FStar.Seq.Base.create", "FStar.HyperStack.ST.mstackref", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val malloca (#a:Type0) (#rrel:srel a) (init:a) (len:U32.t) :HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> alloca_pre len)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init) /\ frameOf b == HS.get_tip h0))

[]

LowStar.Monotonic.Buffer.malloca

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

init: a -> len: FStar.UInt32.t -> FStar.HyperStack.ST.StackInline (LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len))

{ "end_col": 41, "end_line": 1515, "start_col": 2, "start_line": 1511 }

FStar.HyperStack.ST.ST

val mmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ freeable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true

val mmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ freeable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len))) let mmalloc_and_blit #_ #_ r #_ #_ src id_src len =

true

null

false

alloc_heap_common r len (read_sub_buffer src id_src len) true

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.Monotonic.HyperHeap.rid", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.alloc_heap_common", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.UInt32.v", "FStar.Seq.Base.seq", "Prims.eq2", "Prims.int", "Prims.l_or", "Prims.b2t", "Prims.op_GreaterThanOrEqual", "FStar.UInt.size", "FStar.Seq.Base.length", "LowStar.Monotonic.Buffer.read_sub_buffer", "Prims.l_and", "LowStar.Monotonic.Buffer.frameOf", "LowStar.Monotonic.Buffer.freeable" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val mmalloc_and_blit (#a:Type0) (#rrel:srel a) (r:HS.rid) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == r /\ freeable b}) (requires fun h0 -> malloc_pre r len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)))

[]

LowStar.Monotonic.Buffer.mmalloc_and_blit

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

r: FStar.Monotonic.HyperHeap.rid -> src: LowStar.Monotonic.Buffer.mbuffer a rrel1 rel1 -> id_src: FStar.UInt32.t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.ST (b: LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len) {LowStar.Monotonic.Buffer.frameOf b == r /\ LowStar.Monotonic.Buffer.freeable b})

{ "end_col": 63, "end_line": 1508, "start_col": 2, "start_line": 1508 }

FStar.HyperStack.ST.StackInline

val malloca_of_list (#a:Type0) (#rrel:srel a) (init: list a) :HST.StackInline (lmbuffer a rrel rrel (normalize_term (List.Tot.length init))) (requires (fun _ -> alloca_of_list_pre init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init) /\ frameOf b == HS.get_tip h0))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len)

val malloca_of_list (#a:Type0) (#rrel:srel a) (init: list a) :HST.StackInline (lmbuffer a rrel rrel (normalize_term (List.Tot.length init))) (requires (fun _ -> alloca_of_list_pre init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init) /\ frameOf b == HS.get_tip h0)) let malloca_of_list #a #rrel init =

true

null

false

let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len)

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "Prims.list", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.Pervasives.normalize_term", "Prims.nat", "FStar.List.Tot.Base.length", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "FStar.UInt32.v", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.salloc", "FStar.HyperStack.ST.mstackref", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive", "FStar.Seq.Base.seq", "Prims.b2t", "Prims.op_Equality", "FStar.Seq.Base.length", "FStar.Seq.Properties.seq_of_list", "FStar.UInt32.uint_to_t" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len)

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val malloca_of_list (#a:Type0) (#rrel:srel a) (init: list a) :HST.StackInline (lmbuffer a rrel rrel (normalize_term (List.Tot.length init))) (requires (fun _ -> alloca_of_list_pre init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init) /\ frameOf b == HS.get_tip h0))

[]

LowStar.Monotonic.Buffer.malloca_of_list

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

init: Prims.list a -> FStar.HyperStack.ST.StackInline (LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.Pervasives.normalize_term (FStar.List.Tot.Base.length init)))

{ "end_col": 41, "end_line": 1531, "start_col": 35, "start_line": 1524 }

FStar.HyperStack.ST.StackInline

val malloca_and_blit (#a:Type0) (#rrel:srel a) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires fun h0 -> alloca_pre len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)) /\ frameOf b == HS.get_tip h0)

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len)

val malloca_and_blit (#a:Type0) (#rrel:srel a) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires fun h0 -> alloca_pre len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)) /\ frameOf b == HS.get_tip h0) let malloca_and_blit #a #rrel #_ #_ src id_src len =

true

null

false

lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len)

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.UInt32.v", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.salloc", "FStar.HyperStack.ST.mstackref", "LowStar.Monotonic.Buffer.read_sub_buffer", "FStar.Seq.Base.seq", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len)

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val malloca_and_blit (#a:Type0) (#rrel:srel a) (#rrel1 #rel1:srel a) (src:mbuffer a rrel1 rel1) (id_src:U32.t) (len:U32.t) : HST.StackInline (lmbuffer a rrel rrel (U32.v len)) (requires fun h0 -> alloca_pre len /\ live h0 src /\ U32.v id_src + U32.v len <= length src) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.slice (as_seq h0 src) (U32.v id_src) (U32.v id_src + U32.v len)) /\ frameOf b == HS.get_tip h0)

[]

LowStar.Monotonic.Buffer.malloca_and_blit

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

src: LowStar.Monotonic.Buffer.mbuffer a rrel1 rel1 -> id_src: FStar.UInt32.t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.StackInline (LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len))

{ "end_col": 41, "end_line": 1522, "start_col": 2, "start_line": 1518 }

FStar.HyperStack.ST.ST

val alloc_heap_common (#a: Type0) (#rrel: srel a) (r: HST.erid) (len: U32.t{U32.v len > 0}) (s: Seq.seq a {Seq.length s == U32.v len}) (mm: bool) : HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b

val alloc_heap_common (#a: Type0) (#rrel: srel a) (r: HST.erid) (len: U32.t{U32.v len > 0}) (s: Seq.seq a {Seq.length s == U32.v len}) (mm: bool) : HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) let alloc_heap_common (#a: Type0) (#rrel: srel a) (r: HST.erid) (len: U32.t{U32.v len > 0}) (s: Seq.seq a {Seq.length s == U32.v len}) (mm: bool) : HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) =

true

null

false

lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.HyperStack.ST.erid", "FStar.UInt32.t", "Prims.b2t", "Prims.op_GreaterThan", "FStar.UInt32.v", "FStar.Seq.Base.seq", "Prims.eq2", "Prims.int", "Prims.l_or", "Prims.op_GreaterThanOrEqual", "FStar.UInt.size", "FStar.UInt32.n", "FStar.Seq.Base.length", "Prims.bool", "LowStar.Monotonic.Buffer.mbuffer", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.ralloc_mm", "FStar.HyperStack.ST.mmmref", "FStar.HyperStack.ST.ralloc", "FStar.HyperStack.ST.mref", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive", "FStar.Monotonic.HyperStack.mem", "Prims.l_True", "Prims.l_and", "LowStar.Monotonic.Buffer.alloc_post_mem_common", "FStar.Monotonic.HyperHeap.rid", "LowStar.Monotonic.Buffer.frameOf", "FStar.Monotonic.HyperStack.is_mm", "LowStar.Monotonic.Buffer.__proj__Buffer__item__max_length", "LowStar.Monotonic.Buffer.__proj__Buffer__item__content", "LowStar.Monotonic.Buffer.__proj__Buffer__item__idx", "FStar.Ghost.reveal", "LowStar.Monotonic.Buffer.__proj__Buffer__item__length" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val alloc_heap_common (#a: Type0) (#rrel: srel a) (r: HST.erid) (len: U32.t{U32.v len > 0}) (s: Seq.seq a {Seq.length s == U32.v len}) (mm: bool) : HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b))

[]

LowStar.Monotonic.Buffer.alloc_heap_common

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

r: FStar.HyperStack.ST.erid -> len: FStar.UInt32.t{FStar.UInt32.v len > 0} -> s: FStar.Seq.Base.seq a {FStar.Seq.Base.length s == FStar.UInt32.v len} -> mm: Prims.bool -> FStar.HyperStack.ST.ST (LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len))

{ "end_col": 5, "end_line": 1481, "start_col": 4, "start_line": 1476 }

Prims.Tot

val cloc_cls: MG.cls abuffer

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let cloc_cls = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.cls abuffer) cls

val cloc_cls: MG.cls abuffer let cloc_cls =

false

null

false

assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.cls abuffer) cls

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[ "total" ]

[ "LowStar.Monotonic.Buffer.coerce", "FStar.ModifiesGen.cls", "LowStar.Monotonic.Buffer.abuffer", "LowStar.Monotonic.Buffer.ubuffer", "LowStar.Monotonic.Buffer.cls", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.eq2" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64" let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> () #push-options "--z3rlimit 128 --max_fuel 0 --max_ifuel 1 --initial_ifuel 1 --z3cliopt smt.qi.EAGER_THRESHOLD=4" let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b) )) = let open HST in if len = 0ul then () else begin let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src)); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h //for modifies clause end #pop-options let fill #t #rrel #rel b z len = fill' b z len let abuffer' = ubuffer' let coerce (t2: Type) (#t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1)) = x1

false

true

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 64, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val cloc_cls: MG.cls abuffer

[]

LowStar.Monotonic.Buffer.cloc_cls

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

FStar.ModifiesGen.cls LowStar.Monotonic.Buffer.abuffer

{ "end_col": 29, "end_line": 1656, "start_col": 2, "start_line": 1655 }

FStar.HyperStack.ST.ST

val mgcmalloc_of_list (#a:Type0) (#rrel:srel a) (r:HS.rid) (init:list a) :HST.ST (b:lmbuffer a rrel rrel (normalize_term (List.Tot.length init)){frameOf b == r /\ recallable b}) (requires (fun _ -> gcmalloc_of_list_pre r init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init)))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len)

val mgcmalloc_of_list (#a:Type0) (#rrel:srel a) (r:HS.rid) (init:list a) :HST.ST (b:lmbuffer a rrel rrel (normalize_term (List.Tot.length init)){frameOf b == r /\ recallable b}) (requires (fun _ -> gcmalloc_of_list_pre r init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init))) let mgcmalloc_of_list #a #rrel r init =

true

null

false

let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len)

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.Monotonic.HyperHeap.rid", "Prims.list", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.Pervasives.normalize_term", "Prims.nat", "FStar.List.Tot.Base.length", "Prims.l_and", "Prims.eq2", "LowStar.Monotonic.Buffer.frameOf", "LowStar.Monotonic.Buffer.recallable", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "FStar.UInt32.v", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.ralloc", "FStar.HyperStack.ST.mref", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive", "FStar.Seq.Base.seq", "Prims.b2t", "Prims.op_Equality", "FStar.Seq.Base.length", "FStar.Seq.Properties.seq_of_list", "FStar.UInt32.uint_to_t" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len)

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val mgcmalloc_of_list (#a:Type0) (#rrel:srel a) (r:HS.rid) (init:list a) :HST.ST (b:lmbuffer a rrel rrel (normalize_term (List.Tot.length init)){frameOf b == r /\ recallable b}) (requires (fun _ -> gcmalloc_of_list_pre r init)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.seq_of_list init)))

[]

LowStar.Monotonic.Buffer.mgcmalloc_of_list

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

r: FStar.Monotonic.HyperHeap.rid -> init: Prims.list a -> FStar.HyperStack.ST.ST (b: LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.Pervasives.normalize_term (FStar.List.Tot.Base.length init)) {LowStar.Monotonic.Buffer.frameOf b == r /\ LowStar.Monotonic.Buffer.recallable b})

{ "end_col": 41, "end_line": 1540, "start_col": 39, "start_line": 1533 }

Prims.Tot

val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let cloc_of_loc l = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.loc cloc_cls) l

val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls) let cloc_of_loc l =

false

null

false

assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.loc cloc_cls) l

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[ "total" ]

[ "LowStar.Monotonic.Buffer.loc", "LowStar.Monotonic.Buffer.coerce", "FStar.ModifiesGen.loc", "LowStar.Monotonic.Buffer.abuffer", "LowStar.Monotonic.Buffer.cloc_cls", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.eq2", "FStar.ModifiesGen.cls", "LowStar.Monotonic.Buffer.ubuffer" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64" let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> () #push-options "--z3rlimit 128 --max_fuel 0 --max_ifuel 1 --initial_ifuel 1 --z3cliopt smt.qi.EAGER_THRESHOLD=4" let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b) )) = let open HST in if len = 0ul then () else begin let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src)); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h //for modifies clause end #pop-options let fill #t #rrel #rel b z len = fill' b z len let abuffer' = ubuffer' let coerce (t2: Type) (#t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1)) = x1 let cloc_cls = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.cls abuffer) cls

false

true

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 64, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val cloc_of_loc (l: loc) : Tot (MG.loc cloc_cls)

[]

LowStar.Monotonic.Buffer.cloc_of_loc

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

l: LowStar.Monotonic.Buffer.loc -> FStar.ModifiesGen.loc LowStar.Monotonic.Buffer.cloc_cls

{ "end_col": 28, "end_line": 1660, "start_col": 2, "start_line": 1659 }

Prims.Tot

val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let loc_of_cloc l = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce loc l

val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc let loc_of_cloc l =

false

null

false

assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce loc l

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[ "total" ]

[ "FStar.ModifiesGen.loc", "LowStar.Monotonic.Buffer.abuffer", "LowStar.Monotonic.Buffer.cloc_cls", "LowStar.Monotonic.Buffer.coerce", "LowStar.Monotonic.Buffer.loc", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.eq2", "FStar.ModifiesGen.cls", "LowStar.Monotonic.Buffer.ubuffer" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64" let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> () #push-options "--z3rlimit 128 --max_fuel 0 --max_ifuel 1 --initial_ifuel 1 --z3cliopt smt.qi.EAGER_THRESHOLD=4" let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b) )) = let open HST in if len = 0ul then () else begin let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src)); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h //for modifies clause end #pop-options let fill #t #rrel #rel b z len = fill' b z len let abuffer' = ubuffer' let coerce (t2: Type) (#t1: Type) (x1: t1) : Pure t2 (requires (t1 == t2)) (ensures (fun y -> y == x1)) = x1 let cloc_cls = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.cls abuffer) cls let cloc_of_loc l = assert_norm (MG.cls abuffer == MG.cls ubuffer); coerce (MG.loc cloc_cls) l

false

true

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 64, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val loc_of_cloc (l: MG.loc cloc_cls) : Tot loc

[]

LowStar.Monotonic.Buffer.loc_of_cloc

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

l: FStar.ModifiesGen.loc LowStar.Monotonic.Buffer.cloc_cls -> LowStar.Monotonic.Buffer.loc

{ "end_col": 14, "end_line": 1664, "start_col": 2, "start_line": 1663 }

FStar.HyperStack.ST.ST

val mmalloc_drgn_mm (#a:Type0) (#rrel:srel a) (d:HST.drgn) (init:a) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == HST.rid_of_drgn d /\ freeable b}) (requires fun h -> alloc_drgn_pre h d len) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len

val mmalloc_drgn_mm (#a:Type0) (#rrel:srel a) (d:HST.drgn) (init:a) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == HST.rid_of_drgn d /\ freeable b}) (requires fun h -> alloc_drgn_pre h d len) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init)) let mmalloc_drgn_mm #a #rrel d init len =

true

null

false

lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content:HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "FStar.HyperStack.ST.drgn", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.Buffer", "FStar.UInt32.__uint_to_t", "FStar.Ghost.hide", "LowStar.Monotonic.Buffer.lmbuffer", "FStar.UInt32.v", "Prims.l_and", "Prims.eq2", "FStar.Monotonic.HyperHeap.rid", "LowStar.Monotonic.Buffer.frameOf", "FStar.HyperStack.ST.rid_of_drgn", "LowStar.Monotonic.Buffer.freeable", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.HyperStack.ST.ralloc_drgn_mm", "FStar.Seq.Base.create", "Prims.unit", "LowStar.Monotonic.Buffer.lemma_seq_sub_compatilibity_is_reflexive" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val mmalloc_drgn_mm (#a:Type0) (#rrel:srel a) (d:HST.drgn) (init:a) (len:U32.t) : HST.ST (b:lmbuffer a rrel rrel (U32.v len){frameOf b == HST.rid_of_drgn d /\ freeable b}) (requires fun h -> alloc_drgn_pre h d len) (ensures fun h0 b h1 -> alloc_post_mem_common b h0 h1 (Seq.create (U32.v len) init))

[]

LowStar.Monotonic.Buffer.mmalloc_drgn_mm

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

d: FStar.HyperStack.ST.drgn -> init: a -> len: FStar.UInt32.t -> FStar.HyperStack.ST.ST (b: LowStar.Monotonic.Buffer.lmbuffer a rrel rrel (FStar.UInt32.v len) { LowStar.Monotonic.Buffer.frameOf b == FStar.HyperStack.ST.rid_of_drgn d /\ LowStar.Monotonic.Buffer.freeable b })

{ "end_col": 28, "end_line": 1554, "start_col": 2, "start_line": 1550 }

FStar.HyperStack.ST.Stack

val fill (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) == Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) == Seq.slice (as_seq h0 b) (U32.v len) (length b) ))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let fill #t #rrel #rel b z len = fill' b z len

val fill (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) == Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) == Seq.slice (as_seq h0 b) (U32.v len) (length b) )) let fill #t #rrel #rel b z len =

true

null

false

fill' b z len

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.fill'", "Prims.unit" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64" let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> () #push-options "--z3rlimit 128 --max_fuel 0 --max_ifuel 1 --initial_ifuel 1 --z3cliopt smt.qi.EAGER_THRESHOLD=4" let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b) )) = let open HST in if len = 0ul then () else begin let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src)); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h //for modifies clause end #pop-options

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 64, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val fill (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) == Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) == Seq.slice (as_seq h0 b) (U32.v len) (length b) ))

[]

LowStar.Monotonic.Buffer.fill

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

b: LowStar.Monotonic.Buffer.mbuffer t rrel rel -> z: t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.Stack Prims.unit

{ "end_col": 46, "end_line": 1648, "start_col": 33, "start_line": 1648 }

FStar.HyperStack.ST.Stack

val blit (#a:Type0) (#rrel1 #rrel2 #rel1 #rel2:srel a) (src:mbuffer a rrel1 rel1) (idx_src:U32.t) (dst:mbuffer a rrel2 rel2) (idx_dst:U32.t) (len:U32.t) :HST.Stack unit (requires (fun h -> live h src /\ live h dst /\ U32.v idx_src + U32.v len <= length src /\ U32.v idx_dst + U32.v len <= length dst /\ (* TODO: remove the rhs part of this disjunction once patterns on loc_buffer_from_to are introduced *) (loc_disjoint (loc_buffer_from_to src idx_src (idx_src `U32.add` len)) (loc_buffer_from_to dst idx_dst (idx_dst `U32.add` len)) \/ disjoint src dst) /\ rel2 (as_seq h dst) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len))))) (ensures (fun h _ h' -> modifies (loc_buffer dst) h h' /\ live h' dst /\ Seq.slice (as_seq h' dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) == Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) /\ Seq.slice (as_seq h' dst) 0 (U32.v idx_dst) == Seq.slice (as_seq h dst) 0 (U32.v idx_dst) /\ Seq.slice (as_seq h' dst) (U32.v idx_dst + U32.v len) (length dst) == Seq.slice (as_seq h dst) (U32.v idx_dst + U32.v len) (length dst)))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> ()

val blit (#a:Type0) (#rrel1 #rrel2 #rel1 #rel2:srel a) (src:mbuffer a rrel1 rel1) (idx_src:U32.t) (dst:mbuffer a rrel2 rel2) (idx_dst:U32.t) (len:U32.t) :HST.Stack unit (requires (fun h -> live h src /\ live h dst /\ U32.v idx_src + U32.v len <= length src /\ U32.v idx_dst + U32.v len <= length dst /\ (* TODO: remove the rhs part of this disjunction once patterns on loc_buffer_from_to are introduced *) (loc_disjoint (loc_buffer_from_to src idx_src (idx_src `U32.add` len)) (loc_buffer_from_to dst idx_dst (idx_dst `U32.add` len)) \/ disjoint src dst) /\ rel2 (as_seq h dst) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len))))) (ensures (fun h _ h' -> modifies (loc_buffer dst) h h' /\ live h' dst /\ Seq.slice (as_seq h' dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) == Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) /\ Seq.slice (as_seq h' dst) 0 (U32.v idx_dst) == Seq.slice (as_seq h dst) 0 (U32.v idx_dst) /\ Seq.slice (as_seq h' dst) (U32.v idx_dst + U32.v len) (length dst) == Seq.slice (as_seq h dst) (U32.v idx_dst + U32.v len) (length dst))) let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len =

true

null

false

let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); assert (s_full2' `Seq.equal` (Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len))))); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` (Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2)))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h | _, _ -> ()

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "FStar.Pervasives.Native.Mktuple2", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "FStar.UInt32.v", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.Ghost.erased", "Prims.b2t", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "FStar.Ghost.reveal", "Prims.op_Equality", "FStar.UInt32.__uint_to_t", "Prims.unit", "Prims.bool", "LowStar.Monotonic.Buffer.g_upd_seq_as_seq", "FStar.Seq.Base.slice", "Prims._assert", "Prims.eq2", "FStar.Monotonic.HyperStack.mem", "LowStar.Monotonic.Buffer.g_upd_seq", "FStar.Seq.Base.equal", "FStar.Seq.Properties.replace_subseq", "FStar.HyperStack.ST.get", "FStar.HyperStack.ST.op_Colon_Equals", "LowStar.Monotonic.Buffer.as_seq", "LowStar.Monotonic.Buffer.length", "FStar.Seq.Base.seq", "FStar.HyperStack.ST.op_Bang" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64"

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 64, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val blit (#a:Type0) (#rrel1 #rrel2 #rel1 #rel2:srel a) (src:mbuffer a rrel1 rel1) (idx_src:U32.t) (dst:mbuffer a rrel2 rel2) (idx_dst:U32.t) (len:U32.t) :HST.Stack unit (requires (fun h -> live h src /\ live h dst /\ U32.v idx_src + U32.v len <= length src /\ U32.v idx_dst + U32.v len <= length dst /\ (* TODO: remove the rhs part of this disjunction once patterns on loc_buffer_from_to are introduced *) (loc_disjoint (loc_buffer_from_to src idx_src (idx_src `U32.add` len)) (loc_buffer_from_to dst idx_dst (idx_dst `U32.add` len)) \/ disjoint src dst) /\ rel2 (as_seq h dst) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len))))) (ensures (fun h _ h' -> modifies (loc_buffer dst) h h' /\ live h' dst /\ Seq.slice (as_seq h' dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) == Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) /\ Seq.slice (as_seq h' dst) 0 (U32.v idx_dst) == Seq.slice (as_seq h dst) 0 (U32.v idx_dst) /\ Seq.slice (as_seq h' dst) (U32.v idx_dst + U32.v len) (length dst) == Seq.slice (as_seq h dst) (U32.v idx_dst + U32.v len) (length dst)))

[]

LowStar.Monotonic.Buffer.blit

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

src: LowStar.Monotonic.Buffer.mbuffer a rrel1 rel1 -> idx_src: FStar.UInt32.t -> dst: LowStar.Monotonic.Buffer.mbuffer a rrel2 rel2 -> idx_dst: FStar.UInt32.t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.Stack Prims.unit

{ "end_col": 14, "end_line": 1608, "start_col": 2, "start_line": 1565 }

FStar.Pervasives.Lemma

val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) )

val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' =

false

null

true

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[ "lemma" ]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "LowStar.Monotonic.Buffer.loc", "FStar.Monotonic.HyperStack.mem", "FStar.ModifiesGen.modifies_strengthen", "LowStar.Monotonic.Buffer.ubuffer", "LowStar.Monotonic.Buffer.cls", "LowStar.Monotonic.Buffer.ubuffer_of_buffer_from_to", "FStar.Preorder.preorder", "FStar.Monotonic.HyperStack.mreference", "Prims.unit", "Prims.l_and", "Prims.eq2", "FStar.Monotonic.HyperHeap.rid", "FStar.Monotonic.HyperStack.frameOf", "Prims.int", "Prims.l_or", "Prims.b2t", "Prims.op_GreaterThanOrEqual", "Prims.op_GreaterThan", "FStar.Monotonic.HyperStack.as_addr", "FStar.Monotonic.HyperStack.contains", "Prims.squash", "Prims.Nil", "FStar.Pervasives.pattern", "LowStar.Monotonic.Buffer.ubuffer_preserved_intro", "FStar.Seq.Properties.lseq", "FStar.UInt32.v", "LowStar.Monotonic.Buffer.__proj__Buffer__item__max_length", "LowStar.Monotonic.Buffer.srel_to_lsrel", "LowStar.Monotonic.Buffer.__proj__Buffer__item__content", "Prims.nat", "Prims.bool", "Prims._assert", "FStar.Seq.Base.equal", "FStar.Classical.forall_intro", "Prims.l_imp", "Prims.op_LessThan", "FStar.Seq.Base.index", "FStar.Classical.move_requires", "Prims.op_BarBar", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "LowStar.Monotonic.Buffer.length", "FStar.ModifiesGen.modifies_aloc_elim", "LowStar.Monotonic.Buffer.loc_union", "LowStar.Monotonic.Buffer.loc_buffer", "LowStar.Monotonic.Buffer.loc_disjoint", "FStar.ModifiesGen.loc_disjoint_aloc_intro", "FStar.Seq.Base.slice", "Prims.op_Subtraction", "LowStar.Monotonic.Buffer.loc_disjoint_includes", "FStar.ModifiesGen.loc_of_aloc", "FStar.ModifiesGen.loc_includes_aloc", "FStar.ModifiesGen.loc", "LowStar.Monotonic.Buffer.as_seq", "FStar.Ghost.hide", "LowStar.Monotonic.Buffer.ubuffer'", "LowStar.Monotonic.Buffer.Mkubuffer_", "FStar.Seq.Base.seq", "LowStar.Monotonic.Buffer.frameOf", "LowStar.Monotonic.Buffer.as_addr", "FStar.Ghost.reveal", "LowStar.Monotonic.Buffer.ubuffer_of_buffer", "FStar.UInt.uint_t", "LowStar.Monotonic.Buffer.__proj__Buffer__item__idx", "LowStar.Monotonic.Buffer.lemma_equal_instances_implies_equal_types", "FStar.Pervasives.coerce_eq", "FStar.Monotonic.Heap.lemma_distinct_addrs_distinct_mm", "FStar.Monotonic.Heap.lemma_distinct_addrs_distinct_preorders", "LowStar.Monotonic.Buffer.modifies_loc_includes", "LowStar.Monotonic.Buffer.loc_addresses", "FStar.Set.singleton" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16"

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 16, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h'))

[]

LowStar.Monotonic.Buffer.modifies_loc_buffer_from_to_intro'

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

b: LowStar.Monotonic.Buffer.mbuffer a rrel rel -> from: FStar.UInt32.t -> to: FStar.UInt32.t -> l: LowStar.Monotonic.Buffer.loc -> h: FStar.Monotonic.HyperStack.mem -> h': FStar.Monotonic.HyperStack.mem -> FStar.Pervasives.Lemma (requires (let s = LowStar.Monotonic.Buffer.as_seq h b in let s' = LowStar.Monotonic.Buffer.as_seq h' b in Prims.op_Negation (LowStar.Monotonic.Buffer.g_is_null b) /\ LowStar.Monotonic.Buffer.live h b /\ LowStar.Monotonic.Buffer.modifies (LowStar.Monotonic.Buffer.loc_union l (LowStar.Monotonic.Buffer.loc_buffer b)) h h' /\ FStar.UInt32.v from <= FStar.UInt32.v to /\ FStar.UInt32.v to <= LowStar.Monotonic.Buffer.length b /\ FStar.Seq.Base.equal (FStar.Seq.Base.slice s 0 (FStar.UInt32.v from)) (FStar.Seq.Base.slice s' 0 (FStar.UInt32.v from)) /\ FStar.Seq.Base.equal (FStar.Seq.Base.slice s (FStar.UInt32.v to) (LowStar.Monotonic.Buffer.length b)) (FStar.Seq.Base.slice s' (FStar.UInt32.v to) (LowStar.Monotonic.Buffer.length b)))) (ensures LowStar.Monotonic.Buffer.modifies (LowStar.Monotonic.Buffer.loc_union l (LowStar.Monotonic.Buffer.loc_buffer_from_to b from to)) h h')

{ "end_col": 3, "end_line": 1188, "start_col": 71, "start_line": 1132 }

FStar.Pervasives.Lemma

val g_upd_modifies_strong (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (i:nat{i < length b}) (v:a) (h:HS.mem{live h b}) : Lemma (modifies (loc_buffer_from_to b (U32.uint_to_t i) (U32.uint_to_t (i + 1))) h (g_upd b i v h))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h'

val g_upd_modifies_strong (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (i:nat{i < length b}) (v:a) (h:HS.mem{live h b}) : Lemma (modifies (loc_buffer_from_to b (U32.uint_to_t i) (U32.uint_to_t (i + 1))) h (g_upd b i v h)) let g_upd_modifies_strong #_ #_ #_ b i v h =

false

null

true

let h' = g_upd b i v h in Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h'

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[ "lemma" ]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "LowStar.Monotonic.Buffer.length", "FStar.Monotonic.HyperStack.mem", "LowStar.Monotonic.Buffer.live", "LowStar.Monotonic.Buffer.modifies_1_from_to_modifies", "FStar.UInt32.uint_to_t", "Prims.op_Addition", "Prims.unit", "LowStar.Monotonic.Buffer.s_lemma_equal_instances_implies_equal_types", "FStar.Monotonic.Heap.lemma_distinct_addrs_distinct_mm", "FStar.Monotonic.Heap.lemma_distinct_addrs_distinct_preorders", "LowStar.Monotonic.Buffer.g_upd" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 48, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val g_upd_modifies_strong (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (i:nat{i < length b}) (v:a) (h:HS.mem{live h b}) : Lemma (modifies (loc_buffer_from_to b (U32.uint_to_t i) (U32.uint_to_t (i + 1))) h (g_upd b i v h))

[]

LowStar.Monotonic.Buffer.g_upd_modifies_strong

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

b: LowStar.Monotonic.Buffer.mbuffer a rrel rel -> i: Prims.nat{i < LowStar.Monotonic.Buffer.length b} -> v: a -> h: FStar.Monotonic.HyperStack.mem{LowStar.Monotonic.Buffer.live h b} -> FStar.Pervasives.Lemma (ensures LowStar.Monotonic.Buffer.modifies (LowStar.Monotonic.Buffer.loc_buffer_from_to b (FStar.UInt32.uint_to_t i) (FStar.UInt32.uint_to_t (i + 1))) h (LowStar.Monotonic.Buffer.g_upd b i v h))

{ "end_col": 80, "end_line": 1345, "start_col": 44, "start_line": 1339 }

FStar.HyperStack.ST.Stack

val fill' (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z: t) (len: U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)))) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ (Seq.slice (as_seq h1 b) 0 (U32.v len)) `Seq.equal` (Seq.create (U32.v len) z) /\ (Seq.slice (as_seq h1 b) (U32.v len) (length b)) `Seq.equal` (Seq.slice (as_seq h0 b) (U32.v len) (length b))))

[ { "abbrev": true, "full_module": "FStar.ModifiesGen", "short_module": "MG" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "HST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "Seq" }, { "abbrev": true, "full_module": "FStar.UInt32", "short_module": "U32" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "P" }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "LowStar.Monotonic", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b) )) = let open HST in if len = 0ul then () else begin let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src)); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h //for modifies clause end

val fill' (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z: t) (len: U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)))) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ (Seq.slice (as_seq h1 b) 0 (U32.v len)) `Seq.equal` (Seq.create (U32.v len) z) /\ (Seq.slice (as_seq h1 b) (U32.v len) (length b)) `Seq.equal` (Seq.slice (as_seq h0 b) (U32.v len) (length b)))) let fill' (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z: t) (len: U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)))) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ (Seq.slice (as_seq h1 b) 0 (U32.v len)) `Seq.equal` (Seq.create (U32.v len) z) /\ (Seq.slice (as_seq h1 b) (U32.v len) (length b)) `Seq.equal` (Seq.slice (as_seq h0 b) (U32.v len) (length b)))) =

true

null

false

let open HST in if len = 0ul then () else let h = get () in let Buffer max_length content idx length = b in let s_full = !content in let s = Seq.slice s_full (U32.v idx) (U32.v max_length) in let s_src = Seq.create (U32.v len) z in let s' = Seq.replace_subseq s 0 (U32.v len) s_src in let s_full' = Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v len) s_src in assert (s_full' `Seq.equal` (Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.replace_subseq (Seq.slice s_full (U32.v idx) (U32.v idx + U32.v length)) 0 (U32.v len) s_src))); content := s_full'; let h' = HST.get () in assert (s_full' `Seq.equal` (Seq.replace_subseq s_full (U32.v idx) (U32.v idx + U32.v length) (Seq.slice s' 0 (U32.v length)))); assert (h' == g_upd_seq b (Seq.slice s' 0 (U32.v length)) h); g_upd_seq_as_seq b (Seq.slice s' 0 (U32.v length)) h

{ "checked_file": "LowStar.Monotonic.Buffer.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Set.fsti.checked", "FStar.Seq.fst.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.ModifiesGen.fsti.checked", "FStar.Map.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Heap.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "LowStar.Monotonic.Buffer.fst" }

[]

[ "LowStar.Monotonic.Buffer.srel", "LowStar.Monotonic.Buffer.mbuffer", "FStar.UInt32.t", "Prims.op_Equality", "FStar.UInt32.__uint_to_t", "Prims.unit", "Prims.bool", "FStar.HyperStack.ST.mreference", "FStar.Seq.Properties.lseq", "FStar.UInt32.v", "LowStar.Monotonic.Buffer.srel_to_lsrel", "FStar.Ghost.erased", "Prims.b2t", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "FStar.Ghost.reveal", "LowStar.Monotonic.Buffer.g_upd_seq_as_seq", "FStar.Seq.Base.slice", "Prims._assert", "Prims.eq2", "FStar.Monotonic.HyperStack.mem", "LowStar.Monotonic.Buffer.g_upd_seq", "FStar.Seq.Base.equal", "FStar.Seq.Properties.replace_subseq", "FStar.HyperStack.ST.get", "FStar.HyperStack.ST.op_Colon_Equals", "FStar.Seq.Base.seq", "FStar.Seq.Base.create", "FStar.HyperStack.ST.op_Bang", "Prims.l_and", "LowStar.Monotonic.Buffer.live", "LowStar.Monotonic.Buffer.length", "LowStar.Monotonic.Buffer.as_seq", "LowStar.Monotonic.Buffer.modifies", "LowStar.Monotonic.Buffer.loc_buffer" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module LowStar.Monotonic.Buffer module P = FStar.Preorder module G = FStar.Ghost module U32 = FStar.UInt32 module Seq = FStar.Seq module HS = FStar.HyperStack module HST = FStar.HyperStack.ST private let srel_to_lsrel (#a:Type0) (len:nat) (pre:srel a) :P.preorder (Seq.lseq a len) = pre (* * Counterpart of compatible_sub from the fsti but using sequences * * The patterns are guarded tightly, the proof of transitivity gets quite flaky otherwise * The cost is that we have to additional asserts as triggers *) let compatible_sub_preorder (#a:Type0) (len:nat) (rel:srel a) (i:nat) (j:nat{i <= j /\ j <= len}) (sub_rel:srel a) = compatible_subseq_preorder len rel i j sub_rel (* * Reflexivity of the compatibility relation *) let lemma_seq_sub_compatilibity_is_reflexive (#a:Type0) (len:nat) (rel:srel a) :Lemma (compatible_sub_preorder len rel 0 len rel) = assert (forall (s1 s2:Seq.seq a). Seq.length s1 == Seq.length s2 ==> Seq.equal (Seq.replace_subseq s1 0 (Seq.length s1) s2) s2) (* * Transitivity of the compatibility relation * * i2 and j2 are relative offsets within [i1, j1) (i.e. assuming i1 = 0) *) let lemma_seq_sub_compatibility_is_transitive (#a:Type0) (len:nat) (rel:srel a) (i1 j1:nat) (rel1:srel a) (i2 j2:nat) (rel2:srel a) :Lemma (requires (i1 <= j1 /\ j1 <= len /\ i2 <= j2 /\ j2 <= j1 - i1 /\ compatible_sub_preorder len rel i1 j1 rel1 /\ compatible_sub_preorder (j1 - i1) rel1 i2 j2 rel2)) (ensures (compatible_sub_preorder len rel (i1 + i2) (i1 + j2) rel2)) = let t1 (s1 s2:Seq.seq a) = Seq.length s1 == len /\ Seq.length s2 == len /\ rel s1 s2 in let t2 (s1 s2:Seq.seq a) = t1 s1 s2 /\ rel2 (Seq.slice s1 (i1 + i2) (i1 + j2)) (Seq.slice s2 (i1 + i2) (i1 + j2)) in let aux0 (s1 s2:Seq.seq a) :Lemma (t1 s1 s2 ==> t2 s1 s2) = Classical.arrow_to_impl #(t1 s1 s2) #(t2 s1 s2) (fun _ -> assert (rel1 (Seq.slice s1 i1 j1) (Seq.slice s2 i1 j1)); assert (rel2 (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice (Seq.slice s2 i1 j1) i2 j2)); assert (Seq.equal (Seq.slice (Seq.slice s1 i1 j1) i2 j2) (Seq.slice s1 (i1 + i2) (i1 + j2))); assert (Seq.equal (Seq.slice (Seq.slice s2 i1 j1) i2 j2) (Seq.slice s2 (i1 + i2) (i1 + j2)))) in let t1 (s s2:Seq.seq a) = Seq.length s == len /\ Seq.length s2 == j2 - i2 /\ rel2 (Seq.slice s (i1 + i2) (i1 + j2)) s2 in let t2 (s s2:Seq.seq a) = t1 s s2 /\ rel s (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2) in let aux1 (s s2:Seq.seq a) :Lemma (t1 s s2 ==> t2 s s2) = Classical.arrow_to_impl #(t1 s s2) #(t2 s s2) (fun _ -> assert (Seq.equal (Seq.slice s (i1 + i2) (i1 + j2)) (Seq.slice (Seq.slice s i1 j1) i2 j2)); assert (rel1 (Seq.slice s i1 j1) (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)); assert (rel s (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2))); assert (Seq.equal (Seq.replace_subseq s i1 j1 (Seq.replace_subseq (Seq.slice s i1 j1) i2 j2 s2)) (Seq.replace_subseq s (i1 + i2) (i1 + j2) s2))) in Classical.forall_intro_2 aux0; Classical.forall_intro_2 aux1 noeq type mbuffer (a:Type0) (rrel:srel a) (rel:srel a) :Type0 = | Null | Buffer: max_length:U32.t -> content:HST.mreference (Seq.lseq a (U32.v max_length)) (srel_to_lsrel (U32.v max_length) rrel) -> idx:U32.t -> length:Ghost.erased U32.t{U32.v idx + U32.v (Ghost.reveal length) <= U32.v max_length} -> mbuffer a rrel rel let g_is_null #_ #_ #_ b = Null? b let mnull #_ #_ #_ = Null let null_unique #_ #_ #_ _ = () let unused_in #_ #_ #_ b h = match b with | Null -> False | Buffer _ content _ _ -> content `HS.unused_in` h let buffer_compatible (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) : GTot Type0 = match b with | Null -> True | Buffer max_length content idx length -> compatible_sub_preorder (U32.v max_length) rrel (U32.v idx) (U32.v idx + U32.v length) rel //proof of compatibility let live #_ #rrel #rel h b = match b with | Null -> True | Buffer max_length content idx length -> h `HS.contains` content /\ buffer_compatible b let live_null _ _ _ _ = () let live_not_unused_in #_ #_ #_ _ _ = () let lemma_live_equal_mem_domains #_ #_ #_ _ _ _ = () let frameOf #_ #_ #_ b = if Null? b then HS.root else HS.frameOf (Buffer?.content b) let as_addr #_ #_ #_ b = if g_is_null b then 0 else HS.as_addr (Buffer?.content b) let unused_in_equiv #_ #_ #_ b h = if g_is_null b then Heap.not_addr_unused_in_nullptr (Map.sel (HS.get_hmap h) HS.root) else () let live_region_frameOf #_ #_ #_ _ _ = () let len #_ #_ #_ b = match b with | Null -> 0ul | Buffer _ _ _ len -> len let len_null a _ _ = () let as_seq #_ #_ #_ h b = match b with | Null -> Seq.empty | Buffer max_len content idx len -> Seq.slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len) let length_as_seq #_ #_ #_ _ _ = () let mbuffer_injectivity_in_first_preorder () = () let mgsub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content idx length -> Buffer max_len content (U32.add idx i) (Ghost.hide len) let live_gsub #_ #rrel #rel _ b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> let prf () : Lemma (requires (buffer_compatible b)) (ensures (buffer_compatible (mgsub sub_rel b i len))) = lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel in Classical.move_requires prf () let gsub_is_null #_ #_ #_ _ _ _ _ = () let len_gsub #_ #_ #_ _ _ _ _ = () let frameOf_gsub #_ #_ #_ _ _ _ _ = () let as_addr_gsub #_ #_ #_ _ _ _ _ = () let mgsub_inj #_ #_ #_ _ _ _ _ _ _ _ _ = () #push-options "--z3rlimit 20" let gsub_gsub #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let prf () : Lemma (requires (compatible_sub b i1 len1 sub_rel1 /\ compatible_sub (mgsub sub_rel1 b i1 len1) i2 len2 sub_rel2)) (ensures (compatible_sub b (U32.add i1 i2) len2 sub_rel2)) = lemma_seq_sub_compatibility_is_transitive (length b) rel (U32.v i1) (U32.v i1 + U32.v len1) sub_rel1 (U32.v i2) (U32.v i2 + U32.v len2) sub_rel2 in Classical.move_requires prf () #pop-options /// A buffer ``b`` is equal to its "largest" sub-buffer, at index 0 and /// length ``len b``. let gsub_zero_length #_ #_ #rel b = lemma_seq_sub_compatilibity_is_reflexive (length b) rel let as_seq_gsub #_ #_ #_ h b i len _ = match b with | Null -> () | Buffer _ content idx len0 -> Seq.slice_slice (HS.sel h content) (U32.v idx) (U32.v idx + U32.v len0) (U32.v i) (U32.v i + U32.v len) let lemma_equal_instances_implies_equal_types (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b) : Lemma (requires s1 === s2) (ensures a == b) = Seq.lemma_equal_instances_implies_equal_types () let s_lemma_equal_instances_implies_equal_types (_:unit) : Lemma (forall (a:Type) (b:Type) (s1:Seq.seq a) (s2:Seq.seq b). {:pattern (has_type s1 (Seq.seq a)); (has_type s2 (Seq.seq b)) } s1 === s2 ==> a == b) = Seq.lemma_equal_instances_implies_equal_types() let live_same_addresses_equal_types_and_preorders' (#a1 #a2: Type0) (#rrel1 #rel1: srel a1) (#rrel2 #rel2: srel a2) (b1: mbuffer a1 rrel1 rel1) (b2: mbuffer a2 rrel2 rel2) (h: HS.mem) : Lemma (requires frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ live h b1 /\ live h b2 /\ (~ (g_is_null b1 /\ g_is_null b2))) (ensures a1 == a2 /\ rrel1 == rrel2) = Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); let s1 : Seq.seq a1 = as_seq h b1 in assert (Seq.seq a1 == Seq.seq a2); let s1' : Seq.seq a2 = coerce_eq _ s1 in assert (s1 === s1'); lemma_equal_instances_implies_equal_types a1 a2 s1 s1' let live_same_addresses_equal_types_and_preorders #_ #_ #_ #_ #_ #_ b1 b2 h = Classical.move_requires (live_same_addresses_equal_types_and_preorders' b1 b2) h (* Untyped view of buffers, used only to implement the generic modifies clause. DO NOT USE in client code. *) noeq type ubuffer_ : Type0 = { b_max_length: nat; b_offset: nat; b_length: nat; b_is_mm: bool; } val ubuffer' (region: HS.rid) (addr: nat) : Tot Type0 let ubuffer' region addr = (x: ubuffer_ { x.b_offset + x.b_length <= x.b_max_length } ) let ubuffer (region: HS.rid) (addr: nat) : Tot Type0 = G.erased (ubuffer' region addr) let ubuffer_of_buffer' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) = if Null? b then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else Ghost.hide ({ b_max_length = U32.v (Buffer?.max_length b); b_offset = U32.v (Buffer?.idx b); b_length = U32.v (Buffer?.length b); b_is_mm = HS.is_mm (Buffer?.content b); }) let ubuffer_preserved' (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 = forall (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) . ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) val ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h h' : HS.mem) : GTot Type0 let ubuffer_preserved = ubuffer_preserved' let ubuffer_preserved_intro (#r:HS.rid) (#a:nat) (b:ubuffer r a) (h h' :HS.mem) (f0: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires (frameOf b' == r /\ as_addr b' == a /\ live h b')) (ensures (live h' b')) )) (f: ( (t':Type0) -> (rrel:srel t') -> (rel:srel t') -> (b':mbuffer t' rrel rel) -> Lemma (requires ( frameOf b' == r /\ as_addr b' == a /\ live h b' /\ live h' b' /\ Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len )))) (ensures ( Buffer? b' /\ ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len /\ Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))) )) : Lemma (ubuffer_preserved b h h') = let g' (t':Type0) (rrel rel:srel t') (b':mbuffer t' rrel rel) : Lemma ((frameOf b' == r /\ as_addr b' == a) ==> ( (live h b' ==> live h' b') /\ ( ((live h b' /\ live h' b' /\ Buffer? b') ==> ( let ({ b_max_length = bmax; b_offset = boff; b_length = blen }) = Ghost.reveal b in let Buffer max _ idx len = b' in ( U32.v max == bmax /\ U32.v idx <= boff /\ boff + blen <= U32.v idx + U32.v len ) ==> Seq.equal (Seq.slice (as_seq h b') (boff - U32.v idx) (boff - U32.v idx + blen)) (Seq.slice (as_seq h' b') (boff - U32.v idx) (boff - U32.v idx + blen)) ))))) = Classical.move_requires (f0 t' rrel rel) b'; Classical.move_requires (f t' rrel rel) b' in Classical.forall_intro_4 g' val ubuffer_preserved_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h : HS.mem) : Lemma (ubuffer_preserved b h h) let ubuffer_preserved_refl #r #a b h = () val ubuffer_preserved_trans (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2 h3 : HS.mem) : Lemma (requires (ubuffer_preserved b h1 h2 /\ ubuffer_preserved b h2 h3)) (ensures (ubuffer_preserved b h1 h3)) let ubuffer_preserved_trans #r #a b h1 h2 h3 = () val same_mreference_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) (f: ( (a' : Type) -> (pre: Preorder.preorder a') -> (r': HS.mreference a' pre) -> Lemma (requires (h1 `HS.contains` r' /\ r == HS.frameOf r' /\ a == HS.as_addr r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) )) : Lemma (ubuffer_preserved b h1 h2) let same_mreference_ubuffer_preserved #r #a b h1 h2 f = ubuffer_preserved_intro b h1 h2 (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) (fun t' _ _ b' -> if Null? b' then () else f _ _ (Buffer?.content b') ) val addr_unused_in_ubuffer_preserved (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (HS.live_region h1 r ==> a `Heap.addr_unused_in` (Map.sel (HS.get_hmap h1) r))) (ensures (ubuffer_preserved b h1 h2)) let addr_unused_in_ubuffer_preserved #r #a b h1 h2 = () val ubuffer_of_buffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) :Tot (ubuffer (frameOf b) (as_addr b)) let ubuffer_of_buffer #_ #_ #_ b = ubuffer_of_buffer' b let ubuffer_of_buffer_from_to_none_cond #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot bool = g_is_null b || U32.v to < U32.v from || U32.v from > length b let ubuffer_of_buffer_from_to #a #rrel #rel (b: mbuffer a rrel rel) from to : GTot (ubuffer (frameOf b) (as_addr b)) = if ubuffer_of_buffer_from_to_none_cond b from to then Ghost.hide ({ b_max_length = 0; b_offset = 0; b_length = 0; b_is_mm = false; }) else let to' = if U32.v to > length b then length b else U32.v to in let b1 = ubuffer_of_buffer b in Ghost.hide ({ Ghost.reveal b1 with b_offset = (Ghost.reveal b1).b_offset + U32.v from; b_length = to' - U32.v from }) val ubuffer_preserved_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' /\ live h b)) (ensures (live h' b /\ as_seq h b == as_seq h' b)) let ubuffer_preserved_elim #_ #_ #_ _ _ _ = () val ubuffer_preserved_from_to_elim (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h h' : HS.mem) :Lemma (requires (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) h h' /\ live h b)) (ensures (live h' b /\ ((U32.v from <= U32.v to /\ U32.v to <= length b) ==> Seq.slice (as_seq h b) (U32.v from) (U32.v to) == Seq.slice (as_seq h' b) (U32.v from) (U32.v to)))) let ubuffer_preserved_from_to_elim #_ #_ #_ _ _ _ _ _ = () let unused_in_ubuffer_preserved (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h h':HS.mem) : Lemma (requires (b `unused_in` h)) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h')) = Classical.move_requires (fun b -> live_not_unused_in h b) b; live_null a rrel rel h; null_unique b; unused_in_equiv b h; addr_unused_in_ubuffer_preserved #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) h h' let ubuffer_includes' (larger smaller: ubuffer_) : GTot Type0 = larger.b_is_mm == smaller.b_is_mm /\ larger.b_max_length == smaller.b_max_length /\ larger.b_offset <= smaller.b_offset /\ smaller.b_offset + smaller.b_length <= larger.b_offset + larger.b_length (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_includes0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (larger:ubuffer r1 a1) (smaller:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_includes' (G.reveal larger) (G.reveal smaller) val ubuffer_includes (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) : GTot Type0 let ubuffer_includes #r #a larger smaller = ubuffer_includes0 larger smaller val ubuffer_includes_refl (#r: HS.rid) (#a: nat) (b: ubuffer r a) : Lemma (b `ubuffer_includes` b) let ubuffer_includes_refl #r #a b = () val ubuffer_includes_trans (#r: HS.rid) (#a: nat) (b1 b2 b3: ubuffer r a) : Lemma (requires (b1 `ubuffer_includes` b2 /\ b2 `ubuffer_includes` b3)) (ensures (b1 `ubuffer_includes` b3)) let ubuffer_includes_trans #r #a b1 b2 b3 = () (* * TODO: not sure how to make this lemma work with preorders * it creates a buffer larger' in the proof * we need a compatible preorder for that * may be take that as an argument? *) (*val ubuffer_includes_ubuffer_preserved (#r: HS.rid) (#a: nat) (larger smaller: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (larger `ubuffer_includes` smaller /\ ubuffer_preserved larger h1 h2)) (ensures (ubuffer_preserved smaller h1 h2)) let ubuffer_includes_ubuffer_preserved #r #a larger smaller h1 h2 = ubuffer_preserved_intro smaller h1 h2 (fun t' b' -> if Null? b' then () else let (Buffer max_len content idx' len') = b' in let idx = U32.uint_to_t (G.reveal larger).b_offset in let len = U32.uint_to_t (G.reveal larger).b_length in let larger' = Buffer max_len content idx len in assert (b' == gsub larger' (U32.sub idx' idx) len'); ubuffer_preserved_elim larger' h1 h2 )*) let ubuffer_disjoint' (x1 x2: ubuffer_) : GTot Type0 = if x1.b_length = 0 || x2.b_length = 0 then True else (x1.b_max_length == x2.b_max_length /\ (x1.b_offset + x1.b_length <= x2.b_offset \/ x2.b_offset + x2.b_length <= x1.b_offset)) (* TODO: added this because of #606, now that it is fixed, we may not need it anymore *) let ubuffer_disjoint0 (#r1 #r2:HS.rid) (#a1 #a2:nat) (b1:ubuffer r1 a1) (b2:ubuffer r2 a2) = r1 == r2 /\ a1 == a2 /\ ubuffer_disjoint' (G.reveal b1) (G.reveal b2) val ubuffer_disjoint (#r:HS.rid) (#a:nat) (b1 b2:ubuffer r a) :GTot Type0 let ubuffer_disjoint #r #a b1 b2 = ubuffer_disjoint0 b1 b2 val ubuffer_disjoint_sym (#r:HS.rid) (#a: nat) (b1 b2:ubuffer r a) :Lemma (ubuffer_disjoint b1 b2 <==> ubuffer_disjoint b2 b1) let ubuffer_disjoint_sym #_ #_ b1 b2 = () val ubuffer_disjoint_includes (#r: HS.rid) (#a: nat) (larger1 larger2: ubuffer r a) (smaller1 smaller2: ubuffer r a) : Lemma (requires (ubuffer_disjoint larger1 larger2 /\ larger1 `ubuffer_includes` smaller1 /\ larger2 `ubuffer_includes` smaller2)) (ensures (ubuffer_disjoint smaller1 smaller2)) let ubuffer_disjoint_includes #r #a larger1 larger2 smaller1 smaller2 = () val liveness_preservation_intro (#a:Type0) (#rrel:srel a) (#rel:srel a) (h h':HS.mem) (b:mbuffer a rrel rel) (f: ( (t':Type0) -> (pre: Preorder.preorder t') -> (r: HS.mreference t' pre) -> Lemma (requires (HS.frameOf r == frameOf b /\ HS.as_addr r == as_addr b /\ h `HS.contains` r)) (ensures (h' `HS.contains` r)) )) :Lemma (requires (live h b)) (ensures (live h' b)) let liveness_preservation_intro #_ #_ #_ _ _ b f = if Null? b then () else f _ _ (Buffer?.content b) (* Basic, non-compositional modifies clauses, used only to implement the generic modifies clause. DO NOT USE in client code *) let modifies_0_preserves_mreferences (h1 h2: HS.mem) : GTot Type0 = forall (a: Type) (pre: Preorder.preorder a) (r: HS.mreference a pre) . h1 `HS.contains` r ==> (h2 `HS.contains` r /\ HS.sel h1 r == HS.sel h2 r) let modifies_0_preserves_regions (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) . HS.live_region h1 r ==> HS.live_region h2 r let modifies_0_preserves_not_unused_in (h1 h2: HS.mem) : GTot Type0 = forall (r: HS.rid) (n: nat) . ( HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) ) ==> ( n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r) ) let modifies_0' (h1 h2: HS.mem) : GTot Type0 = modifies_0_preserves_mreferences h1 h2 /\ modifies_0_preserves_regions h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 val modifies_0 (h1 h2: HS.mem) : GTot Type0 let modifies_0 = modifies_0' val modifies_0_live_region (h1 h2: HS.mem) (r: HS.rid) : Lemma (requires (modifies_0 h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_0_live_region h1 h2 r = () val modifies_0_mreference (#a: Type) (#pre: Preorder.preorder a) (h1 h2: HS.mem) (r: HS.mreference a pre) : Lemma (requires (modifies_0 h1 h2 /\ h1 `HS.contains` r)) (ensures (h2 `HS.contains` r /\ h1 `HS.sel` r == h2 `HS.sel` r)) let modifies_0_mreference #a #pre h1 h2 r = () let modifies_0_ubuffer (#r: HS.rid) (#a: nat) (b: ubuffer r a) (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (ubuffer_preserved b h1 h2)) = same_mreference_ubuffer_preserved b h1 h2 (fun a' pre r' -> modifies_0_mreference h1 h2 r') val modifies_0_unused_in (h1 h2: HS.mem) (r: HS.rid) (n: nat) : Lemma (requires ( modifies_0 h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r) )) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_0_unused_in h1 h2 r n = () let modifies_1_preserves_mreferences (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). ((frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r') ==> (h2 `HS.contains` r' /\ HS.sel h1 r' == HS.sel h2 r') let modifies_1_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_from_to_preserves_ubuffers (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = forall (b':ubuffer (frameOf b) (as_addr b)). (ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b') ==> ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2 let modifies_1_preserves_livenesses (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = forall (a':Type) (pre:Preorder.preorder a') (r':HS.mreference a' pre). h1 `HS.contains` r' ==> h2 `HS.contains` r' let modifies_1' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_preserves_ubuffers b h1 h2 val modifies_1 (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_1 = modifies_1' let modifies_1_from_to (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) : GTot Type0 = if ubuffer_of_buffer_from_to_none_cond b from to then modifies_0 h1 h2 else modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_1_preserves_livenesses b h1 h2 /\ modifies_0_preserves_not_unused_in h1 h2 /\ modifies_1_from_to_preserves_ubuffers b from to h1 h2 val modifies_1_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_1_live_region #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) = () val modifies_1_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1 b h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) let modifies_1_liveness #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_liveness (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r')) = () val modifies_1_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1 b h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_1_unused_in #_ #_ #_ _ _ _ _ _ = () let modifies_1_from_to_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (r:HS.rid) (n:nat) :Lemma (requires (modifies_1_from_to b from to h1 h2 /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) = () val modifies_1_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1 b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_1_mreference #_ #_ #_ _ _ _ #_ #_ _ = () let modifies_1_from_to_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r': HS.mreference a' pre) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) = () val modifies_1_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1 b h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) let modifies_1_ubuffer #_ #_ #_ _ _ _ _ = () let modifies_1_from_to_ubuffer (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) (b':ubuffer (frameOf b) (as_addr b)) : Lemma (requires (modifies_1_from_to b from to h1 h2 /\ ubuffer_disjoint #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) b')) (ensures (ubuffer_preserved #(frameOf b) #(as_addr b) b' h1 h2)) = () val modifies_1_null (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) : Lemma (requires (modifies_1 b h1 h2 /\ g_is_null b)) (ensures (modifies_0 h1 h2)) let modifies_1_null #_ #_ #_ _ _ _ = () let modifies_addr_of_preserves_not_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = forall (r: HS.rid) (n: nat) . ((r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r)) ==> (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r)) let modifies_addr_of' (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 = modifies_0_preserves_regions h1 h2 /\ modifies_1_preserves_mreferences b h1 h2 /\ modifies_addr_of_preserves_not_unused_in b h1 h2 val modifies_addr_of (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :GTot Type0 let modifies_addr_of = modifies_addr_of' val modifies_addr_of_live_region (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) :Lemma (requires (modifies_addr_of b h1 h2 /\ HS.live_region h1 r)) (ensures (HS.live_region h2 r)) let modifies_addr_of_live_region #_ #_ #_ _ _ _ _ = () val modifies_addr_of_mreference (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (#a':Type0) (#pre:Preorder.preorder a') (r':HS.mreference a' pre) : Lemma (requires (modifies_addr_of b h1 h2 /\ (frameOf b <> HS.frameOf r' \/ as_addr b <> HS.as_addr r') /\ h1 `HS.contains` r')) (ensures (h2 `HS.contains` r' /\ h1 `HS.sel` r' == h2 `HS.sel` r')) let modifies_addr_of_mreference #_ #_ #_ _ _ _ #_ #_ _ = () val modifies_addr_of_unused_in (#a:Type0) (#rrel:srel a) (#rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) (r:HS.rid) (n:nat) : Lemma (requires (modifies_addr_of b h1 h2 /\ (r <> frameOf b \/ n <> as_addr b) /\ HS.live_region h1 r /\ HS.live_region h2 r /\ n `Heap.addr_unused_in` (HS.get_hmap h2 `Map.sel` r))) (ensures (n `Heap.addr_unused_in` (HS.get_hmap h1 `Map.sel` r))) let modifies_addr_of_unused_in #_ #_ #_ _ _ _ _ _ = () module MG = FStar.ModifiesGen let cls : MG.cls ubuffer = MG.Cls #ubuffer ubuffer_includes (fun #r #a x -> ubuffer_includes_refl x) (fun #r #a x1 x2 x3 -> ubuffer_includes_trans x1 x2 x3) ubuffer_disjoint (fun #r #a x1 x2 -> ubuffer_disjoint_sym x1 x2) (fun #r #a larger1 larger2 smaller1 smaller2 -> ubuffer_disjoint_includes larger1 larger2 smaller1 smaller2) ubuffer_preserved (fun #r #a x h -> ubuffer_preserved_refl x h) (fun #r #a x h1 h2 h3 -> ubuffer_preserved_trans x h1 h2 h3) (fun #r #a b h1 h2 f -> same_mreference_ubuffer_preserved b h1 h2 f) let loc = MG.loc cls let _ = intro_ambient loc let loc_none = MG.loc_none let _ = intro_ambient loc_none let loc_union = MG.loc_union let _ = intro_ambient loc_union let loc_union_idem = MG.loc_union_idem let loc_union_comm = MG.loc_union_comm let loc_union_assoc = MG.loc_union_assoc let loc_union_loc_none_l = MG.loc_union_loc_none_l let loc_union_loc_none_r = MG.loc_union_loc_none_r let loc_buffer_from_to #a #rrel #rel b from to = if ubuffer_of_buffer_from_to_none_cond b from to then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) let loc_buffer #_ #_ #_ b = if g_is_null b then MG.loc_none else MG.loc_of_aloc #_ #_ #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_buffer_eq #_ #_ #_ _ = () let loc_buffer_from_to_high #_ #_ #_ _ _ _ = () let loc_buffer_from_to_none #_ #_ #_ _ _ _ = () let loc_buffer_from_to_mgsub #_ #_ #_ _ _ _ _ _ _ = () let loc_buffer_mgsub_eq #_ #_ #_ _ _ _ _ = () let loc_buffer_null _ _ _ = () let loc_buffer_from_to_eq #_ #_ #_ _ _ _ = () let loc_buffer_mgsub_rel_eq #_ #_ #_ _ _ _ _ _ = () let loc_addresses = MG.loc_addresses let loc_regions = MG.loc_regions let loc_includes = MG.loc_includes let loc_includes_refl = MG.loc_includes_refl let loc_includes_trans = MG.loc_includes_trans let loc_includes_union_r = MG.loc_includes_union_r let loc_includes_union_l = MG.loc_includes_union_l let loc_includes_none = MG.loc_includes_none val loc_includes_buffer (#a:Type0) (#rrel1:srel a) (#rrel2:srel a) (#rel1:srel a) (#rel2:srel a) (b1:mbuffer a rrel1 rel1) (b2:mbuffer a rrel2 rel2) :Lemma (requires (frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2 /\ ubuffer_includes0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_includes (loc_buffer b1) (loc_buffer b2))) let loc_includes_buffer #t #_ #_ #_ #_ b1 b2 = let t1 = ubuffer (frameOf b1) (as_addr b1) in MG.loc_includes_aloc #_ #cls #(frameOf b1) #(as_addr b1) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_includes_gsub_buffer_r l #_ #_ #_ b i len sub_rel = let b' = mgsub sub_rel b i len in loc_includes_buffer b b'; loc_includes_trans l (loc_buffer b) (loc_buffer b') let loc_includes_gsub_buffer_l #_ #_ #rel b i1 len1 sub_rel1 i2 len2 sub_rel2 = let b1 = mgsub sub_rel1 b i1 len1 in let b2 = mgsub sub_rel2 b i2 len2 in loc_includes_buffer b1 b2 let loc_includes_loc_buffer_loc_buffer_from_to #_ #_ #_ b from to = if ubuffer_of_buffer_from_to_none_cond b from to then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) (ubuffer_of_buffer_from_to b from to) let loc_includes_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_includes_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) #push-options "--z3rlimit 20" let loc_includes_as_seq #_ #rrel #_ #_ h1 h2 larger smaller = if Null? smaller then () else if Null? larger then begin MG.loc_includes_none_elim (loc_buffer smaller); MG.loc_of_aloc_not_none #_ #cls #(frameOf smaller) #(as_addr smaller) (ubuffer_of_buffer smaller) end else begin MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller); let ul = Ghost.reveal (ubuffer_of_buffer larger) in let us = Ghost.reveal (ubuffer_of_buffer smaller) in assert (as_seq h1 smaller == Seq.slice (as_seq h1 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)); assert (as_seq h2 smaller == Seq.slice (as_seq h2 larger) (us.b_offset - ul.b_offset) (us.b_offset - ul.b_offset + length smaller)) end #pop-options let loc_includes_addresses_buffer #a #rrel #srel preserve_liveness r s p = MG.loc_includes_addresses_aloc #_ #cls preserve_liveness r s #(as_addr p) (ubuffer_of_buffer p) let loc_includes_region_buffer #_ #_ #_ preserve_liveness s b = MG.loc_includes_region_aloc #_ #cls preserve_liveness s #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let loc_includes_region_addresses = MG.loc_includes_region_addresses #_ #cls let loc_includes_region_region = MG.loc_includes_region_region #_ #cls let loc_includes_region_union_l = MG.loc_includes_region_union_l let loc_includes_addresses_addresses = MG.loc_includes_addresses_addresses cls let loc_disjoint = MG.loc_disjoint let loc_disjoint_sym = MG.loc_disjoint_sym let loc_disjoint_none_r = MG.loc_disjoint_none_r let loc_disjoint_union_r = MG.loc_disjoint_union_r let loc_disjoint_includes = MG.loc_disjoint_includes val loc_disjoint_buffer (#a1 #a2:Type0) (#rrel1 #rel1:srel a1) (#rrel2 #rel2:srel a2) (b1:mbuffer a1 rrel1 rel1) (b2:mbuffer a2 rrel2 rel2) :Lemma (requires ((frameOf b1 == frameOf b2 /\ as_addr b1 == as_addr b2) ==> ubuffer_disjoint0 #(frameOf b1) #(frameOf b2) #(as_addr b1) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2))) (ensures (loc_disjoint (loc_buffer b1) (loc_buffer b2))) let loc_disjoint_buffer #_ #_ #_ #_ #_ #_ b1 b2 = MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) let loc_disjoint_gsub_buffer #_ #_ #_ b i1 len1 sub_rel1 i2 len2 sub_rel2 = loc_disjoint_buffer (mgsub sub_rel1 b i1 len1) (mgsub sub_rel2 b i2 len2) let loc_disjoint_loc_buffer_from_to #_ #_ #_ b from1 to1 from2 to2 = if ubuffer_of_buffer_from_to_none_cond b from1 to1 || ubuffer_of_buffer_from_to_none_cond b from2 to2 then () else MG.loc_disjoint_aloc_intro #_ #cls #(frameOf b) #(as_addr b) #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from1 to1) (ubuffer_of_buffer_from_to b from2 to2) let loc_disjoint_addresses = MG.loc_disjoint_addresses_intro #_ #cls let loc_disjoint_regions = MG.loc_disjoint_regions #_ #cls let modifies = MG.modifies let modifies_live_region = MG.modifies_live_region let modifies_mreference_elim = MG.modifies_mreference_elim let modifies_buffer_elim #_ #_ #_ b p h h' = if g_is_null b then assert (as_seq h b `Seq.equal` as_seq h' b) else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) p h h' ; ubuffer_preserved_elim b h h' end let modifies_buffer_from_to_elim #_ #_ #_ b from to p h h' = if g_is_null b then () else begin MG.modifies_aloc_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) p h h' ; ubuffer_preserved_from_to_elim b from to h h' end let modifies_refl = MG.modifies_refl let modifies_loc_includes = MG.modifies_loc_includes let address_liveness_insensitive_locs = MG.address_liveness_insensitive_locs _ let region_liveness_insensitive_locs = MG.region_liveness_insensitive_locs _ let address_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_address_liveness_insensitive_locs_aloc #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let address_liveness_insensitive_addresses = MG.loc_includes_address_liveness_insensitive_locs_addresses cls let region_liveness_insensitive_buffer #_ #_ #_ b = MG.loc_includes_region_liveness_insensitive_locs_loc_of_aloc #_ cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) let region_liveness_insensitive_addresses = MG.loc_includes_region_liveness_insensitive_locs_loc_addresses cls let region_liveness_insensitive_regions = MG.loc_includes_region_liveness_insensitive_locs_loc_regions cls let region_liveness_insensitive_address_liveness_insensitive = MG.loc_includes_region_liveness_insensitive_locs_address_liveness_insensitive_locs cls let modifies_liveness_insensitive_mreference = MG.modifies_preserves_liveness let modifies_liveness_insensitive_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else liveness_preservation_intro h h' x (fun t' pre r -> MG.modifies_preserves_liveness_strong l1 l2 h h' r (ubuffer_of_buffer x)) let modifies_liveness_insensitive_region = MG.modifies_preserves_region_liveness let modifies_liveness_insensitive_region_mreference = MG.modifies_preserves_region_liveness_reference let modifies_liveness_insensitive_region_buffer l1 l2 h h' #_ #_ #_ x = if g_is_null x then () else MG.modifies_preserves_region_liveness_aloc l1 l2 h h' #(frameOf x) #(as_addr x) (ubuffer_of_buffer x) let modifies_trans = MG.modifies_trans let modifies_only_live_regions = MG.modifies_only_live_regions let no_upd_fresh_region = MG.no_upd_fresh_region let new_region_modifies = MG.new_region_modifies #_ cls let modifies_fresh_frame_popped = MG.modifies_fresh_frame_popped let modifies_loc_regions_intro = MG.modifies_loc_regions_intro #_ #cls let modifies_loc_addresses_intro = MG.modifies_loc_addresses_intro #_ #cls let modifies_ralloc_post = MG.modifies_ralloc_post #_ #cls let modifies_salloc_post = MG.modifies_salloc_post #_ #cls let modifies_free = MG.modifies_free #_ #cls let modifies_none_modifies = MG.modifies_none_modifies #_ #cls let modifies_upd = MG.modifies_upd #_ #cls val modifies_0_modifies (h1 h2: HS.mem) : Lemma (requires (modifies_0 h1 h2)) (ensures (modifies loc_none h1 h2)) let modifies_0_modifies h1 h2 = MG.modifies_none_intro #_ #cls h1 h2 (fun r -> modifies_0_live_region h1 h2 r) (fun t pre b -> modifies_0_mreference #t #pre h1 h2 b) (fun r n -> modifies_0_unused_in h1 h2 r n) val modifies_1_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_1 b h1 h2)) (ensures (modifies (loc_buffer b) h1 h2)) let modifies_1_modifies #t #_ #_ b h1 h2 = if g_is_null b then begin modifies_1_null b h1 h2; modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer b) h1 h2 (fun r -> modifies_1_live_region b h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer b); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer b) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_mreference b h1 h2 p ) (fun t pre p -> modifies_1_liveness b h1 h2 p ) (fun r n -> modifies_1_unused_in b h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer b); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer b) b'; if frameOf b = r' && as_addr b = a' then modifies_1_ubuffer #t b h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_mreference b h1 h2 r_) ) val modifies_1_from_to_modifies (#a:Type0)(#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (h1 h2:HS.mem) :Lemma (requires (modifies_1_from_to b from to h1 h2)) (ensures (modifies (loc_buffer_from_to b from to) h1 h2)) let modifies_1_from_to_modifies #t #_ #_ b from to h1 h2 = if ubuffer_of_buffer_from_to_none_cond b from to then begin modifies_0_modifies h1 h2 end else MG.modifies_intro (loc_buffer_from_to b from to) h1 h2 (fun r -> modifies_1_from_to_live_region b from to h1 h2 r) (fun t pre p -> loc_disjoint_sym (loc_mreference p) (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_addresses_elim #_ #cls #(frameOf b) #(as_addr b) (ubuffer_of_buffer_from_to b from to) true (HS.frameOf p) (Set.singleton (HS.as_addr p)); modifies_1_from_to_mreference b from to h1 h2 p ) (fun t pre p -> modifies_1_from_to_liveness b from to h1 h2 p ) (fun r n -> modifies_1_from_to_unused_in b from to h1 h2 r n ) (fun r' a' b' -> loc_disjoint_sym (MG.loc_of_aloc b') (loc_buffer_from_to b from to); MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b) #(as_addr b) #r' #a' (ubuffer_of_buffer_from_to b from to) b'; if frameOf b = r' && as_addr b = a' then modifies_1_from_to_ubuffer #t b from to h1 h2 b' else same_mreference_ubuffer_preserved #r' #a' b' h1 h2 (fun a_ pre_ r_ -> modifies_1_from_to_mreference b from to h1 h2 r_) ) val modifies_addr_of_modifies (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (h1 h2:HS.mem) :Lemma (requires (modifies_addr_of b h1 h2)) (ensures (modifies (loc_addr_of_buffer b) h1 h2)) let modifies_addr_of_modifies #t #_ #_ b h1 h2 = MG.modifies_address_intro #_ #cls (frameOf b) (as_addr b) h1 h2 (fun r -> modifies_addr_of_live_region b h1 h2 r) (fun t pre p -> modifies_addr_of_mreference b h1 h2 p ) (fun r n -> modifies_addr_of_unused_in b h1 h2 r n ) val modifies_loc_buffer_from_to_intro' (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (from to: U32.t) (l: loc) (h h' : HS.mem) : Lemma (requires ( let s = as_seq h b in let s' = as_seq h' b in not (g_is_null b) /\ live h b /\ modifies (loc_union l (loc_buffer b)) h h' /\ U32.v from <= U32.v to /\ U32.v to <= length b /\ Seq.slice s 0 (U32.v from) `Seq.equal` Seq.slice s' 0 (U32.v from) /\ Seq.slice s (U32.v to) (length b) `Seq.equal` Seq.slice s' (U32.v to) (length b) )) (ensures (modifies (loc_union l (loc_buffer_from_to b from to)) h h')) #push-options "--z3rlimit 16" let modifies_loc_buffer_from_to_intro' #a #rrel #rel b from to l h h' = let r0 = frameOf b in let a0 = as_addr b in let bb : ubuffer r0 a0 = ubuffer_of_buffer b in modifies_loc_includes (loc_union l (loc_addresses true r0 (Set.singleton a0))) h h' (loc_union l (loc_buffer b)); MG.modifies_strengthen l #r0 #a0 (ubuffer_of_buffer_from_to b from to) h h' (fun f (x: ubuffer r0 a0) -> ubuffer_preserved_intro x h h' (fun t' rrel' rel' b' -> f _ _ (Buffer?.content b')) (fun t' rrel' rel' b' -> // prove that the types, rrels, rels are equal Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); assert (Seq.seq t' == Seq.seq a); let _s0 : Seq.seq a = as_seq h b in let _s1 : Seq.seq t' = coerce_eq _ _s0 in lemma_equal_instances_implies_equal_types a t' _s0 _s1; let boff = U32.v (Buffer?.idx b) in let from_ = boff + U32.v from in let to_ = boff + U32.v to in let ({ b_max_length = ml; b_offset = xoff; b_length = xlen; b_is_mm = is_mm }) = Ghost.reveal x in let ({ b_max_length = _; b_offset = b'off; b_length = b'len }) = Ghost.reveal (ubuffer_of_buffer b') in let bh = as_seq h b in let bh' = as_seq h' b in let xh = Seq.slice (as_seq h b') (xoff - b'off) (xoff - b'off + xlen) in let xh' = Seq.slice (as_seq h' b') (xoff - b'off) (xoff - b'off + xlen) in let prf (i: nat) : Lemma (requires (i < xlen)) (ensures (i < xlen /\ Seq.index xh i == Seq.index xh' i)) = let xi = xoff + i in let bi : ubuffer r0 a0 = Ghost.hide ({ b_max_length = ml; b_offset = xi; b_length = 1; b_is_mm = is_mm; }) in assert (Seq.index xh i == Seq.index (Seq.slice (as_seq h b') (xi - b'off) (xi - b'off + 1)) 0); assert (Seq.index xh' i == Seq.index (Seq.slice (as_seq h' b') (xi - b'off) (xi - b'off + 1)) 0); let li = MG.loc_of_aloc bi in MG.loc_includes_aloc #_ #cls x bi; loc_disjoint_includes l (MG.loc_of_aloc x) l li; if xi < boff || boff + length b <= xi then begin MG.loc_disjoint_aloc_intro #_ #cls bb bi; assert (loc_disjoint (loc_union l (loc_buffer b)) li); MG.modifies_aloc_elim bi (loc_union l (loc_buffer b)) h h' end else if xi < from_ then begin assert (Seq.index xh i == Seq.index (Seq.slice bh 0 (U32.v from)) (xi - boff)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' 0 (U32.v from)) (xi - boff)) end else begin assert (to_ <= xi); assert (Seq.index xh i == Seq.index (Seq.slice bh (U32.v to) (length b)) (xi - to_)); assert (Seq.index xh' i == Seq.index (Seq.slice bh' (U32.v to) (length b)) (xi - to_)) end in Classical.forall_intro (Classical.move_requires prf); assert (xh `Seq.equal` xh') ) ) #pop-options let modifies_loc_buffer_from_to_intro #a #rrel #rel b from to l h h' = if g_is_null b then () else modifies_loc_buffer_from_to_intro' b from to l h h' let does_not_contain_addr = MG.does_not_contain_addr let not_live_region_does_not_contain_addr = MG.not_live_region_does_not_contain_addr let unused_in_does_not_contain_addr = MG.unused_in_does_not_contain_addr let addr_unused_in_does_not_contain_addr = MG.addr_unused_in_does_not_contain_addr let free_does_not_contain_addr = MG.free_does_not_contain_addr let does_not_contain_addr_elim = MG.does_not_contain_addr_elim let modifies_only_live_addresses = MG.modifies_only_live_addresses let loc_not_unused_in = MG.loc_not_unused_in _ let loc_unused_in = MG.loc_unused_in _ let loc_regions_unused_in = MG.loc_regions_unused_in cls let loc_unused_in_not_unused_in_disjoint = MG.loc_unused_in_not_unused_in_disjoint cls let not_live_region_loc_not_unused_in_disjoint = MG.not_live_region_loc_not_unused_in_disjoint cls let live_loc_not_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.does_not_contain_addr_addr_unused_in h) (frameOf b, as_addr b); MG.loc_addresses_not_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let unused_in_loc_unused_in #_ #_ #_ b h = unused_in_equiv b h; Classical.move_requires (MG.addr_unused_in_does_not_contain_addr h) (frameOf b, as_addr b); MG.loc_addresses_unused_in cls (frameOf b) (Set.singleton (as_addr b)) h; () let modifies_address_liveness_insensitive_unused_in = MG.modifies_address_liveness_insensitive_unused_in cls let modifies_only_not_unused_in = MG.modifies_only_not_unused_in let mreference_live_loc_not_unused_in = MG.mreference_live_loc_not_unused_in cls let mreference_unused_in_loc_unused_in = MG.mreference_unused_in_loc_unused_in cls let modifies_loc_unused_in l h1 h2 l' = modifies_loc_includes address_liveness_insensitive_locs h1 h2 l; modifies_address_liveness_insensitive_unused_in h1 h2; loc_includes_trans (loc_unused_in h1) (loc_unused_in h2) l' let fresh_frame_modifies h0 h1 = MG.fresh_frame_modifies #_ cls h0 h1 let popped_modifies = MG.popped_modifies #_ cls let modifies_remove_new_locs l_fresh l_aux l_goal h1 h2 h3 = modifies_only_not_unused_in l_goal h1 h3 let disjoint_neq #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () let empty_disjoint #t1 #t2 #rrel1 #rel1 #rrel2 #rel2 b1 b2 = let r = frameOf b1 in let a = as_addr b1 in if r = frameOf b2 && a = as_addr b2 then MG.loc_disjoint_aloc_intro #_ #cls #r #a #r #a (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) else () (* let includes_live #a #rrel #rel1 #rel2 h larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let includes_frameOf_as_addr #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) let pointer_distinct_sel_disjoint #a #_ #_ #_ #_ b1 b2 h = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then begin HS.mreference_distinct_sel_disjoint h (Buffer?.content b1) (Buffer?.content b2); loc_disjoint_buffer b1 b2 end else loc_disjoint_buffer b1 b2 let is_null #_ #_ #_ b = Null? b let msub #a #rrel #rel sub_rel b i len = match b with | Null -> Null | Buffer max_len content i0 len0 -> Buffer max_len content (U32.add i0 i) len let moffset #a #rrel #rel sub_rel b i = match b with | Null -> Null | Buffer max_len content i0 len -> Buffer max_len content (U32.add i0 i) (Ghost.hide ((U32.sub (Ghost.reveal len) i))) let index #_ #_ #_ b i = let open HST in let s = ! (Buffer?.content b) in Seq.index s (U32.v (Buffer?.idx b) + U32.v i) let g_upd_seq #_ #_ #_ b s h = if Seq.length s = 0 then h else let s0 = HS.sel h (Buffer?.content b) in let Buffer _ content idx length = b in HS.upd h (Buffer?.content b) (Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v length) s) let lemma_g_upd_with_same_seq #_ #_ #_ b h = if Null? b then () else let open FStar.UInt32 in let Buffer _ content idx length = b in let s = HS.sel h content in assert (Seq.equal (Seq.replace_subseq s (v idx) (v idx + v length) (Seq.slice s (v idx) (v idx + v length))) s); HS.lemma_heap_equality_upd_with_sel h (Buffer?.content b) #push-options "--z3rlimit 48" let g_upd_seq_as_seq #a #_ #_ b s h = let h' = g_upd_seq b s h in if g_is_null b then assert (Seq.equal s Seq.empty) else begin assert (Seq.equal (as_seq h' b) s); // prove modifies_1_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_modifies b h h' end let g_upd_modifies_strong #_ #_ #_ b i v h = let h' = g_upd b i v h in // prove modifies_1_from_to_preserves_ubuffers Heap.lemma_distinct_addrs_distinct_preorders (); Heap.lemma_distinct_addrs_distinct_mm (); s_lemma_equal_instances_implies_equal_types (); modifies_1_from_to_modifies b (U32.uint_to_t i) (U32.uint_to_t (i + 1)) h h' #pop-options let upd' #_ #_ #_ b i v = let open HST in let h = get() in let Buffer max_length content idx len = b in let s0 = !content in let sb0 = Seq.slice s0 (U32.v idx) (U32.v max_length) in let s_upd = Seq.upd sb0 (U32.v i) v in let sf = Seq.replace_subseq s0 (U32.v idx) (U32.v max_length) s_upd in assert (sf `Seq.equal` Seq.replace_subseq s0 (U32.v idx) (U32.v idx + U32.v len) (Seq.upd (as_seq h b) (U32.v i) v)); content := sf let recallable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) :GTot Type0 = (not (g_is_null b)) ==> ( HST.is_eternal_region (frameOf b) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_buf #_ #_ #_ b = (not (g_is_null b)) ==> ( HS.is_heap_color (HS.color (frameOf b)) /\ not (HS.is_mm (Buffer?.content b)) /\ buffer_compatible b ) let region_lifetime_sub #a #rrel #rel #subrel b0 b1 = match b1 with | Null -> () | Buffer max_len content idx length -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j subrel) let recallable_null #_ #_ #_ = () let recallable_mgsub #_ #rrel #rel b i len sub_rel = match b with | Null -> () | Buffer max_len content idx length -> lemma_seq_sub_compatibility_is_transitive (U32.v max_len) rrel (U32.v idx) (U32.v idx + U32.v length) rel (U32.v i) (U32.v i + U32.v len) sub_rel (* let recallable_includes #_ #_ #_ #_ #_ #_ larger smaller = if Null? larger || Null? smaller then () else MG.loc_includes_aloc_elim #_ #cls #(frameOf larger) #(frameOf smaller) #(as_addr larger) #(as_addr smaller) (ubuffer_of_buffer larger) (ubuffer_of_buffer smaller) *) let recall #_ #_ #_ b = if Null? b then () else HST.recall (Buffer?.content b) private let spred_as_mempred (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :HST.mem_predicate = fun h -> buffer_compatible b ==> p (as_seq h b) let witnessed #_ #rrel #rel b p = match b with | Null -> p Seq.empty | Buffer max_length content idx length -> HST.token_p content (spred_as_mempred b p) private let lemma_stable_on_rel_is_stable_on_rrel (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (p:spred a) :Lemma (requires (Buffer? b /\ stable_on p rel)) (ensures (HST.stable_on (spred_as_mempred b p) (Buffer?.content b))) = let Buffer max_length content idx length = b in let mp = spred_as_mempred b p in let aux (h0 h1:HS.mem) :Lemma ((mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content)) ==> mp h1) = Classical.arrow_to_impl #(mp h0 /\ rrel (HS.sel h0 content) (HS.sel h1 content) /\ buffer_compatible b) #(mp h1) (fun _ -> assert (rel (as_seq h0 b) (as_seq h1 b))) in Classical.forall_intro_2 aux let witness_p #a #rrel #rel b p = match b with | Null -> () | Buffer _ content _ _ -> lemma_stable_on_rel_is_stable_on_rrel b p; //AR: TODO: the proof doesn't go through without this assertion, which should follow directly from the lemma call assert (HST.stable_on #(Seq.lseq a (U32.v (Buffer?.max_length b))) #(srel_to_lsrel (U32.v (Buffer?.max_length b)) rrel) (spred_as_mempred b p) (Buffer?.content b)); HST.witness_p content (spred_as_mempred b p) let recall_p #_ #_ #_ b p = match b with | Null -> () | Buffer _ content _ _ -> HST.recall_p content (spred_as_mempred b p) let witnessed_functorial #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> assert (as_seq HS.empty_mem b1 == Seq.empty) | Buffer _ content _ _, _ -> assert (forall (len:nat) (i:nat) (j:nat{i <= j /\ j <= len}). compatible_sub_preorder len rrel i j rel1); HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let witnessed_functorial_st #a #rrel #rel1 #rel2 b1 b2 i len s1 s2 = match b1, b2 with | Null, Null -> () | Buffer _ content _ _, _ -> HST.token_functoriality content (spred_as_mempred b1 s1) (spred_as_mempred b2 s2) let freeable (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) = (not (g_is_null b)) /\ HS.is_mm (Buffer?.content b) /\ HS.is_heap_color (HS.color (frameOf b)) /\ U32.v (Buffer?.max_length b) > 0 /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b let free #_ #_ #_ b = HST.rfree (Buffer?.content b) let freeable_length #_ #_ #_ b = () let freeable_disjoint #_ #_ #_ #_ #_ #_ b1 b2 = if frameOf b1 = frameOf b2 && as_addr b1 = as_addr b2 then MG.loc_disjoint_aloc_elim #_ #cls #(frameOf b1) #(as_addr b1) #(frameOf b2) #(as_addr b2) (ubuffer_of_buffer b1) (ubuffer_of_buffer b2) private let alloc_heap_common (#a:Type0) (#rrel:srel a) (r:HST.erid) (len:U32.t{U32.v len > 0}) (s:Seq.seq a{Seq.length s == U32.v len}) (mm:bool) :HST.ST (lmbuffer a rrel rrel (U32.v len)) (requires (fun _ -> True)) (ensures (fun h0 b h1 -> alloc_post_mem_common b h0 h1 s /\ frameOf b == r /\ HS.is_mm (Buffer?.content b) == mm /\ Buffer?.idx b == 0ul /\ Ghost.reveal (Buffer?.length b) == Buffer?.max_length b)) = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = if mm then HST.ralloc_mm r s else HST.ralloc r s in let b = Buffer len content 0ul (Ghost.hide len) in b let mgcmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) false private let read_sub_buffer (#a:Type0) (#rrel #rel:srel a) (b:mbuffer a rrel rel) (idx len:U32.t) : HST.ST (Seq.seq a) (requires fun h0 -> live h0 b /\ U32.v len > 0 /\ U32.v idx + U32.v len <= length b) (ensures fun h0 s h1 -> h0 == h1 /\ s == Seq.slice (as_seq h0 b) (U32.v idx) (U32.v idx + U32.v len)) = let open HST in let s = ! (Buffer?.content b) in //the whole allocation unit let s = Seq.slice s (U32.v (Buffer?.idx b)) (U32.v (Buffer?.max_length b)) in //b buffer Seq.slice s (U32.v idx) (U32.v idx + U32.v len) //slice of b let mgcmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) false let mmalloc #_ #_ r init len = alloc_heap_common r len (Seq.create (U32.v len) init) true let mmalloc_and_blit #_ #_ r #_ #_ src id_src len = alloc_heap_common r len (read_sub_buffer src id_src len) true let malloca #a #rrel init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (Seq.create (U32.v len) init) in Buffer len content 0ul (Ghost.hide len) let malloca_and_blit #a #rrel #_ #_ src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc (read_sub_buffer src id_src len) in Buffer len content 0ul (Ghost.hide len) let malloca_of_list #a #rrel init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.salloc s in Buffer len content 0ul (Ghost.hide len) let mgcmalloc_of_list #a #rrel r init = let len = U32.uint_to_t (FStar.List.Tot.length init) in let s = Seq.seq_of_list init in lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc r s in Buffer len content 0ul (Ghost.hide len) let mmalloc_drgn #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_mm #a #rrel d init len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content : HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn_mm d (Seq.create (U32.v len) init) in Buffer len content 0ul len let mmalloc_drgn_and_blit #a #rrel #_ #_ d src id_src len = lemma_seq_sub_compatilibity_is_reflexive (U32.v len) rrel; let content: HST.mreference (Seq.lseq a (U32.v len)) (srel_to_lsrel (U32.v len) rrel) = HST.ralloc_drgn d (read_sub_buffer src id_src len) in Buffer len content 0ul len #push-options "--max_fuel 0 --initial_ifuel 1 --max_ifuel 1 --z3rlimit 64" let blit #a #rrel1 #rrel2 #rel1 #rel2 src idx_src dst idx_dst len = let open HST in match src, dst with | Buffer _ _ _ _, Buffer _ _ _ _ -> if len = 0ul then () else let h = get () in let Buffer max_length1 content1 idx1 length1 = src in let Buffer max_length2 content2 idx2 length2 = dst in let s_full1 = !content1 in let s_full2 = !content2 in let s1 = Seq.slice s_full1 (U32.v idx1) (U32.v max_length1) in let s2 = Seq.slice s_full2 (U32.v idx2) (U32.v max_length2) in let s_sub_src = Seq.slice s1 (U32.v idx_src) (U32.v idx_src + U32.v len) in let s2' = Seq.replace_subseq s2 (U32.v idx_dst) (U32.v idx_dst + U32.v len) s_sub_src in let s_full2' = Seq.replace_subseq s_full2 (U32.v idx2) (U32.v max_length2) s2' in assert (Seq.equal (Seq.slice s2' (U32.v idx_dst) (U32.v idx_dst + U32.v len)) s_sub_src); assert (Seq.equal (Seq.slice s2' 0 (U32.v idx_dst)) (Seq.slice s2 0 (U32.v idx_dst))); assert (Seq.equal (Seq.slice s2' (U32.v idx_dst + U32.v len) (length dst)) (Seq.slice s2 (U32.v idx_dst + U32.v len) (length dst))); // AF: Needed to trigger the preorder relation. A bit verbose because the second sequence // has a ghost computation (U32.v (Ghost.reveal length)) assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.replace_subseq (as_seq h dst) (U32.v idx_dst) (U32.v idx_dst + U32.v len) (Seq.slice (as_seq h src) (U32.v idx_src) (U32.v idx_src + U32.v len) ) ) ); content2 := s_full2'; let h1 = get () in assert (s_full2' `Seq.equal` Seq.replace_subseq s_full2 (U32.v idx2) (U32.v idx2 + U32.v length2) (Seq.slice s2' 0 (U32.v length2))); assert (h1 == g_upd_seq dst (Seq.slice s2' 0 (U32.v length2)) h); g_upd_seq_as_seq dst (Seq.slice s2' 0 (U32.v length2)) h //for modifies clause | _, _ -> () #push-options "--z3rlimit 128 --max_fuel 0 --max_ifuel 1 --initial_ifuel 1 --z3cliopt smt.qi.EAGER_THRESHOLD=4" let fill' (#t:Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z:t) (len:U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)) )) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ Seq.slice (as_seq h1 b) 0 (U32.v len) `Seq.equal` Seq.create (U32.v len) z /\ Seq.slice (as_seq h1 b) (U32.v len) (length b) `Seq.equal` Seq.slice (as_seq h0 b) (U32.v len) (length b)

false

LowStar.Monotonic.Buffer.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 0, "max_ifuel": 1, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [ "smt.qi.EAGER_THRESHOLD=4" ], "z3refresh": false, "z3rlimit": 128, "z3rlimit_factor": 4, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val fill' (#t: Type) (#rrel #rel: srel t) (b: mbuffer t rrel rel) (z: t) (len: U32.t) : HST.Stack unit (requires (fun h -> live h b /\ U32.v len <= length b /\ rel (as_seq h b) (Seq.replace_subseq (as_seq h b) 0 (U32.v len) (Seq.create (U32.v len) z)))) (ensures (fun h0 _ h1 -> modifies (loc_buffer b) h0 h1 /\ live h1 b /\ (Seq.slice (as_seq h1 b) 0 (U32.v len)) `Seq.equal` (Seq.create (U32.v len) z) /\ (Seq.slice (as_seq h1 b) (U32.v len) (length b)) `Seq.equal` (Seq.slice (as_seq h0 b) (U32.v len) (length b))))

[]

LowStar.Monotonic.Buffer.fill'

{ "file_name": "ulib/LowStar.Monotonic.Buffer.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

b: LowStar.Monotonic.Buffer.mbuffer t rrel rel -> z: t -> len: FStar.UInt32.t -> FStar.HyperStack.ST.Stack Prims.unit

{ "end_col": 5, "end_line": 1645, "start_col": 2, "start_line": 1627 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let tu = twice ()

let tu =

false

null

false

twice ()

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.twice", "Prims.unit" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p}

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val tu : FStar.Relational.Relational.rel Prims.unit Prims.unit

[]

FStar.Relational.Relational.tu

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

FStar.Relational.Relational.rel Prims.unit Prims.unit

{ "end_col": 17, "end_line": 28, "start_col": 9, "start_line": 28 }

Prims.Tot

val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) =

false

null

false

R (f x1 y1) (f x2 y2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.double", "FStar.Pervasives.Native.Mktuple2", "FStar.Relational.Relational.rel", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c)

[]

FStar.Relational.Relational.rel_map2T

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: 'a -> _: 'b -> 'c) -> _: FStar.Relational.Relational.double 'a -> _: FStar.Relational.Relational.double 'b -> FStar.Relational.Relational.double 'c

{ "end_col": 59, "end_line": 38, "start_col": 38, "start_line": 38 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let op_Hat_Minus = rel_map2T (fun x y -> x - y)

let op_Hat_Minus =

false

null

false

rel_map2T (fun x y -> x - y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.int", "Prims.op_Subtraction" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val op_Hat_Minus : _: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

[]

FStar.Relational.Relational.op_Hat_Minus

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

{ "end_col": 47, "end_line": 51, "start_col": 19, "start_line": 51 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let twice x = R x x

let twice x =

false

null

false

R x x

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.R", "FStar.Relational.Relational.rel" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p}

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val twice : x: _ -> FStar.Relational.Relational.rel _ _

[]

FStar.Relational.Relational.twice

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

x: _ -> FStar.Relational.Relational.rel _ _

{ "end_col": 19, "end_line": 27, "start_col": 14, "start_line": 27 }

Prims.Tot

val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) =

false

null

false

R (f x1 y1) (f x2 y2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "Prims.eqtype", "FStar.Relational.Relational.double", "FStar.Pervasives.Native.Mktuple2", "FStar.Relational.Relational.rel", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c)

[]

FStar.Relational.Relational.rel_map2Teq

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: a -> _: b -> c) -> _: FStar.Relational.Relational.double a -> _: FStar.Relational.Relational.double b -> FStar.Relational.Relational.double c

{ "end_col": 70, "end_line": 35, "start_col": 49, "start_line": 35 }

Prims.GTot

val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) =

false

null

false

R (f x1 y1) (f x2 y2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "sometrivial" ]

[ "FStar.Relational.Relational.double", "FStar.Pervasives.Native.Mktuple2", "FStar.Relational.Relational.rel", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c)

[]

FStar.Relational.Relational.rel_map2G

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: 'a -> _: 'b -> Prims.GTot 'c) -> _: FStar.Relational.Relational.double 'a -> _: FStar.Relational.Relational.double 'b -> Prims.GTot (FStar.Relational.Relational.double 'c)

{ "end_col": 59, "end_line": 41, "start_col": 38, "start_line": 41 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y)

let op_Hat_Star =

false

null

false

rel_map2T (fun x y -> op_Multiply x y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.int", "Prims.op_Multiply" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val op_Hat_Star : _: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

[]

FStar.Relational.Relational.op_Hat_Star

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

{ "end_col": 56, "end_line": 52, "start_col": 18, "start_line": 52 }

Prims.Tot

val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map1T f (R x1 x2) = R (f x1) (f x2)

val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) =

false

null

false

R (f x1) (f x2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.double", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b)

[]

FStar.Relational.Relational.rel_map1T

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: 'a -> 'b) -> _: FStar.Relational.Relational.double 'a -> FStar.Relational.Relational.double 'b

{ "end_col": 44, "end_line": 32, "start_col": 29, "start_line": 32 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let op_Hat_Plus = rel_map2T (fun x y -> x + y)

let op_Hat_Plus =

false

null

false

rel_map2T (fun x y -> x + y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.int", "Prims.op_Addition" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val op_Hat_Plus : _: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

[]

FStar.Relational.Relational.op_Hat_Plus

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.int -> FStar.Relational.Relational.double Prims.int

{ "end_col": 46, "end_line": 50, "start_col": 18, "start_line": 50 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let snd_rel = rel_map1T snd

let snd_rel =

false

null

false

rel_map1T snd

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map1T", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.snd", "FStar.Relational.Relational.double" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val snd_rel : _: FStar.Relational.Relational.double (_ * _) -> FStar.Relational.Relational.double _

[]

FStar.Relational.Relational.snd_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double (_ * _) -> FStar.Relational.Relational.double _

{ "end_col": 27, "end_line": 63, "start_col": 14, "start_line": 63 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let op_Hat_Slash = rel_map2T (fun x y -> x / y)

let op_Hat_Slash =

false

null

false

rel_map2T (fun x y -> x / y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.int", "Prims.nonzero", "Prims.op_Division" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val op_Hat_Slash : _: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.nonzero -> FStar.Relational.Relational.double Prims.int

[]

FStar.Relational.Relational.op_Hat_Slash

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.int -> _: FStar.Relational.Relational.double Prims.nonzero -> FStar.Relational.Relational.double Prims.int

{ "end_col": 47, "end_line": 53, "start_col": 19, "start_line": 53 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f)

let triple_rel (R a b) (R c d) (R e f) =

false

null

false

R (a, c, e) (b, d, f)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel", "FStar.Pervasives.Native.Mktuple3", "FStar.Relational.Relational.R", "FStar.Pervasives.Native.tuple3" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val triple_rel : _: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> FStar.Relational.Relational.rel ((_ * _) * _) ((_ * _) * _)

[]

FStar.Relational.Relational.triple_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> FStar.Relational.Relational.rel ((_ * _) * _) ((_ * _) * _)

{ "end_col": 58, "end_line": 61, "start_col": 41, "start_line": 61 }

Prims.Tot

val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2)

val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) =

false

null

false

R (f x1 y1 z1) (f x2 y2 z2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.double", "FStar.Pervasives.Native.Mktuple3", "FStar.Relational.Relational.rel", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd)

[]

FStar.Relational.Relational.rel_map3T

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: 'a -> _: 'b -> _: 'c -> 'd) -> _: FStar.Relational.Relational.double 'a -> _: FStar.Relational.Relational.double 'b -> _: FStar.Relational.Relational.double 'c -> FStar.Relational.Relational.double 'd

{ "end_col": 75, "end_line": 44, "start_col": 48, "start_line": 44 }

Prims.GTot

val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd)

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2)

val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) =

false

null

false

R (f x1 y1 z1) (f x2 y2 z2)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "sometrivial" ]

[ "FStar.Relational.Relational.double", "FStar.Pervasives.Native.Mktuple3", "FStar.Relational.Relational.rel", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd)

[]

FStar.Relational.Relational.rel_map3G

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

f: (_: 'a -> _: 'b -> _: 'c -> Prims.GTot 'd) -> _: FStar.Relational.Relational.double 'a -> _: FStar.Relational.Relational.double 'b -> _: FStar.Relational.Relational.double 'c -> Prims.GTot (FStar.Relational.Relational.double 'd)

{ "end_col": 75, "end_line": 47, "start_col": 48, "start_line": 47 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let fst_rel = rel_map1T fst

let fst_rel =

false

null

false

rel_map1T fst

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map1T", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.fst", "FStar.Relational.Relational.double" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val fst_rel : _: FStar.Relational.Relational.double (_ * _) -> FStar.Relational.Relational.double _

[]

FStar.Relational.Relational.fst_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double (_ * _) -> FStar.Relational.Relational.double _

{ "end_col": 27, "end_line": 62, "start_col": 14, "start_line": 62 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let eq_rel = rel_map2Teq (fun (x y:bool) -> x = y)

let eq_rel =

false

null

false

rel_map2Teq (fun (x: bool) (y: bool) -> x = y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2Teq", "Prims.bool", "Prims.op_Equality" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *) let and_rel = rel_map2T (fun x y -> x && y)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val eq_rel : _: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

[]

FStar.Relational.Relational.eq_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

{ "end_col": 50, "end_line": 68, "start_col": 13, "start_line": 68 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys)

let cons_rel (R x y) (R xs ys) =

false

null

false

R (x :: xs) (y :: ys)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel", "Prims.list", "FStar.Pervasives.Native.Mktuple2", "FStar.Relational.Relational.R", "Prims.Cons" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a))

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val cons_rel : _: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel (Prims.list _) (Prims.list _) -> FStar.Relational.Relational.rel (Prims.list _) (Prims.list _)

[]

FStar.Relational.Relational.cons_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel (Prims.list _) (Prims.list _) -> FStar.Relational.Relational.rel (Prims.list _) (Prims.list _)

{ "end_col": 50, "end_line": 58, "start_col": 33, "start_line": 58 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let pair_rel (R a b) (R c d) = R (a,c) (b,d)

let pair_rel (R a b) (R c d) =

false

null

false

R (a, c) (b, d)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel", "FStar.Pervasives.Native.Mktuple2", "FStar.Relational.Relational.R", "FStar.Pervasives.Native.tuple2" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val pair_rel : _: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> FStar.Relational.Relational.rel (_ * _) (_ * _)

[]

FStar.Relational.Relational.pair_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.rel _ _ -> _: FStar.Relational.Relational.rel _ _ -> FStar.Relational.Relational.rel (_ * _) (_ * _)

{ "end_col": 44, "end_line": 60, "start_col": 31, "start_line": 60 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let or_irel (R a b) = a || b

let or_irel (R a b) =

false

null

false

a || b

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel", "Prims.bool", "Prims.op_BarBar" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *) let and_rel = rel_map2T (fun x y -> x && y) let or_rel = rel_map2T (fun x y -> x || y) let eq_rel = rel_map2Teq (fun (x y:bool) -> x = y) (* Some convenient functions combining left and right side (for specification only) *)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val or_irel : _: FStar.Relational.Relational.rel Prims.bool Prims.bool -> Prims.bool

[]

FStar.Relational.Relational.or_irel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.rel Prims.bool Prims.bool -> Prims.bool

{ "end_col": 28, "end_line": 72, "start_col": 22, "start_line": 72 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let eq_irel (#t:eqtype) (x:(rel t t)) = match x with | R a b -> a = b

let eq_irel (#t: eqtype) (x: (rel t t)) =

false

null

false

match x with | R a b -> a = b

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "Prims.eqtype", "FStar.Relational.Relational.rel", "Prims.op_Equality", "Prims.bool" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *) let and_rel = rel_map2T (fun x y -> x && y) let or_rel = rel_map2T (fun x y -> x || y) let eq_rel = rel_map2Teq (fun (x y:bool) -> x = y) (* Some convenient functions combining left and right side (for specification only) *) let and_irel (R a b) = a && b

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val eq_irel : x: FStar.Relational.Relational.rel t t -> Prims.bool

[]

FStar.Relational.Relational.eq_irel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

x: FStar.Relational.Relational.rel t t -> Prims.bool

{ "end_col": 18, "end_line": 74, "start_col": 40, "start_line": 73 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let and_irel (R a b) = a && b

let and_irel (R a b) =

false

null

false

a && b

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel", "Prims.bool", "Prims.op_AmpAmp" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *) let and_rel = rel_map2T (fun x y -> x && y) let or_rel = rel_map2T (fun x y -> x || y) let eq_rel = rel_map2Teq (fun (x y:bool) -> x = y)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val and_irel : _: FStar.Relational.Relational.rel Prims.bool Prims.bool -> Prims.bool

[]

FStar.Relational.Relational.and_irel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.rel Prims.bool Prims.bool -> Prims.bool

{ "end_col": 29, "end_line": 71, "start_col": 23, "start_line": 71 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let and_rel = rel_map2T (fun x y -> x && y)

let and_rel =

false

null

false

rel_map2T (fun x y -> x && y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.bool", "Prims.op_AmpAmp" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val and_rel : _: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

[]

FStar.Relational.Relational.and_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

{ "end_col": 43, "end_line": 66, "start_col": 14, "start_line": 66 }

Prims.Tot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let or_rel = rel_map2T (fun x y -> x || y)

let or_rel =

false

null

false

rel_map2T (fun x y -> x || y)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.rel_map2T", "Prims.bool", "Prims.op_BarBar" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *)

false

true

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val or_rel : _: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

[]

FStar.Relational.Relational.or_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

_: FStar.Relational.Relational.double Prims.bool -> _: FStar.Relational.Relational.double Prims.bool -> FStar.Relational.Relational.double Prims.bool

{ "end_col": 42, "end_line": 67, "start_col": 13, "start_line": 67 }

Prims.GTot

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let sel_rel1 (#a:Type) (h:double heap) (r:ref a) = rel_map2G sel h (twice r)

let sel_rel1 (#a: Type) (h: double heap) (r: ref a) =

false

null

false

rel_map2G sel h (twice r)

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "sometrivial" ]

[ "FStar.Relational.Relational.double", "FStar.Monotonic.Heap.heap", "FStar.Heap.ref", "FStar.Relational.Relational.rel_map2G", "FStar.Monotonic.Heap.mref", "FStar.Heap.trivial_preorder", "FStar.Monotonic.Heap.sel", "FStar.Relational.Relational.twice" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *) val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_::xs) (_::ys)) = R xs ys let cons_rel (R x y) (R xs ys) = R (x::xs) (y::ys) (* Some convenient tuple functions *) let pair_rel (R a b) (R c d) = R (a,c) (b,d) let triple_rel (R a b) (R c d) (R e f) = R (a,c,e) (b,d,f) let fst_rel = rel_map1T fst let snd_rel = rel_map1T snd (* Some convenient boolean functions *) let and_rel = rel_map2T (fun x y -> x && y) let or_rel = rel_map2T (fun x y -> x || y) let eq_rel = rel_map2Teq (fun (x y:bool) -> x = y) (* Some convenient functions combining left and right side (for specification only) *) let and_irel (R a b) = a && b let or_irel (R a b) = a || b let eq_irel (#t:eqtype) (x:(rel t t)) = match x with | R a b -> a = b

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val sel_rel1 : h: FStar.Relational.Relational.double FStar.Monotonic.Heap.heap -> r: FStar.Heap.ref a -> Prims.GTot (FStar.Relational.Relational.double a)

[]

FStar.Relational.Relational.sel_rel1

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

h: FStar.Relational.Relational.double FStar.Monotonic.Heap.heap -> r: FStar.Heap.ref a -> Prims.GTot (FStar.Relational.Relational.double a)

{ "end_col": 77, "end_line": 77, "start_col": 52, "start_line": 77 }

Prims.Tot

val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a))

[ { "abbrev": false, "full_module": "FStar.Heap", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Relational", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let tl_rel #a (R (_::xs) (_::ys)) = R xs ys

val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a)) let tl_rel #a (R (_ :: xs) (_ :: ys)) =

false

null

false

R xs ys

{ "checked_file": "FStar.Relational.Relational.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Heap.fst.checked" ], "interface_file": false, "source_file": "FStar.Relational.Relational.fst" }

[ "total" ]

[ "FStar.Relational.Relational.double", "Prims.list", "Prims.l_and", "Prims.b2t", "Prims.uu___is_Cons", "FStar.Relational.Relational.__proj__R__item__l", "FStar.Relational.Relational.__proj__R__item__r", "FStar.Relational.Relational.R" ]

[]

(* Copyright 2008-2018 Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) module FStar.Relational.Relational open FStar.Heap (* Relational Type constructor (Equivalent to pairs) *) type rel (a:Type) (b:Type) : Type = | R : l:a -> r:b -> rel a b (* Some frequently used abbreviations *) type double (t:Type) = rel t t type eq (t:Type) = p:(double t){R?.l p == R?.r p} let twice x = R x x let tu = twice () (* functions to lift normal functions to Relational functions *) val rel_map1T : ('a -> Tot 'b) -> (double 'a) -> Tot (double 'b) let rel_map1T f (R x1 x2) = R (f x1) (f x2) val rel_map2Teq : #a:eqtype -> #b:eqtype -> #c:Type -> (a -> b -> Tot c) -> (double a) -> (double b) -> Tot (double c) let rel_map2Teq #a #b #c f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2T : ('a -> 'b -> Tot 'c) -> (double 'a) -> (double 'b) -> Tot (double 'c) let rel_map2T f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map2G : ('a -> 'b -> GTot 'c) -> (double 'a) -> (double 'b) -> GTot (double 'c) let rel_map2G f (R x1 x2) (R y1 y2) = R (f x1 y1) (f x2 y2) val rel_map3T : ('a -> 'b -> 'c -> Tot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> Tot (double 'd) let rel_map3T f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) val rel_map3G : ('a -> 'b -> 'c -> GTot 'd) -> (double 'a) -> (double 'b) -> (double 'c) -> GTot (double 'd) let rel_map3G f (R x1 x2) (R y1 y2) (R z1 z2) = R (f x1 y1 z1) (f x2 y2 z2) (* Some convenient arithmetic functions *) let op_Hat_Plus = rel_map2T (fun x y -> x + y) let op_Hat_Minus = rel_map2T (fun x y -> x - y) let op_Hat_Star = rel_map2T (fun x y -> op_Multiply x y) let op_Hat_Slash = rel_map2T (fun x y -> x / y) (* Some convenient list functions *)

false

FStar.Relational.Relational.fst

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val tl_rel: #a:Type -> l:double (list a){Cons? (R?.l l) /\ Cons? (R?.r l)}-> Tot (double (list a))

[]

FStar.Relational.Relational.tl_rel

{ "file_name": "ulib/legacy/FStar.Relational.Relational.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

l: FStar.Relational.Relational.double (Prims.list a) {Cons? (R?.l l) /\ Cons? (R?.r l)} -> FStar.Relational.Relational.double (Prims.list a)

{ "end_col": 43, "end_line": 57, "start_col": 36, "start_line": 57 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rt_subst = L.map rt_subst_elt

let rt_subst =

false

null

false

L.map rt_subst_elt

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.List.Tot.Base.map", "Pulse.Syntax.Naming.subst_elt", "FStar.Reflection.Typing.subst_elt", "Pulse.Syntax.Naming.rt_subst_elt" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rt_subst : x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list FStar.Reflection.Typing.subst_elt

[]

Pulse.Syntax.Naming.rt_subst

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list FStar.Reflection.Typing.subst_elt

{ "end_col": 33, "end_line": 368, "start_col": 15, "start_line": 368 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_st (t:st_term) = ln_st' t (-1)

let ln_st (t: st_term) =

false

null

false

ln_st' t (- 1)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Pulse.Syntax.Naming.ln_st'", "Prims.op_Minus", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_st : t: Pulse.Syntax.Base.st_term -> Prims.bool

[]

Pulse.Syntax.Naming.ln_st

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> Prims.bool

{ "end_col": 37, "end_line": 343, "start_col": 24, "start_line": 343 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst = list subst_elt

let subst =

false

null

false

list subst_elt

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Naming.subst_elt" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst : Type0

[]

Pulse.Syntax.Naming.subst

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

Type0

{ "end_col": 26, "end_line": 357, "start_col": 12, "start_line": 357 }

Prims.Tot

val open_term_list' (t: list term) (v: term) (i: index) : Tot (list term)

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ]

val open_term_list' (t: list term) (v: term) (i: index) : Tot (list term) let open_term_list' (t: list term) (v: term) (i: index) : Tot (list term) =

false

null

false

subst_term_list t [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_list", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_term_list' (t: list term) (v: term) (i: index) : Tot (list term)

[]

Pulse.Syntax.Naming.open_term_list'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Prims.list Pulse.Syntax.Base.term

{ "end_col": 50, "end_line": 453, "start_col": 22, "start_line": 453 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln (t:term) = ln' t (-1)

let ln (t: term) =

false

null

false

ln' t (- 1)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.ln'", "Prims.op_Minus", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln : t: Pulse.Syntax.Base.term -> Prims.bool

[]

Pulse.Syntax.Naming.ln

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> Prims.bool

{ "end_col": 28, "end_line": 342, "start_col": 18, "start_line": 342 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0

let open_st_term_nv t nv =

false

null

false

open_st_term' t (U.term_of_nvar nv) 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Pulse.Syntax.Base.nvar", "Pulse.Syntax.Naming.open_st_term'", "Pulse.Syntax.Pure.term_of_nvar" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_st_term_nv : t: Pulse.Syntax.Base.st_term -> nv: Pulse.Syntax.Base.nvar -> Pulse.Syntax.Base.st_term

[]

Pulse.Syntax.Naming.open_st_term_nv

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> nv: Pulse.Syntax.Base.nvar -> Pulse.Syntax.Base.st_term

{ "end_col": 41, "end_line": 628, "start_col": 4, "start_line": 628 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i]

let close_term_pairs' (t: list (term * term)) (x: var) (i: index) =

false

null

false

subst_term_pairs t [ND x i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_pairs", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term_pairs' : t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> x: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term)

[]

Pulse.Syntax.Naming.close_term_pairs'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> x: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term)

{ "end_col": 29, "end_line": 482, "start_col": 2, "start_line": 482 }

Prims.Tot

val open_comp' (c: comp) (v: term) (i: index) : comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ]

val open_comp' (c: comp) (v: term) (i: index) : comp let open_comp' (c: comp) (v: term) (i: index) : comp =

false

null

false

subst_comp c [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_comp", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_comp' (c: comp) (v: term) (i: index) : comp

[]

Pulse.Syntax.Naming.open_comp'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.comp

{ "end_col": 25, "end_line": 435, "start_col": 2, "start_line": 435 }

Prims.Tot

val open_term_opt' (t: option term) (v: term) (i: index) : Tot (option term)

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ]

val open_term_opt' (t: option term) (v: term) (i: index) : Tot (option term) let open_term_opt' (t: option term) (v: term) (i: index) : Tot (option term) =

false

null

false

subst_term_opt t [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Pervasives.Native.option", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_opt", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_term_opt' (t: option term) (v: term) (i: index) : Tot (option term)

[]

Pulse.Syntax.Naming.open_term_opt'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: FStar.Pervasives.Native.option Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> FStar.Pervasives.Native.option Pulse.Syntax.Base.term

{ "end_col": 51, "end_line": 444, "start_col": 24, "start_line": 444 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_binder b v i = subst_binder b [ ND v i ]

let close_binder b v i =

false

null

false

subst_binder b [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.binder", "Pulse.Syntax.Base.var", "Prims.nat", "Pulse.Syntax.Naming.subst_binder", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_binder : b: Pulse.Syntax.Base.binder -> v: Pulse.Syntax.Base.var -> i: Prims.nat -> Pulse.Syntax.Base.binder

[]

Pulse.Syntax.Naming.close_binder

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

b: Pulse.Syntax.Base.binder -> v: Pulse.Syntax.Base.var -> i: Prims.nat -> Pulse.Syntax.Base.binder

{ "end_col": 27, "end_line": 652, "start_col": 2, "start_line": 652 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i]

let close_proof_hint' (ht: proof_hint_type) (x: var) (i: index) =

false

null

false

subst_proof_hint ht [ND x i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.proof_hint_type", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_proof_hint", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_proof_hint' : ht: Pulse.Syntax.Base.proof_hint_type -> x: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.proof_hint_type

[]

Pulse.Syntax.Naming.close_proof_hint'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

ht: Pulse.Syntax.Base.proof_hint_type -> x: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.proof_hint_type

{ "end_col": 30, "end_line": 488, "start_col": 2, "start_line": 488 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i}

let open_binder b v i =

false

null

false

{ b with binder_ty = open_term' b.binder_ty v i }

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.binder", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Base.Mkbinder", "Pulse.Syntax.Naming.open_term'", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ty", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ppname" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss}

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_binder : b: Pulse.Syntax.Base.binder -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.binder

[]

Pulse.Syntax.Naming.open_binder

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

b: Pulse.Syntax.Base.binder -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.binder

{ "end_col": 46, "end_line": 459, "start_col": 3, "start_line": 459 }

Prims.Tot

val subst_st_comp (s: st_comp) (ss: subst) : st_comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) }

val subst_st_comp (s: st_comp) (ss: subst) : st_comp let subst_st_comp (s: st_comp) (ss: subst) : st_comp =

false

null

false

{ s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) }

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Naming.subst", "Pulse.Syntax.Base.Mkst_comp", "Pulse.Syntax.Base.__proj__Mkst_comp__item__u", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Base.__proj__Mkst_comp__item__res", "Pulse.Syntax.Base.__proj__Mkst_comp__item__pre", "Pulse.Syntax.Base.__proj__Mkst_comp__item__post", "Pulse.Syntax.Naming.shift_subst" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp =

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_st_comp (s: st_comp) (ss: subst) : st_comp

[]

Pulse.Syntax.Naming.subst_st_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

s: Pulse.Syntax.Base.st_comp -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.st_comp

{ "end_col": 51, "end_line": 413, "start_col": 3, "start_line": 411 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v]

let open_term_pairs' (t: list (term * term)) (v: term) (i: index) =

false

null

false

subst_term_pairs t [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_pairs", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss }

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_term_pairs' : t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term)

[]

Pulse.Syntax.Naming.open_term_pairs'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term)

{ "end_col": 29, "end_line": 479, "start_col": 2, "start_line": 479 }

Prims.Tot

val close_comp' (c: comp) (v: var) (i: index) : comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ]

val close_comp' (c: comp) (v: var) (i: index) : comp let close_comp' (c: comp) (v: var) (i: index) : comp =

false

null

false

subst_comp c [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_comp", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_comp' (c: comp) (v: var) (i: index) : comp

[]

Pulse.Syntax.Naming.close_comp'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.comp

{ "end_col": 25, "end_line": 643, "start_col": 2, "start_line": 643 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let shift_subst = shift_subst_n 1

let shift_subst =

false

null

false

shift_subst_n 1

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Naming.shift_subst_n" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val shift_subst : x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list Pulse.Syntax.Naming.subst_elt

[]

Pulse.Syntax.Naming.shift_subst

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list Pulse.Syntax.Naming.subst_elt

{ "end_col": 33, "end_line": 361, "start_col": 18, "start_line": 361 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term t v = close_term' t v 0

let close_term t v =

false

null

false

close_term' t v 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.close_term'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ] let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term : t: Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.term

[]

Pulse.Syntax.Naming.close_term

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.term

{ "end_col": 38, "end_line": 657, "start_col": 21, "start_line": 657 }

Prims.Tot

val close_st_term' (t: st_term) (v: var) (i: index) : st_term

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ]

val close_st_term' (t: st_term) (v: var) (i: index) : st_term let close_st_term' (t: st_term) (v: var) (i: index) : st_term =

false

null

false

subst_st_term t [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_st_term", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_st_term' (t: st_term) (v: var) (i: index) : st_term

[]

Pulse.Syntax.Naming.close_st_term'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.st_term

{ "end_col": 28, "end_line": 655, "start_col": 2, "start_line": 655 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ]

let open_term' (t v: term) (i: index) =

false

null

false

subst_term t [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss))

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_term' : t: Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.term

[]

Pulse.Syntax.Naming.open_term'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.term

{ "end_col": 25, "end_line": 406, "start_col": 2, "start_line": 406 }

Prims.Tot

val close_term_opt' (t: option term) (v: var) (i: index) : option term

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ]

val close_term_opt' (t: option term) (v: var) (i: index) : option term let close_term_opt' (t: option term) (v: var) (i: index) : option term =

false

null

false

subst_term_opt t [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Pervasives.Native.option", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_opt", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term_opt' (t: option term) (v: var) (i: index) : option term

[]

Pulse.Syntax.Naming.close_term_opt'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: FStar.Pervasives.Native.option Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> FStar.Pervasives.Native.option Pulse.Syntax.Base.term

{ "end_col": 29, "end_line": 646, "start_col": 2, "start_line": 646 }

Prims.Tot

val close_term_list' (t: list term) (v: var) (i: index) : list term

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ]

val close_term_list' (t: list term) (v: var) (i: index) : list term let close_term_list' (t: list term) (v: var) (i: index) : list term =

false

null

false

subst_term_list t [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term_list", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term_list' (t: list term) (v: var) (i: index) : list term

[]

Pulse.Syntax.Naming.close_term_list'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Prims.list Pulse.Syntax.Base.term

{ "end_col": 30, "end_line": 649, "start_col": 2, "start_line": 649 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_st_term t v = close_st_term' t v 0

let close_st_term t v =

false

null

false

close_st_term' t v 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.close_st_term'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ] let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_st_term : t: Pulse.Syntax.Base.st_term -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.st_term

[]

Pulse.Syntax.Naming.close_st_term

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.st_term

{ "end_col": 44, "end_line": 658, "start_col": 24, "start_line": 658 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let shift_subst_n (n:nat) = L.map (shift_subst_elt n)

let shift_subst_n (n: nat) =

false

null

false

L.map (shift_subst_elt n)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.nat", "FStar.List.Tot.Base.map", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.shift_subst_elt", "Prims.list" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val shift_subst_n : n: Prims.nat -> x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list Pulse.Syntax.Naming.subst_elt

[]

Pulse.Syntax.Naming.shift_subst_n

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

n: Prims.nat -> x: Prims.list Pulse.Syntax.Naming.subst_elt -> Prims.list Pulse.Syntax.Naming.subst_elt

{ "end_col": 53, "end_line": 359, "start_col": 28, "start_line": 359 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v]

let open_proof_hint' (ht: proof_hint_type) (v: term) (i: index) =

false

null

false

subst_proof_hint ht [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.proof_hint_type", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_proof_hint", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_proof_hint' : ht: Pulse.Syntax.Base.proof_hint_type -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.proof_hint_type

[]

Pulse.Syntax.Naming.open_proof_hint'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

ht: Pulse.Syntax.Base.proof_hint_type -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.proof_hint_type

{ "end_col": 30, "end_line": 485, "start_col": 2, "start_line": 485 }

Prims.Tot

val open_st_comp' (s: st_comp) (v: term) (i: index) : st_comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ]

val open_st_comp' (s: st_comp) (v: term) (i: index) : st_comp let open_st_comp' (s: st_comp) (v: term) (i: index) : st_comp =

false

null

false

subst_st_comp s [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_st_comp", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) }

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_st_comp' (s: st_comp) (v: term) (i: index) : st_comp

[]

Pulse.Syntax.Naming.open_st_comp'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

s: Pulse.Syntax.Base.st_comp -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.st_comp

{ "end_col": 28, "end_line": 416, "start_col": 2, "start_line": 416 }

Prims.Tot

val ln_st_comp (s: st_comp) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1)

val ln_st_comp (s: st_comp) (i: int) : bool let ln_st_comp (s: st_comp) (i: int) : bool =

false

null

false

ln' s.res i && ln' s.pre i && ln' s.post (i + 1)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_comp", "Prims.int", "Prims.op_AmpAmp", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Base.__proj__Mkst_comp__item__res", "Pulse.Syntax.Base.__proj__Mkst_comp__item__pre", "Pulse.Syntax.Base.__proj__Mkst_comp__item__post", "Prims.op_Addition", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_st_comp (s: st_comp) (i: int) : bool

[]

Pulse.Syntax.Naming.ln_st_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

s: Pulse.Syntax.Base.st_comp -> i: Prims.int -> Prims.bool

{ "end_col": 20, "end_line": 175, "start_col": 2, "start_line": 173 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_c (c:comp) = ln_c' c (-1)

let ln_c (c: comp) =

false

null

false

ln_c' c (- 1)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Naming.ln_c'", "Prims.op_Minus", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_c : c: Pulse.Syntax.Base.comp -> Prims.bool

[]

Pulse.Syntax.Naming.ln_c

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> Prims.bool

{ "end_col": 32, "end_line": 344, "start_col": 20, "start_line": 344 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0

let open_term_nv t nv =

false

null

false

open_term' t (U.term_of_nvar nv) 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.nvar", "Pulse.Syntax.Naming.open_term'", "Pulse.Syntax.Pure.term_of_nvar" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_term_nv : t: Pulse.Syntax.Base.term -> nv: Pulse.Syntax.Base.nvar -> Pulse.Syntax.Base.term

[]

Pulse.Syntax.Naming.open_term_nv

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> nv: Pulse.Syntax.Base.nvar -> Pulse.Syntax.Base.term

{ "end_col": 38, "end_line": 621, "start_col": 4, "start_line": 621 }

Prims.Tot

val open_st_term' (t: st_term) (v: term) (i: index) : st_term

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ]

val open_st_term' (t: st_term) (v: term) (i: index) : st_term let open_st_term' (t: st_term) (v: term) (i: index) : st_term =

false

null

false

subst_st_term t [DT i v]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_st_term", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.DT", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_st_term' (t: st_term) (v: term) (i: index) : st_term

[]

Pulse.Syntax.Naming.open_st_term'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> v: Pulse.Syntax.Base.term -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.st_term

{ "end_col": 28, "end_line": 618, "start_col": 2, "start_line": 618 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let open_comp_with (c:comp) (x:term) = open_comp' c x 0

let open_comp_with (c: comp) (x: term) =

false

null

false

open_comp' c x 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.open_comp'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val open_comp_with : c: Pulse.Syntax.Base.comp -> x: Pulse.Syntax.Base.term -> Pulse.Syntax.Base.comp

[]

Pulse.Syntax.Naming.open_comp_with

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> x: Pulse.Syntax.Base.term -> Pulse.Syntax.Base.comp

{ "end_col": 55, "end_line": 634, "start_col": 39, "start_line": 634 }

Prims.Tot

val close_st_comp' (s: st_comp) (v: var) (i: index) : st_comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ]

val close_st_comp' (s: st_comp) (v: var) (i: index) : st_comp let close_st_comp' (s: st_comp) (v: var) (i: index) : st_comp =

false

null

false

subst_st_comp s [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_st_comp", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_st_comp' (s: st_comp) (v: var) (i: index) : st_comp

[]

Pulse.Syntax.Naming.close_st_comp'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

s: Pulse.Syntax.Base.st_comp -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.st_comp

{ "end_col": 28, "end_line": 640, "start_col": 2, "start_line": 640 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss}

let subst_binder b ss =

false

null

false

{ b with binder_ty = subst_term b.binder_ty ss }

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.binder", "Pulse.Syntax.Naming.subst", "Pulse.Syntax.Base.Mkbinder", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ty", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ppname" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ]

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_binder : b: Pulse.Syntax.Base.binder -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.binder

[]

Pulse.Syntax.Naming.subst_binder

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

b: Pulse.Syntax.Base.binder -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.binder

{ "end_col": 45, "end_line": 456, "start_col": 3, "start_line": 456 }

Prims.Tot

val close_term' (t: term) (v: var) (i: index) : term

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ]

val close_term' (t: term) (v: var) (i: index) : term let close_term' (t: term) (v: var) (i: index) : term =

false

null

false

subst_term t [ND v i]

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.var", "Pulse.Syntax.Base.index", "Pulse.Syntax.Naming.subst_term", "Prims.Cons", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Naming.ND", "Prims.Nil" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term' (t: term) (v: var) (i: index) : term

[]

Pulse.Syntax.Naming.close_term'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> v: Pulse.Syntax.Base.var -> i: Pulse.Syntax.Base.index -> Pulse.Syntax.Base.term

{ "end_col": 25, "end_line": 637, "start_col": 2, "start_line": 637 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_comp t v = close_comp' t v 0

let close_comp t v =

false

null

false

close_comp' t v 0

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.close_comp'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ] let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ] let close_term t v = close_term' t v 0

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_comp : t: Pulse.Syntax.Base.comp -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.comp

[]

Pulse.Syntax.Naming.close_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.comp -> v: Pulse.Syntax.Base.var -> Pulse.Syntax.Base.comp

{ "end_col": 38, "end_line": 659, "start_col": 21, "start_line": 659 }

Prims.Tot

val ln_c' (c: comp) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i

val ln_c' (c: comp) (i: int) : bool let ln_c' (c: comp) (i: int) : bool =

false

null

false

match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Prims.int", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Naming.ln_st_comp", "Prims.op_AmpAmp", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_c' (c: comp) (i: int) : bool

[]

Pulse.Syntax.Naming.ln_c'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> i: Prims.int -> Prims.bool

{ "end_col": 20, "end_line": 186, "start_col": 4, "start_line": 180 }

Prims.Tot

val subst_comp (c: comp) (ss: subst) : comp

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss)

val subst_comp (c: comp) (ss: subst) : comp let subst_comp (c: comp) (ss: subst) : comp =

false

null

false

match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Naming.subst", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.C_Tot", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Base.C_ST", "Pulse.Syntax.Naming.subst_st_comp", "Pulse.Syntax.Base.C_STAtomic", "Pulse.Syntax.Base.C_STGhost" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_comp (c: comp) (ss: subst) : comp

[]

Pulse.Syntax.Naming.subst_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.comp

{ "end_col": 36, "end_line": 432, "start_col": 4, "start_line": 420 }

Prims.Tot

val ln_list' (t: list term) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i

val ln_list' (t: list term) (i: int) : bool let rec ln_list' (t: list term) (i: int) : bool =

false

null

false

match t with | [] -> true | hd :: tl -> ln' hd i && ln_list' tl i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Base.term", "Prims.int", "Prims.op_AmpAmp", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Naming.ln_list'", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_list' (t: list term) (i: int) : bool

[ "recursion" ]

Pulse.Syntax.Naming.ln_list'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list Pulse.Syntax.Base.term -> i: Prims.int -> Prims.bool

{ "end_col": 39, "end_line": 196, "start_col": 2, "start_line": 194 }

Prims.Tot

val subst_term_pairs (t: list (term & term)) (ss: subst) : Tot (list (term & term))

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss

val subst_term_pairs (t: list (term & term)) (ss: subst) : Tot (list (term & term)) let rec subst_term_pairs (t: list (term & term)) (ss: subst) : Tot (list (term & term)) =

false

null

false

match t with | [] -> [] | (t1, t2) :: tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.subst", "Prims.Nil", "Prims.Cons", "FStar.Pervasives.Native.Mktuple2", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Naming.subst_term_pairs" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_term_pairs (t: list (term & term)) (ss: subst) : Tot (list (term & term))

[ "recursion" ]

Pulse.Syntax.Naming.subst_term_pairs

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> ss: Pulse.Syntax.Naming.subst -> Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term)

{ "end_col": 84, "end_line": 465, "start_col": 4, "start_line": 463 }

Prims.Tot

val ln_proof_hint' (ht: proof_hint_type) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i

val ln_proof_hint' (ht: proof_hint_type) (i: int) : bool let ln_proof_hint' (ht: proof_hint_type) (i: int) : bool =

false

null

false

match ht with | ASSERT { p = p } | UNFOLD { p = p } | FOLD { p = p } -> ln' p i | RENAME { pairs = pairs ; goal = goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1 = t1 ; t2 = t2 } -> ln' t1 i && ln' t2 i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.proof_hint_type", "Prims.int", "Pulse.Syntax.Base.vprop", "Pulse.Syntax.Naming.ln'", "FStar.Pervasives.Native.option", "Prims.list", "Prims.string", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Prims.op_AmpAmp", "Pulse.Syntax.Naming.ln_terms'", "Pulse.Syntax.Naming.ln_opt'", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_proof_hint' (ht: proof_hint_type) (i: int) : bool

[]

Pulse.Syntax.Naming.ln_proof_hint'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

ht: Pulse.Syntax.Base.proof_hint_type -> i: Prims.int -> Prims.bool

{ "end_col": 12, "end_line": 213, "start_col": 2, "start_line": 204 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n)

let shift_subst_elt (n: nat) =

false

null

false

function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.nat", "Pulse.Syntax.Naming.subst_elt", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.DT", "Prims.op_Addition", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.NT", "Pulse.Syntax.Naming.ND" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val shift_subst_elt : n: Prims.nat -> _: Pulse.Syntax.Naming.subst_elt -> Pulse.Syntax.Naming.subst_elt

[]

Pulse.Syntax.Naming.shift_subst_elt

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

n: Prims.nat -> _: Pulse.Syntax.Naming.subst_elt -> Pulse.Syntax.Naming.subst_elt

{ "end_col": 26, "end_line": 355, "start_col": 30, "start_line": 352 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i

let rt_subst_elt =

false

null

false

function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Naming.subst_elt", "Prims.nat", "Pulse.Syntax.Base.term", "FStar.Reflection.Typing.DT", "Pulse.Elaborate.Pure.elab_term", "Pulse.Syntax.Base.var", "FStar.Reflection.Typing.NT", "FStar.Reflection.Typing.ND", "FStar.Reflection.Typing.subst_elt" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val rt_subst_elt : _: Pulse.Syntax.Naming.subst_elt -> FStar.Reflection.Typing.subst_elt

[]

Pulse.Syntax.Naming.rt_subst_elt

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

_: Pulse.Syntax.Naming.subst_elt -> FStar.Reflection.Typing.subst_elt

{ "end_col": 23, "end_line": 366, "start_col": 19, "start_line": 363 }

Prims.Tot

val subst_proof_hint (ht: proof_hint_type) (ss: subst) : proof_hint_type

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss }

val subst_proof_hint (ht: proof_hint_type) (ss: subst) : proof_hint_type let subst_proof_hint (ht: proof_hint_type) (ss: subst) : proof_hint_type =

false

null

false

match ht with | ASSERT { p = p } -> ASSERT ({ p = subst_term p ss }) | UNFOLD { names = names ; p = p } -> UNFOLD ({ names = names; p = subst_term p ss }) | FOLD { names = names ; p = p } -> FOLD ({ names = names; p = subst_term p ss }) | RENAME { pairs = pairs ; goal = goal } -> RENAME ({ pairs = subst_term_pairs pairs ss; goal = subst_term_opt goal ss }) | REWRITE { t1 = t1 ; t2 = t2 } -> REWRITE ({ t1 = subst_term t1 ss; t2 = subst_term t2 ss })

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.proof_hint_type", "Pulse.Syntax.Naming.subst", "Pulse.Syntax.Base.vprop", "Pulse.Syntax.Base.ASSERT", "Pulse.Syntax.Base.Mkproof_hint_type__ASSERT__payload", "Pulse.Syntax.Naming.subst_term", "FStar.Pervasives.Native.option", "Prims.list", "Prims.string", "Pulse.Syntax.Base.UNFOLD", "Pulse.Syntax.Base.Mkproof_hint_type__UNFOLD__payload", "Pulse.Syntax.Base.FOLD", "Pulse.Syntax.Base.Mkproof_hint_type__FOLD__payload", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.RENAME", "Pulse.Syntax.Base.Mkproof_hint_type__RENAME__payload", "Pulse.Syntax.Naming.subst_term_pairs", "Pulse.Syntax.Naming.subst_term_opt", "Pulse.Syntax.Base.REWRITE", "Pulse.Syntax.Base.Mkproof_hint_type__REWRITE__payload" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_proof_hint (ht: proof_hint_type) (ss: subst) : proof_hint_type

[]

Pulse.Syntax.Naming.subst_proof_hint

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

ht: Pulse.Syntax.Base.proof_hint_type -> ss: Pulse.Syntax.Naming.subst -> Pulse.Syntax.Base.proof_hint_type

{ "end_col": 59, "end_line": 476, "start_col": 4, "start_line": 469 }

Prims.Tot

val subst_term (t: term) (ss: subst) : Tot term (decreases t)

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss))

val subst_term (t: term) (ss: subst) : Tot term (decreases t) let rec subst_term (t: term) (ss: subst) : Tot term (decreases t) =

false

null

false

let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u ({ b with binder_ty = subst_term b.binder_ty ss }) (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u ({ b with binder_ty = subst_term b.binder_ty ss }) (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss))

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total", "" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.subst", "Pulse.Syntax.Base.__proj__Mkterm__item__t", "Pulse.Syntax.Base.Tm_Pure", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Base.Tm_Star", "Pulse.Syntax.Base.universe", "Pulse.Syntax.Base.binder", "Pulse.Syntax.Base.Tm_ExistsSL", "Pulse.Syntax.Base.Mkbinder", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ty", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ppname", "Pulse.Syntax.Naming.shift_subst", "Pulse.Syntax.Base.Tm_ForallSL", "Pulse.Syntax.Base.host_term", "Pulse.Syntax.Base.Tm_FStar", "Pulse.Syntax.Naming.subst_host_term", "Pulse.Syntax.Base.term'", "Pulse.Syntax.Base.with_range", "Pulse.Syntax.Base.__proj__Mkterm__item__range" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_term (t: term) (ss: subst) : Tot term (decreases t)

[ "recursion" ]

Pulse.Syntax.Naming.subst_term

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> ss: Pulse.Syntax.Naming.subst -> Prims.Tot Pulse.Syntax.Base.term

{ "end_col": 41, "end_line": 403, "start_col": 3, "start_line": 379 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_st_term_n t vs = let rec aux (i:nat) (vs:list var) (t:st_term) : Tot st_term (decreases vs) = match vs with | [] -> t | v::vs -> aux (i+1) vs (close_st_term' t v i) in aux 0 (List.rev vs) t

let close_st_term_n t vs =

false

null

false

let rec aux (i: nat) (vs: list var) (t: st_term) : Tot st_term (decreases vs) = match vs with | [] -> t | v :: vs -> aux (i + 1) vs (close_st_term' t v i) in aux 0 (List.rev vs) t

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_term", "Prims.list", "Pulse.Syntax.Base.var", "FStar.List.Tot.Base.rev", "Prims.nat", "Prims.op_Addition", "Pulse.Syntax.Naming.close_st_term'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ] let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ] let close_term t v = close_term' t v 0 let close_st_term t v = close_st_term' t v 0 let close_comp t v = close_comp' t v 0 let close_term_n t vs = let rec aux (i:nat) (vs:list var) (t:term) : Tot term (decreases vs) = match vs with | [] -> t | v::vs -> aux (i+1) vs (close_term' t v i) in aux 0 (List.rev vs) t

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_st_term_n : t: Pulse.Syntax.Base.st_term -> vs: Prims.list Pulse.Syntax.Base.var -> Pulse.Syntax.Base.st_term

[]

Pulse.Syntax.Naming.close_st_term_n

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.st_term -> vs: Prims.list Pulse.Syntax.Base.var -> Pulse.Syntax.Base.st_term

{ "end_col": 23, "end_line": 677, "start_col": 26, "start_line": 670 }

Prims.Tot

val freevars_st_comp (s: st_comp) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post

val freevars_st_comp (s: st_comp) : Set.set var let freevars_st_comp (s: st_comp) : Set.set var =

false

null

false

((freevars s.res) `Set.union` (freevars s.pre)) `Set.union` (freevars s.post)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.st_comp", "FStar.Set.union", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Base.__proj__Mkst_comp__item__res", "Pulse.Syntax.Base.__proj__Mkst_comp__item__pre", "Pulse.Syntax.Base.__proj__Mkst_comp__item__post", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_st_comp (s: st_comp) : Set.set var

[]

Pulse.Syntax.Naming.freevars_st_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

s: Pulse.Syntax.Base.st_comp -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 17, "end_line": 35, "start_col": 2, "start_line": 33 }

Prims.Tot

val freevars_proof_hint (ht: proof_hint_type) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2)

val freevars_proof_hint (ht: proof_hint_type) : Set.set var let freevars_proof_hint (ht: proof_hint_type) : Set.set var =

false

null

false

match ht with | ASSERT { p = p } | FOLD { p = p } | UNFOLD { p = p } -> freevars p | RENAME { pairs = pairs ; goal = goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1 = t1 ; t2 = t2 } -> Set.union (freevars t1) (freevars t2)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.proof_hint_type", "Pulse.Syntax.Base.vprop", "Pulse.Syntax.Naming.freevars", "FStar.Pervasives.Native.option", "Prims.list", "Prims.string", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "FStar.Set.union", "Pulse.Syntax.Base.var", "Pulse.Syntax.Naming.freevars_pairs", "Pulse.Syntax.Naming.freevars_term_opt", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_proof_hint (ht: proof_hint_type) : Set.set var

[]

Pulse.Syntax.Naming.freevars_proof_hint

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

ht: Pulse.Syntax.Base.proof_hint_type -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 41, "end_line": 72, "start_col": 2, "start_line": 65 }

Prims.Tot

val freevars_term_opt (t: option term) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t

val freevars_term_opt (t: option term) : Set.set var let freevars_term_opt (t: option term) : Set.set var =

false

null

false

freevars_opt freevars t

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Pervasives.Native.option", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.freevars_opt", "Pulse.Syntax.Naming.freevars", "FStar.Set.set", "Pulse.Syntax.Base.var" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_term_opt (t: option term) : Set.set var

[]

Pulse.Syntax.Naming.freevars_term_opt

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: FStar.Pervasives.Native.option Pulse.Syntax.Base.term -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 25, "end_line": 52, "start_col": 2, "start_line": 52 }

Prims.Tot

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let close_term_n t vs = let rec aux (i:nat) (vs:list var) (t:term) : Tot term (decreases vs) = match vs with | [] -> t | v::vs -> aux (i+1) vs (close_term' t v i) in aux 0 (List.rev vs) t

let close_term_n t vs =

false

null

false

let rec aux (i: nat) (vs: list var) (t: term) : Tot term (decreases vs) = match vs with | [] -> t | v :: vs -> aux (i + 1) vs (close_term' t v i) in aux 0 (List.rev vs) t

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Prims.list", "Pulse.Syntax.Base.var", "FStar.List.Tot.Base.rev", "Prims.nat", "Prims.op_Addition", "Pulse.Syntax.Naming.close_term'" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss let open_term_list' (t:list term) (v:term) (i:index) : Tot (list term) = subst_term_list t [ DT i v ] let subst_binder b ss = {b with binder_ty=subst_term b.binder_ty ss} let open_binder b v i = {b with binder_ty=open_term' b.binder_ty v i} let rec subst_term_pairs (t:list (term & term)) (ss:subst) : Tot (list (term & term)) = match t with | [] -> [] | (t1, t2)::tl -> (subst_term t1 ss, subst_term t2 ss) :: subst_term_pairs tl ss let subst_proof_hint (ht:proof_hint_type) (ss:subst) : proof_hint_type = match ht with | ASSERT { p } -> ASSERT { p=subst_term p ss } | UNFOLD { names; p } -> UNFOLD {names; p=subst_term p ss} | FOLD { names; p } -> FOLD { names; p=subst_term p ss } | RENAME { pairs; goal } -> RENAME { pairs=subst_term_pairs pairs ss; goal=subst_term_opt goal ss } | REWRITE { t1; t2 } -> REWRITE { t1=subst_term t1 ss; t2=subst_term t2 ss } let open_term_pairs' (t:list (term * term)) (v:term) (i:index) = subst_term_pairs t [DT i v] let close_term_pairs' (t:list (term * term)) (x:var) (i:index) = subst_term_pairs t [ND x i] let open_proof_hint' (ht:proof_hint_type) (v:term) (i:index) = subst_proof_hint ht [DT i v] let close_proof_hint' (ht:proof_hint_type) (x:var) (i:index) = subst_proof_hint ht [ND x i] let rec subst_pat (p:pattern) (ss:subst) : Tot pattern (decreases p) = match p with | Pat_Constant _ | Pat_Dot_Term None -> p | Pat_Var n t -> let t = RU.map_seal t (fun t -> RT.subst_term t (rt_subst ss)) in Pat_Var n t | Pat_Dot_Term (Some e) -> Pat_Dot_Term (Some (subst_term e ss)) | Pat_Cons d args -> let args = subst_pat_args args ss in Pat_Cons d args and subst_pat_args (args:list (pattern & bool)) (ss:subst) : Tot (list (pattern & bool)) (decreases args) = match args with | [] -> [] | (arg, b)::tl -> let arg' = subst_pat arg ss in let tl = subst_pat_args tl (shift_subst_n (pattern_shift_n arg) ss) in (arg', b)::tl let rec subst_st_term (t:st_term) (ss:subst) : Tot st_term (decreases t) = let t' = match t.term with | Tm_Return { ctag; insert_eq; term } -> Tm_Return { ctag; insert_eq; term=subst_term term ss } | Tm_Abs { b; q; ascription; body } -> Tm_Abs { b=subst_binder b ss; q; ascription=subst_comp ascription (shift_subst ss); body=subst_st_term body (shift_subst ss) } | Tm_STApp { head; arg_qual; arg } -> Tm_STApp { head = subst_term head ss; arg_qual; arg=subst_term arg ss } | Tm_Bind { binder; head; body } -> Tm_Bind { binder = subst_binder binder ss; head = subst_st_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_TotBind { binder; head; body } -> Tm_TotBind { binder = subst_binder binder ss; head = subst_term head ss; body = subst_st_term body (shift_subst ss) } | Tm_If { b; then_; else_; post } -> Tm_If { b = subst_term b ss; then_ = subst_st_term then_ ss; else_ = subst_st_term else_ ss; post = subst_term_opt post (shift_subst ss) } | Tm_Match { sc; returns_; brs } -> Tm_Match { sc = subst_term sc ss; returns_ = subst_term_opt returns_ ss; brs = subst_branches t ss brs } | Tm_IntroPure { p } -> Tm_IntroPure { p = subst_term p ss } | Tm_ElimExists { p } -> Tm_ElimExists { p = subst_term p ss } | Tm_IntroExists { p; witnesses } -> Tm_IntroExists { p = subst_term p ss; witnesses = subst_term_list witnesses ss } | Tm_While { invariant; condition; body; condition_var } -> Tm_While { invariant = subst_term invariant (shift_subst ss); condition = subst_st_term condition ss; body = subst_st_term body ss; condition_var } | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Tm_Par { pre1=subst_term pre1 ss; body1=subst_st_term body1 ss; post1=subst_term post1 (shift_subst ss); pre2=subst_term pre2 ss; body2=subst_st_term body2 ss; post2=subst_term post2 (shift_subst ss) } | Tm_WithLocal { binder; initializer; body } -> Tm_WithLocal { binder = subst_binder binder ss; initializer = subst_term initializer ss; body = subst_st_term body (shift_subst ss) } | Tm_WithLocalArray { binder; initializer; length; body } -> Tm_WithLocalArray { binder = subst_binder binder ss; initializer = subst_term initializer ss; length = subst_term length ss; body = subst_st_term body (shift_subst ss) } | Tm_Rewrite { t1; t2 } -> Tm_Rewrite { t1 = subst_term t1 ss; t2 = subst_term t2 ss } | Tm_Admit { ctag; u; typ; post } -> Tm_Admit { ctag; u; typ=subst_term typ ss; post=subst_term_opt post (shift_subst ss) } | Tm_ProofHintWithBinders { hint_type; binders; t} -> let n = L.length binders in let ss = shift_subst_n n ss in Tm_ProofHintWithBinders { binders; hint_type=subst_proof_hint hint_type ss; t = subst_st_term t ss } in { t with term = t' } and subst_branches (t:st_term) (ss:subst) (brs : list branch{brs << t}) : Tot (list branch) (decreases brs) = map_dec t brs (fun br -> subst_branch ss br) and subst_branch (ss:subst) (b : pattern & st_term) : Tot (pattern & st_term) (decreases b) = let (p, e) = b in let p = subst_pat p ss in let ss = shift_subst_n (pattern_shift_n p) ss in p, subst_st_term e ss let open_st_term' (t:st_term) (v:term) (i:index) : st_term = subst_st_term t [ DT i v ] let open_term_nv t nv = open_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_term t v : GTot term = open_term_nv t (v_as_nv v) let open_st_term_nv t nv = open_st_term' t (U.term_of_nvar nv) 0 // Can use this no-name version in specs only let open_st_term t v : GTot st_term = open_st_term_nv t (v_as_nv v) let open_comp_with (c:comp) (x:term) = open_comp' c x 0 let close_term' (t:term) (v:var) (i:index) : term = subst_term t [ ND v i ] let close_st_comp' (s:st_comp) (v:var) (i:index) : st_comp = subst_st_comp s [ ND v i ] let close_comp' (c:comp) (v:var) (i:index) : comp = subst_comp c [ ND v i ] let close_term_opt' (t:option term) (v:var) (i:index) : option term = subst_term_opt t [ ND v i ] let close_term_list' (t:list term) (v:var) (i:index) : list term = subst_term_list t [ ND v i ] let close_binder b v i = subst_binder b [ ND v i ] let close_st_term' (t:st_term) (v:var) (i:index) : st_term = subst_st_term t [ ND v i ] let close_term t v = close_term' t v 0 let close_st_term t v = close_st_term' t v 0 let close_comp t v = close_comp' t v 0

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val close_term_n : t: Pulse.Syntax.Base.term -> vs: Prims.list Pulse.Syntax.Base.var -> Pulse.Syntax.Base.term

[]

Pulse.Syntax.Naming.close_term_n

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> vs: Prims.list Pulse.Syntax.Base.var -> Pulse.Syntax.Base.term

{ "end_col": 23, "end_line": 668, "start_col": 23, "start_line": 661 }

Prims.Tot

val freevars (t: term) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

val freevars (t: term) : Set.set var let rec freevars (t: term) : Set.set var =

false

null

false

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Pulse.Syntax.Base.term", "Pulse.Syntax.Base.__proj__Mkterm__item__t", "FStar.Set.empty", "Pulse.Syntax.Base.var", "FStar.Set.union", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Base.universe", "Pulse.Syntax.Base.binder", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ty", "Pulse.Syntax.Base.host_term", "FStar.Reflection.Typing.freevars", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars (t: term) : Set.set var

[ "recursion" ]

Pulse.Syntax.Naming.freevars

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 33, "end_line": 30, "start_col": 4, "start_line": 18 }

Prims.Tot

val freevars_list (t: list term) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl

val freevars_list (t: list term) : Set.set var let rec freevars_list (t: list term) : Set.set var =

false

null

false

match t with | [] -> Set.empty | hd :: tl -> (freevars hd) `Set.union` (freevars_list tl)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Base.term", "FStar.Set.empty", "Pulse.Syntax.Base.var", "FStar.Set.union", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Naming.freevars_list", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_list (t: list term) : Set.set var

[ "recursion" ]

Pulse.Syntax.Naming.freevars_list

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list Pulse.Syntax.Base.term -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 54, "end_line": 57, "start_col": 2, "start_line": 55 }

Prims.Tot

val freevars_opt (f: ('a -> Set.set var)) (x: option 'a) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x

val freevars_opt (f: ('a -> Set.set var)) (x: option 'a) : Set.set var let freevars_opt (f: ('a -> Set.set var)) (x: option 'a) : Set.set var =

false

null

false

match x with | None -> Set.empty | Some x -> f x

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Set.set", "Pulse.Syntax.Base.var", "FStar.Pervasives.Native.option", "FStar.Set.empty" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s

false

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_opt (f: ('a -> Set.set var)) (x: option 'a) : Set.set var

[]

Pulse.Syntax.Naming.freevars_opt

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

f: (_: 'a -> FStar.Set.set Pulse.Syntax.Base.var) -> x: FStar.Pervasives.Native.option 'a -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 17, "end_line": 49, "start_col": 2, "start_line": 47 }

Prims.Tot

val ln_terms' (t: list (term & term)) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i

val ln_terms' (t: list (term & term)) (i: int) : bool let rec ln_terms' (t: list (term & term)) (i: int) : bool =

false

null

false

match t with | [] -> true | (t1, t2) :: tl -> ln' t1 i && ln' t2 i && ln_terms' tl i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "Prims.int", "Prims.op_AmpAmp", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Naming.ln_terms'", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_terms' (t: list (term & term)) (i: int) : bool

[ "recursion" ]

Pulse.Syntax.Naming.ln_terms'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> i: Prims.int -> Prims.bool

{ "end_col": 58, "end_line": 201, "start_col": 2, "start_line": 199 }

Prims.Tot

val ln_opt' (t: option term) (i: int) : bool

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i

val ln_opt' (t: option term) (i: int) : bool let ln_opt' (t: option term) (i: int) : bool =

false

null

false

match t with | None -> true | Some t -> ln' t i

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Pervasives.Native.option", "Pulse.Syntax.Base.term", "Prims.int", "Pulse.Syntax.Naming.ln'", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i

false

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln_opt' (t: option term) (i: int) : bool

[]

Pulse.Syntax.Naming.ln_opt'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: FStar.Pervasives.Native.option Pulse.Syntax.Base.term -> i: Prims.int -> Prims.bool

{ "end_col": 21, "end_line": 191, "start_col": 2, "start_line": 189 }

Prims.Tot

val ln' (t: term) (i: int) : Tot bool (decreases t)

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

val ln' (t: term) (i: int) : Tot bool (decreases t) let rec ln' (t: term) (i: int) : Tot bool (decreases t) =

false

null

false

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total", "" ]

[ "Pulse.Syntax.Base.term", "Prims.int", "Pulse.Syntax.Base.__proj__Mkterm__item__t", "Prims.op_AmpAmp", "Pulse.Syntax.Naming.ln'", "Pulse.Syntax.Base.universe", "Pulse.Syntax.Base.binder", "Pulse.Syntax.Base.__proj__Mkbinder__item__binder_ty", "Prims.op_Addition", "Pulse.Syntax.Base.host_term", "FStar.Reflection.Typing.ln'", "Prims.bool" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val ln' (t: term) (i: int) : Tot bool (decreases t)

[ "recursion" ]

Pulse.Syntax.Naming.ln'

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Pulse.Syntax.Base.term -> i: Prims.int -> Prims.Tot Prims.bool

{ "end_col": 14, "end_line": 170, "start_col": 2, "start_line": 150 }

Prims.Tot

val subst_term_opt (t: option term) (ss: subst) : Tot (option term)

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss)

val subst_term_opt (t: option term) (ss: subst) : Tot (option term) let subst_term_opt (t: option term) (ss: subst) : Tot (option term) =

false

null

false

match t with | None -> None | Some t -> Some (subst_term t ss)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "FStar.Pervasives.Native.option", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.subst", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.Some", "Pulse.Syntax.Naming.subst_term" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_term_opt (t: option term) (ss: subst) : Tot (option term)

[]

Pulse.Syntax.Naming.subst_term_opt

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: FStar.Pervasives.Native.option Pulse.Syntax.Base.term -> ss: Pulse.Syntax.Naming.subst -> FStar.Pervasives.Native.option Pulse.Syntax.Base.term

{ "end_col": 38, "end_line": 441, "start_col": 4, "start_line": 439 }

Prims.Tot

val freevars_comp (c: comp) : Tot (Set.set var) (decreases c)

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s

val freevars_comp (c: comp) : Tot (Set.set var) (decreases c) let freevars_comp (c: comp) : Tot (Set.set var) (decreases c) =

false

null

false

match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> (freevars inames) `Set.union` (freevars_st_comp s)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total", "" ]

[ "Pulse.Syntax.Base.comp", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Base.st_comp", "Pulse.Syntax.Naming.freevars_st_comp", "FStar.Set.union", "Pulse.Syntax.Base.var", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_comp (c: comp) : Tot (Set.set var) (decreases c)

[]

Pulse.Syntax.Naming.freevars_comp

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

c: Pulse.Syntax.Base.comp -> Prims.Tot (FStar.Set.set Pulse.Syntax.Base.var)

{ "end_col": 50, "end_line": 44, "start_col": 2, "start_line": 39 }

Prims.Tot

val subst_term_list (t: list term) (ss: subst) : Tot (list term)

[ { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.V2", "short_module": "R2" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec subst_term_list (t:list term) (ss:subst) : Tot (list term) = match t with | [] -> [] | hd::tl -> subst_term hd ss :: subst_term_list tl ss

val subst_term_list (t: list term) (ss: subst) : Tot (list term) let rec subst_term_list (t: list term) (ss: subst) : Tot (list term) =

false

null

false

match t with | [] -> [] | hd :: tl -> subst_term hd ss :: subst_term_list tl ss

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "Pulse.Syntax.Base.term", "Pulse.Syntax.Naming.subst", "Prims.Nil", "Prims.Cons", "Pulse.Syntax.Naming.subst_term", "Pulse.Syntax.Naming.subst_term_list" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl let freevars_proof_hint (ht:proof_hint_type) : Set.set var = match ht with | ASSERT { p } | FOLD { p } | UNFOLD { p } -> freevars p | RENAME { pairs; goal } -> Set.union (freevars_pairs pairs) (freevars_term_opt goal) | REWRITE { t1; t2 } -> Set.union (freevars t1) (freevars t2) let rec freevars_st (t:st_term) : Set.set var = match t.term with | Tm_Return { term } -> freevars term | Tm_Abs { b; ascription; body } -> Set.union (freevars b.binder_ty) (Set.union (freevars_st body) (freevars_comp ascription)) | Tm_STApp { head; arg } -> Set.union (freevars head) (freevars arg) | Tm_Bind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars_st head)) (freevars_st body) | Tm_TotBind { binder; head; body } -> Set.union (Set.union (freevars binder.binder_ty) (freevars head)) (freevars_st body) | Tm_If { b; then_; else_; post } -> Set.union (Set.union (freevars b) (freevars_st then_)) (Set.union (freevars_st else_) (freevars_term_opt post)) | Tm_Match { sc ; returns_; brs } -> let (@@) = Set.union in freevars sc @@ freevars_term_opt returns_ @@ freevars_branches brs | Tm_IntroPure { p } | Tm_ElimExists { p } -> freevars p | Tm_IntroExists { p; witnesses } -> Set.union (freevars p) (freevars_list witnesses) | Tm_While { invariant; condition; body } -> Set.union (freevars invariant) (Set.union (freevars_st condition) (freevars_st body)) | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> Set.union (Set.union (freevars pre1) (Set.union (freevars_st body1) (freevars post1))) (Set.union (freevars pre2) (Set.union (freevars_st body2) (freevars post2))) | Tm_WithLocal { binder; initializer; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (freevars_st body)) | Tm_WithLocalArray { binder; initializer; length; body } -> Set.union (freevars binder.binder_ty) (Set.union (freevars initializer) (Set.union (freevars length) (freevars_st body))) | Tm_Rewrite { t1; t2 } -> Set.union (freevars t1) (freevars t2) | Tm_Admit { typ; post } -> Set.union (freevars typ) (freevars_term_opt post) | Tm_ProofHintWithBinders { binders; hint_type; t } -> Set.union (freevars_proof_hint hint_type) (freevars_st t) and freevars_branches (t:list (pattern & st_term)) : Set.set var = match t with | [] -> Set.empty | (_, b)::tl -> freevars_st b `Set.union` freevars_branches tl let rec ln' (t:term) (i:int) : Tot bool (decreases t) = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> true | Tm_Star t1 t2 -> ln' t1 i && ln' t2 i | Tm_Pure p -> ln' p i | Tm_ExistsSL _ t body | Tm_ForallSL _ t body -> ln' t.binder_ty i && ln' body (i + 1) | Tm_FStar t -> RT.ln' t i let ln_st_comp (s:st_comp) (i:int) : bool = ln' s.res i && ln' s.pre i && ln' s.post (i + 1) (* post has 1 impliict abstraction *) let ln_c' (c:comp) (i:int) : bool = match c with | C_Tot t -> ln' t i | C_ST s -> ln_st_comp s i | C_STAtomic inames s | C_STGhost inames s -> ln' inames i && ln_st_comp s i let ln_opt' (t:option term) (i:int) : bool = match t with | None -> true | Some t -> ln' t i let rec ln_list' (t:list term) (i:int) : bool = match t with | [] -> true | hd::tl -> ln' hd i && ln_list' tl i let rec ln_terms' (t:list (term & term)) (i:int) : bool = match t with | [] -> true | (t1, t2)::tl -> ln' t1 i && ln' t2 i && ln_terms' tl i let ln_proof_hint' (ht:proof_hint_type) (i:int) : bool = match ht with | ASSERT { p } | UNFOLD { p } | FOLD { p } -> ln' p i | RENAME { pairs; goal } -> ln_terms' pairs i && ln_opt' goal i | REWRITE { t1; t2 } -> ln' t1 i && ln' t2 i let rec pattern_shift_n (p:pattern) : Tot nat = match p with | Pat_Constant _ | Pat_Dot_Term _ -> 0 | Pat_Var _ _ -> 1 | Pat_Cons fv l -> pattern_args_shift_n l and pattern_args_shift_n (ps:list (pattern & bool)) : Tot nat = match ps with | [] -> 0 | (p, _)::tl -> pattern_shift_n p + pattern_args_shift_n tl let rec ln_pattern' (p : pattern) (i:int) : Tot bool (decreases p) = match p with | Pat_Constant _ | Pat_Var _ _ | Pat_Dot_Term None -> true | Pat_Dot_Term (Some e) -> ln' e i | Pat_Cons fv l -> ln_pattern_args' l i and ln_pattern_args' (p:list (pattern & bool)) (i:int) : Tot bool (decreases p) = match p with | [] -> true | (p, _)::tl -> ln_pattern' p i && ln_pattern_args' tl (i + pattern_shift_n p) let rec ln_st' (t:st_term) (i:int) : Tot bool (decreases t) = match t.term with | Tm_Return { term } -> ln' term i | Tm_Abs { b; ascription; body } -> ln' b.binder_ty i && ln_st' body (i + 1) && ln_c' ascription (i + 1) | Tm_STApp { head; arg } -> ln' head i && ln' arg i | Tm_Bind { binder; head; body } -> ln' binder.binder_ty i && ln_st' head i && ln_st' body (i + 1) | Tm_TotBind { binder; head; body } -> ln' binder.binder_ty i && ln' head i && ln_st' body (i + 1) | Tm_If { b; then_; else_; post } -> ln' b i && ln_st' then_ i && ln_st' else_ i && ln_opt' post (i + 1) | Tm_Match {sc; returns_; brs } -> ln' sc i && ln_opt' returns_ i && ln_branches' t brs i | Tm_IntroPure { p } | Tm_ElimExists { p } -> ln' p i | Tm_IntroExists { p; witnesses } -> ln' p i && ln_list' witnesses i | Tm_While { invariant; condition; body } -> ln' invariant (i + 1) && ln_st' condition i && ln_st' body i | Tm_Par { pre1; body1; post1; pre2; body2; post2 } -> ln' pre1 i && ln_st' body1 i && ln' post1 (i + 1) && ln' pre2 i && ln_st' body2 i && ln' post2 (i + 1) | Tm_WithLocal { binder; initializer; body } -> ln' binder.binder_ty i && ln' initializer i && ln_st' body (i + 1) | Tm_WithLocalArray { binder; initializer; length; body } -> ln' binder.binder_ty i && ln' initializer i && ln' length i && ln_st' body (i + 1) | Tm_Rewrite { t1; t2 } -> ln' t1 i && ln' t2 i | Tm_Admit { typ; post } -> ln' typ i && ln_opt' post (i + 1) | Tm_ProofHintWithBinders { binders; hint_type; t } -> let n = L.length binders in ln_proof_hint' hint_type (i + n) && ln_st' t (i + n) and ln_branch' (b : pattern & st_term) (i:int) : Tot bool (decreases b) = let (p, e) = b in ln_pattern' p i && ln_st' e (i + pattern_shift_n p) and ln_branches' (t:st_term) (brs : list branch{brs << t}) (i:int) : Tot bool (decreases brs) = for_all_dec t brs (fun b -> ln_branch' b i) let ln (t:term) = ln' t (-1) let ln_st (t:st_term) = ln_st' t (-1) let ln_c (c:comp) = ln_c' c (-1) noeq type subst_elt = | DT : nat -> term -> subst_elt | NT : var -> term -> subst_elt | ND : var -> nat -> subst_elt let shift_subst_elt (n:nat) = function | DT i t -> DT (i + n) t | NT x t -> NT x t | ND x i -> ND x (i + n) let subst = list subst_elt let shift_subst_n (n:nat) = L.map (shift_subst_elt n) let shift_subst = shift_subst_n 1 let rt_subst_elt = function | DT i t -> RT.DT i (E.elab_term t) | NT x t -> RT.NT x (E.elab_term t) | ND x i -> RT.ND x i let rt_subst = L.map rt_subst_elt let open_or_close_host_term (t:host_term) (ss:subst) : Lemma (not_tv_unknown (RT.subst_term t (rt_subst ss))) = admit() val subst_host_term (t:host_term) (ss:subst) : Tot (t':host_term { t' == RT.subst_term t (rt_subst ss) }) let rec subst_term (t:term) (ss:subst) : Tot term (decreases t) = let w t' = with_range t' t.range in match t.t with | Tm_VProp | Tm_Emp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> t | Tm_Pure p -> w (Tm_Pure (subst_term p ss)) | Tm_Star l r -> w (Tm_Star (subst_term l ss) (subst_term r ss)) | Tm_ExistsSL u b body -> w (Tm_ExistsSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_ForallSL u b body -> w (Tm_ForallSL u { b with binder_ty = subst_term b.binder_ty ss } (subst_term body (shift_subst ss))) | Tm_FStar t -> w (Tm_FStar (subst_host_term t ss)) let open_term' (t:term) (v:term) (i:index) = subst_term t [ DT i v ] let subst_st_comp (s:st_comp) (ss:subst) : st_comp = { s with res = subst_term s.res ss; pre = subst_term s.pre ss; post = subst_term s.post (shift_subst ss) } let open_st_comp' (s:st_comp) (v:term) (i:index) : st_comp = subst_st_comp s [ DT i v ] let subst_comp (c:comp) (ss:subst) : comp = match c with | C_Tot t -> C_Tot (subst_term t ss) | C_ST s -> C_ST (subst_st_comp s ss) | C_STAtomic inames s -> C_STAtomic (subst_term inames ss) (subst_st_comp s ss) | C_STGhost inames s -> C_STGhost (subst_term inames ss) (subst_st_comp s ss) let open_comp' (c:comp) (v:term) (i:index) : comp = subst_comp c [ DT i v ] let subst_term_opt (t:option term) (ss:subst) : Tot (option term) = match t with | None -> None | Some t -> Some (subst_term t ss) let open_term_opt' (t:option term) (v:term) (i:index) : Tot (option term) = subst_term_opt t [ DT i v ] let rec subst_term_list (t:list term) (ss:subst)

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val subst_term_list (t: list term) (ss: subst) : Tot (list term)

[ "recursion" ]

Pulse.Syntax.Naming.subst_term_list

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

t: Prims.list Pulse.Syntax.Base.term -> ss: Pulse.Syntax.Naming.subst -> Prims.list Pulse.Syntax.Base.term

{ "end_col": 57, "end_line": 450, "start_col": 4, "start_line": 448 }

Prims.Tot

val freevars_pairs (pairs: list (term & term)) : Set.set var

[ { "abbrev": true, "full_module": "Pulse.Elaborate.Pure", "short_module": "E" }, { "abbrev": true, "full_module": "Pulse.Syntax.Pure", "short_module": "U" }, { "abbrev": true, "full_module": "Pulse.RuntimeUtils", "short_module": "RU" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing", "short_module": "RT" }, { "abbrev": true, "full_module": "FStar.Reflection.Typing.Builtins", "short_module": "RTB" }, { "abbrev": true, "full_module": "FStar.Reflection", "short_module": "R" }, { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": false, "full_module": "Pulse.Common", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax.Base", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Syntax", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]

false

let rec freevars_pairs (pairs:list (term & term)) : Set.set var = match pairs with | [] -> Set.empty | (t1, t2)::tl -> Set.union (freevars t1) (freevars t2) `Set.union` freevars_pairs tl

val freevars_pairs (pairs: list (term & term)) : Set.set var let rec freevars_pairs (pairs: list (term & term)) : Set.set var =

false

null

false

match pairs with | [] -> Set.empty | (t1, t2) :: tl -> (Set.union (freevars t1) (freevars t2)) `Set.union` (freevars_pairs tl)

{ "checked_file": "Pulse.Syntax.Naming.fsti.checked", "dependencies": [ "Pulse.Syntax.Pure.fst.checked", "Pulse.Syntax.Base.fsti.checked", "Pulse.RuntimeUtils.fsti.checked", "Pulse.Elaborate.Pure.fst.checked", "Pulse.Common.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Reflection.Typing.Builtins.fsti.checked", "FStar.Reflection.Typing.fsti.checked", "FStar.Reflection.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked" ], "interface_file": false, "source_file": "Pulse.Syntax.Naming.fsti" }

[ "total" ]

[ "Prims.list", "FStar.Pervasives.Native.tuple2", "Pulse.Syntax.Base.term", "FStar.Set.empty", "Pulse.Syntax.Base.var", "FStar.Set.union", "Pulse.Syntax.Naming.freevars", "Pulse.Syntax.Naming.freevars_pairs", "FStar.Set.set" ]

[]

module Pulse.Syntax.Naming open FStar.List.Tot open Pulse.Syntax.Base open Pulse.Common module L = FStar.List.Tot module R = FStar.Reflection module RTB = FStar.Reflection.Typing.Builtins module RT = FStar.Reflection.Typing module RU = Pulse.RuntimeUtils module U = Pulse.Syntax.Pure module E = Pulse.Elaborate.Pure let rec freevars (t:term) : Set.set var = match t.t with | Tm_Emp | Tm_VProp | Tm_Inames | Tm_EmpInames | Tm_Unknown -> Set.empty | Tm_Star t1 t2 -> Set.union (freevars t1) (freevars t2) | Tm_ExistsSL _ t1 t2 | Tm_ForallSL _ t1 t2 -> Set.union (freevars t1.binder_ty) (freevars t2) | Tm_Pure p -> freevars p | Tm_FStar t -> RT.freevars t let freevars_st_comp (s:st_comp) : Set.set var = freevars s.res `Set.union` freevars s.pre `Set.union` freevars s.post let freevars_comp (c:comp) : Tot (Set.set var) (decreases c) = match c with | C_Tot t -> freevars t | C_ST s -> freevars_st_comp s | C_STAtomic inames s | C_STGhost inames s -> freevars inames `Set.union` freevars_st_comp s let freevars_opt (f: 'a -> Set.set var) (x:option 'a) : Set.set var = match x with | None -> Set.empty | Some x -> f x let freevars_term_opt (t:option term) : Set.set var = freevars_opt freevars t let rec freevars_list (t:list term) : Set.set var = match t with | [] -> Set.empty | hd::tl -> freevars hd `Set.union` freevars_list tl

false

true

Pulse.Syntax.Naming.fsti

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

null

val freevars_pairs (pairs: list (term & term)) : Set.set var

[ "recursion" ]

Pulse.Syntax.Naming.freevars_pairs

{ "file_name": "lib/steel/pulse/Pulse.Syntax.Naming.fsti", "git_rev": "7fbb54e94dd4f48ff7cb867d3bae6889a635541e", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

pairs: Prims.list (Pulse.Syntax.Base.term * Pulse.Syntax.Base.term) -> FStar.Set.set Pulse.Syntax.Base.var

{ "end_col": 87, "end_line": 62, "start_col": 2, "start_line": 60 }