microsoft/FStarDataSet-V2 · Datasets at Hugging Face

Hacl.Spec.Karatsuba.Lemmas.fst

Hacl.Spec.Karatsuba.Lemmas.lemma_bn_halves

val lemma_bn_halves: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a:nat{a < pow2 (pbits * aLen)} -> Lemma (let p = pow2 (aLen / 2 * pbits) in a / p < p /\ a % p < p /\ a == a / p * p + a % p)

let lemma_bn_halves pbits aLen a = lemma_double_p pbits aLen

{ "file_name": "code/bignum/Hacl.Spec.Karatsuba.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 60, "end_line": 42, "start_col": 0, "start_line": 42 }

module Hacl.Spec.Karatsuba.Lemmas open FStar.Mul open Lib.IntTypes #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" type sign = | Positive | Negative let abs (a:nat) (b:nat) : nat = if a b:nat -> Pure (tuple2 sign nat) (requires True) (ensures fun (s, res) -> res == abs a b /\ s == (if a aLen:nat{aLen % 2 = 0} -> Lemma (let p = pow2 (aLen / 2 * pbits) in p * p == pow2 (pbits * aLen)) let lemma_double_p pbits aLen = let p = pow2 (aLen / 2 * pbits) in calc (==) { p * p; (==) { Math.Lemmas.pow2_plus (aLen / 2 * pbits) (aLen / 2 * pbits) } pow2 (aLen / 2 * pbits + aLen / 2 * pbits); (==) { Math.Lemmas.distributivity_add_left (aLen / 2) (aLen / 2) pbits } pow2 ((aLen / 2 * 2) * pbits); (==) { Math.Lemmas.lemma_div_exact aLen 2 } pow2 (aLen * pbits); } val lemma_bn_halves: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a:nat{a < pow2 (pbits * aLen)} ->

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "Lib.IntTypes.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked", "FStar.Calc.fsti.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Karatsuba.Lemmas.fst" }

[ { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

pbits: Prims.pos -> aLen: Prims.nat{aLen % 2 = 0} -> a: Prims.nat{a < Prims.pow2 (pbits * aLen)} -> FStar.Pervasives.Lemma (ensures (let p = Prims.pow2 ((aLen / 2) * pbits) in a / p < p /\ a % p < p /\ a == (a / p) * p + a % p))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.pos", "Prims.nat", "Prims.b2t", "Prims.op_Equality", "Prims.int", "Prims.op_Modulus", "Prims.op_LessThan", "Prims.pow2", "FStar.Mul.op_Star", "Hacl.Spec.Karatsuba.Lemmas.lemma_double_p", "Prims.unit" ]

[]

true

false

true

false

let lemma_bn_halves pbits aLen a =

lemma_double_p pbits aLen

false

Vale.AES.GCM_s.fst

Vale.AES.GCM_s.gcm_decrypt_LE

val gcm_decrypt_LE : alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> iv: Vale.AES.GCM_s.supported_iv_LE -> cipher: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> auth: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> tag: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8 * Prims.bool)

let gcm_decrypt_LE = opaque_make gcm_decrypt_LE_def

{ "file_name": "vale/specs/crypto/Vale.AES.GCM_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 70, "end_line": 95, "start_col": 19, "start_line": 95 }

module Vale.AES.GCM_s open Vale.Def.Opaque_s open Vale.Def.Words_s open Vale.Def.Words.Seq_s open Vale.Def.Types_s open Vale.AES.AES_s open Vale.AES.GCTR_s open Vale.AES.GHash_s open FStar.Seq open FStar.Mul unfold type gcm_plain_LE = gctr_plain_LE unfold type gcm_auth_LE = gctr_plain_LE #reset-options "--z3rlimit 30" type supported_iv_LE:eqtype = iv:seq nat8 { 1 <= 8 * (length iv) /\ 8 * (length iv) < pow2_64 } let compute_iv_BE_def (h_LE:quad32) (iv:supported_iv_LE) : quad32 = if 8 * (length iv) = 96 then ( let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE ) else ( let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE ) [@"opaque_to_smt"] let compute_iv_BE = opaque_make compute_iv_BE_def irreducible let compute_iv_BE_reveal = opaque_revealer (`%compute_iv_BE) compute_iv_BE compute_iv_BE_def // little-endian let gcm_encrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (plain:seq nat8) (auth:seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32 ) (ensures fun (c, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let c = gctr_encrypt_LE (inc32 j0_BE 1) plain alg key_LE in // Sets the first 64-bit number to 8 * length plain, and the second to 8* length auth let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length plain) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits c) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (c, t) [@"opaque_to_smt"] let gcm_encrypt_LE = opaque_make gcm_encrypt_LE_def irreducible let gcm_encrypt_LE_reveal = opaque_revealer (`%gcm_encrypt_LE) gcm_encrypt_LE gcm_encrypt_LE_def let gcm_decrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (cipher:seq nat8) (auth:seq nat8) (tag:seq nat8) : Pure (seq nat8 & bool) (requires is_aes_key alg key /\ length cipher < pow2_32 /\ length auth < pow2_32 ) (ensures fun (p, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let p = gctr_encrypt_LE (inc32 j0_BE 1) cipher alg key_LE in // TODO: Rename gctr_encrypt_LE to gctr_LE let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length cipher) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits cipher) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in

{ "checked_file": "/", "dependencies": [ "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Def.Opaque_s.fsti.checked", "Vale.AES.GHash_s.fst.checked", "Vale.AES.GCTR_s.fst.checked", "Vale.AES.AES_s.fst.checked", "prims.fst.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked" ], "interface_file": false, "source_file": "Vale.AES.GCM_s.fst" }

[ { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GCTR_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Seq_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Opaque_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> iv: Vale.AES.GCM_s.supported_iv_LE -> cipher: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> auth: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> tag: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8 * Prims.bool)

Prims.Pure

[]

[ "Vale.Def.Opaque_s.opaque_make", "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.Def.Types_s.nat8", "Vale.AES.GCM_s.supported_iv_LE", "FStar.Pervasives.Native.tuple2", "Prims.bool", "Prims.l_and", "Vale.AES.AES_common_s.is_aes_key", "Prims.b2t", "Prims.op_LessThan", "FStar.Seq.Base.length", "Vale.Def.Words_s.pow2_32", "Prims.l_True", "Vale.AES.GCM_s.gcm_decrypt_LE_def" ]

[]

false

let gcm_decrypt_LE =

opaque_make gcm_decrypt_LE_def

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.safe_mod

val safe_mod (#t: eqtype) {| c: bounded_unsigned t |} (x y: t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y)

let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None )

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 5, "end_line": 103, "start_col": 0, "start_line": 90 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None )

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

{| c: Pulse.Lib.BoundedIntegers.bounded_unsigned t |} -> x: t -> y: t -> Prims.Pure (FStar.Pervasives.Native.option t)

Prims.Pure

[]

[ "Prims.eqtype", "Pulse.Lib.BoundedIntegers.bounded_unsigned", "Pulse.Lib.BoundedIntegers.__proj__Mkbounded_unsigned__item__static_max_bound", "FStar.Pervasives.Native.Some", "Pulse.Lib.BoundedIntegers.op_Percent", "Pulse.Lib.BoundedIntegers.bounded_from_bounded_unsigned", "Prims.bool", "Pulse.Lib.BoundedIntegers.op_Less_Equals", "Pulse.Lib.BoundedIntegers.max_bound", "Prims.unit", "Prims._assert", "Pulse.Lib.BoundedIntegers.fits", "Prims.int", "Pulse.Lib.BoundedIntegers.bounded_int_int", "Pulse.Lib.BoundedIntegers.v", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.option", "Prims.b2t", "Prims.op_GreaterThan", "Prims.l_imp", "FStar.Pervasives.Native.uu___is_Some", "Prims.eq2", "FStar.Pervasives.Native.__proj__Some__item__v" ]

[]

false

let safe_mod (#t: eqtype) {| c: bounded_unsigned t |} (x y: t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) =

if c.static_max_bound then Some (x % y) else (if y <= max_bound then (assert (fits #t (v x % v y)); Some (x % y)) else None)

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.add_nat_1

val add_nat_1 : x: Prims.nat -> Prims.int

let add_nat_1 (x:nat) = x + 1

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 29, "end_line": 162, "start_col": 0, "start_line": 162 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y //Again, parser doesn't allow using (-) let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

x: Prims.nat -> Prims.int

Prims.Tot

[ "total" ]

[]

[ "Prims.nat", "Pulse.Lib.BoundedIntegers.op_Plus", "Prims.int", "Pulse.Lib.BoundedIntegers.bounded_int_int" ]

[]

false

true

false

let add_nat_1 (x: nat) =

x + 1

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_unsigned_u32

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_unsigned_u32:bounded_unsigned FStar.UInt32.t

instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 133, "start_col": 0, "start_line": 128 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () }

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_unsigned FStar.UInt32.t

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_unsigned", "FStar.UInt32.t", "Pulse.Lib.BoundedIntegers.bounded_int_u32", "Pulse.Lib.BoundedIntegers.bounded_int", "FStar.UInt32.__uint_to_t" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_unsigned_u32:bounded_unsigned FStar.UInt32.t =

{ base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () }

false

Vale.AES.GCM_s.fst

Vale.AES.GCM_s.gcm_decrypt_LE_reveal

val gcm_decrypt_LE_reveal : _: Prims.unit -> FStar.Pervasives.Lemma (ensures Vale.AES.GCM_s.gcm_decrypt_LE == Vale.AES.GCM_s.gcm_decrypt_LE_def)

let gcm_decrypt_LE_reveal = opaque_revealer (`%gcm_decrypt_LE) gcm_decrypt_LE gcm_decrypt_LE_def

{ "file_name": "vale/specs/crypto/Vale.AES.GCM_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 108, "end_line": 96, "start_col": 12, "start_line": 96 }

module Vale.AES.GCM_s open Vale.Def.Opaque_s open Vale.Def.Words_s open Vale.Def.Words.Seq_s open Vale.Def.Types_s open Vale.AES.AES_s open Vale.AES.GCTR_s open Vale.AES.GHash_s open FStar.Seq open FStar.Mul unfold type gcm_plain_LE = gctr_plain_LE unfold type gcm_auth_LE = gctr_plain_LE #reset-options "--z3rlimit 30" type supported_iv_LE:eqtype = iv:seq nat8 { 1 <= 8 * (length iv) /\ 8 * (length iv) < pow2_64 } let compute_iv_BE_def (h_LE:quad32) (iv:supported_iv_LE) : quad32 = if 8 * (length iv) = 96 then ( let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE ) else ( let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE ) [@"opaque_to_smt"] let compute_iv_BE = opaque_make compute_iv_BE_def irreducible let compute_iv_BE_reveal = opaque_revealer (`%compute_iv_BE) compute_iv_BE compute_iv_BE_def // little-endian let gcm_encrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (plain:seq nat8) (auth:seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32 ) (ensures fun (c, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let c = gctr_encrypt_LE (inc32 j0_BE 1) plain alg key_LE in // Sets the first 64-bit number to 8 * length plain, and the second to 8* length auth let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length plain) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits c) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (c, t) [@"opaque_to_smt"] let gcm_encrypt_LE = opaque_make gcm_encrypt_LE_def irreducible let gcm_encrypt_LE_reveal = opaque_revealer (`%gcm_encrypt_LE) gcm_encrypt_LE gcm_encrypt_LE_def let gcm_decrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (cipher:seq nat8) (auth:seq nat8) (tag:seq nat8) : Pure (seq nat8 & bool) (requires is_aes_key alg key /\ length cipher < pow2_32 /\ length auth < pow2_32 ) (ensures fun (p, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let p = gctr_encrypt_LE (inc32 j0_BE 1) cipher alg key_LE in // TODO: Rename gctr_encrypt_LE to gctr_LE let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length cipher) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits cipher) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (p, t = tag)

{ "checked_file": "/", "dependencies": [ "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Def.Opaque_s.fsti.checked", "Vale.AES.GHash_s.fst.checked", "Vale.AES.GCTR_s.fst.checked", "Vale.AES.AES_s.fst.checked", "prims.fst.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked" ], "interface_file": false, "source_file": "Vale.AES.GCM_s.fst" }

[ { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GCTR_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Seq_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Opaque_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

_: Prims.unit -> FStar.Pervasives.Lemma (ensures Vale.AES.GCM_s.gcm_decrypt_LE == Vale.AES.GCM_s.gcm_decrypt_LE_def)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Vale.Def.Opaque_s.opaque_revealer", "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.Def.Types_s.nat8", "Vale.AES.GCM_s.supported_iv_LE", "FStar.Pervasives.Native.tuple2", "Prims.bool", "Prims.l_and", "Vale.AES.AES_common_s.is_aes_key", "Prims.b2t", "Prims.op_LessThan", "FStar.Seq.Base.length", "Vale.Def.Words_s.pow2_32", "Prims.l_True", "Vale.AES.GCM_s.gcm_decrypt_LE", "Vale.AES.GCM_s.gcm_decrypt_LE_def" ]

[]

true

false

true

false

let gcm_decrypt_LE_reveal =

opaque_revealer (`%gcm_decrypt_LE) gcm_decrypt_LE gcm_decrypt_LE_def

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_int_u32

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_int_u32:bounded_int FStar.UInt32.t

instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 126, "start_col": 0, "start_line": 116 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_int FStar.UInt32.t

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_int", "FStar.UInt32.t", "Prims.int", "Prims.l_and", "Prims.b2t", "Pulse.Lib.BoundedIntegers.op_Less_Equals", "Pulse.Lib.BoundedIntegers.bounded_int_int", "Pulse.Lib.BoundedIntegers.op_Less", "Prims.prop", "FStar.UInt32.v", "FStar.UInt32.uint_to_t", "FStar.UInt32.add", "FStar.UInt32.sub", "FStar.UInt32.op_Less_Hat", "Prims.bool", "Prims.op_Equality", "Prims.op_LessThan", "FStar.UInt32.op_Less_Equals_Hat", "Prims.op_LessThanOrEqual", "FStar.UInt32.op_Percent_Hat" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_int_u32:bounded_int FStar.UInt32.t =

{ fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); ( - ) = (fun x y -> FStar.UInt32.sub x y); ( < ) = (let open FStar.UInt32 in fun x y -> x <^ y); ( <= ) = (let open FStar.UInt32 in fun x y -> x <=^ y); ( % ) = (let open FStar.UInt32 in fun x y -> x %^ y); properties = () }

false

Spec.Curve25519.fst

Spec.Curve25519.basepoint_lseq

val basepoint_lseq:Lib.Sequence.lseq byte_t 32

let basepoint_lseq : Lib.Sequence.lseq byte_t 32 = Lib.Sequence.of_list basepoint_list

{ "file_name": "specs/Spec.Curve25519.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 37, "end_line": 137, "start_col": 0, "start_line": 136 }

module Spec.Curve25519 open FStar.Mul open Lib.IntTypes open Lib.Sequence open Lib.ByteSequence open Spec.Curve25519.Lemmas #set-options "--z3rlimit 30 --ifuel 0 --fuel 0" (* Field types and parameters *) let prime : pos = pow2 255 - 19 type elem = x:nat{x < prime} let zero : elem = 0 let one : elem = 1 let fadd (x:elem) (y:elem) : elem = (x + y) % prime let fsub (x:elem) (y:elem) : elem = (x - y) % prime let fmul (x:elem) (y:elem) : elem = (x * y) % prime let ( +% ) = fadd let ( -% ) = fsub let ( *% ) = fmul let fpow (x:elem) (b:nat) : elem = Lib.NatMod.pow_mod #prime x b let ( **% ) = fpow let finv (x:elem) : elem = x **% (prime - 2) let ( /% ) (x:elem) (y:elem) = x *% finv y (* Type aliases *) type scalar = lbytes 32 type serialized_point = lbytes 32 type proj_point = elem & elem let ith_bit (k:scalar) (i:nat{i < 256}) : uint64 = let q = i / 8 in let r = size (i % 8) in to_u64 ((k.[q] >>. r) &. u8 1) let decodeScalar (k:scalar) = let k : scalar = k.[0] <- (k.[0] &. u8 248) in let k : scalar = k.[31] <- (k.[31] &. u8 127) in let k : scalar = k.[31] <- (k.[31] |. u8 64) in k let decodePoint (u:serialized_point) = (nat_from_bytes_le u % pow2 255) % prime let encodePoint (p:proj_point) : Tot serialized_point = let x, z = p in let p = x /% z in nat_to_bytes_le 32 p let add_and_double q nq nqp1 = let x_1, z_1 = q in let x_2, z_2 = nq in let x_3, z_3 = nqp1 in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let c = x_3 +% z_3 in let d = x_3 -% z_3 in let da = d *% a in let cb = c *% b in let x_3 = da +% cb in let z_3 = da -% cb in let aa = a *% a in let bb = b *% b in let x_3 = x_3 *% x_3 in let z_3 = z_3 *% z_3 in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in let z_3 = z_3 *% x_1 in (x_2, z_2), (x_3, z_3) let double nq = let x_2, z_2 = nq in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let aa = a *% a in let bb = b *% b in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in x_2, z_2 let cswap2 (sw:uint64) (nq:proj_point) (nqp1:proj_point) = let open Lib.RawIntTypes in if uint_to_nat sw = 1 then (nqp1, nq) else (nq, nqp1) let ladder_step (k:scalar) (q:proj_point) (i:nat{i < 251}) (nq, nqp1, swap) = let bit = ith_bit k (253-i) in let sw = swap ^. bit in let nq, nqp1 = cswap2 sw nq nqp1 in let nq, nqp1 = add_and_double q nq nqp1 in (nq, nqp1, bit) let montgomery_ladder (init:elem) (k:scalar) : Tot proj_point = let q = (init, one) in let nq = (one, zero) in let nqp1 = (init, one) in // bit 255 is 0 and bit 254 is 1 let nq,nqp1 = cswap2 (u64 1) nq nqp1 in let nq,nqp1 = add_and_double q nq nqp1 in let swap = u64 1 in // bits 253-3 depend on scalar let nq,nqp1,swap = Lib.LoopCombinators.repeati 251 (ladder_step k q) (nq, nqp1, swap) in let nq,nqp1 = cswap2 swap nq nqp1 in // bits 2-0 are 0 let nq = double nq in let nq = double nq in let nq = double nq in nq let scalarmult (k:scalar) (u:serialized_point) : Tot serialized_point = let u = decodePoint u in let res = montgomery_ladder u k in encodePoint res inline_for_extraction let basepoint_list : x:list byte_t{List.Tot.length x == 32} = [@inline_let] let l = [9uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy] in assert_norm (List.Tot.length l == 32); l

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.Lemmas.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.RawIntTypes.fsti.checked", "Lib.NatMod.fsti.checked", "Lib.LoopCombinators.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "FStar.UInt8.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.List.Tot.fst.checked" ], "interface_file": false, "source_file": "Spec.Curve25519.fst" }

[ { "abbrev": false, "full_module": "Spec.Curve25519.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Lib.ByteSequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Spec", "short_module": null }, { "abbrev": false, "full_module": "Spec", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.PUB) 32

Prims.Tot

[ "total" ]

[]

[ "Lib.Sequence.of_list", "Lib.IntTypes.int_t", "Lib.IntTypes.U8", "Lib.IntTypes.PUB", "Spec.Curve25519.basepoint_list" ]

[]

false

let basepoint_lseq:Lib.Sequence.lseq byte_t 32 =

Lib.Sequence.of_list basepoint_list

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.safe_add

val safe_add (#t: eqtype) {| c: bounded_unsigned t |} (x y: t) : o: option t {Some? o ==> v (Some?.v o) == v x + v y}

let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None )

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 5, "end_line": 88, "start_col": 0, "start_line": 70 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

{| c: Pulse.Lib.BoundedIntegers.bounded_unsigned t |} -> x: t -> y: t -> o: FStar.Pervasives.Native.option t { Some? o ==> Pulse.Lib.BoundedIntegers.v (Some?.v o) == Pulse.Lib.BoundedIntegers.v x + Pulse.Lib.BoundedIntegers.v y }

Prims.Tot

[ "total" ]

[]

[ "Prims.eqtype", "Pulse.Lib.BoundedIntegers.bounded_unsigned", "Pulse.Lib.BoundedIntegers.__proj__Mkbounded_unsigned__item__static_max_bound", "Pulse.Lib.BoundedIntegers.op_Less_Equals", "Pulse.Lib.BoundedIntegers.bounded_from_bounded_unsigned", "Pulse.Lib.BoundedIntegers.op_Subtraction", "Pulse.Lib.BoundedIntegers.max_bound", "FStar.Pervasives.Native.Some", "Pulse.Lib.BoundedIntegers.op_Plus", "Prims.bool", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.option", "Prims.l_imp", "Prims.b2t", "FStar.Pervasives.Native.uu___is_Some", "Prims.eq2", "Prims.int", "Pulse.Lib.BoundedIntegers.v", "FStar.Pervasives.Native.__proj__Some__item__v", "Pulse.Lib.BoundedIntegers.bounded_int_int", "Prims.unit", "Prims._assert", "Pulse.Lib.BoundedIntegers.fits" ]

[]

false

let safe_add (#t: eqtype) {| c: bounded_unsigned t |} (x y: t) : o: option t {Some? o ==> v (Some?.v o) == v x + v y} =

if c.static_max_bound then (assert (x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None) else (if x <= max_bound then (assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None) else None)

false

Spec.Curve25519.fst

Spec.Curve25519.scalarmult

val scalarmult (k: scalar) (u: serialized_point) : Tot serialized_point

let scalarmult (k:scalar) (u:serialized_point) : Tot serialized_point = let u = decodePoint u in let res = montgomery_ladder u k in encodePoint res

{ "file_name": "specs/Spec.Curve25519.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 17, "end_line": 123, "start_col": 0, "start_line": 120 }

module Spec.Curve25519 open FStar.Mul open Lib.IntTypes open Lib.Sequence open Lib.ByteSequence open Spec.Curve25519.Lemmas #set-options "--z3rlimit 30 --ifuel 0 --fuel 0" (* Field types and parameters *) let prime : pos = pow2 255 - 19 type elem = x:nat{x < prime} let zero : elem = 0 let one : elem = 1 let fadd (x:elem) (y:elem) : elem = (x + y) % prime let fsub (x:elem) (y:elem) : elem = (x - y) % prime let fmul (x:elem) (y:elem) : elem = (x * y) % prime let ( +% ) = fadd let ( -% ) = fsub let ( *% ) = fmul let fpow (x:elem) (b:nat) : elem = Lib.NatMod.pow_mod #prime x b let ( **% ) = fpow let finv (x:elem) : elem = x **% (prime - 2) let ( /% ) (x:elem) (y:elem) = x *% finv y (* Type aliases *) type scalar = lbytes 32 type serialized_point = lbytes 32 type proj_point = elem & elem let ith_bit (k:scalar) (i:nat{i < 256}) : uint64 = let q = i / 8 in let r = size (i % 8) in to_u64 ((k.[q] >>. r) &. u8 1) let decodeScalar (k:scalar) = let k : scalar = k.[0] <- (k.[0] &. u8 248) in let k : scalar = k.[31] <- (k.[31] &. u8 127) in let k : scalar = k.[31] <- (k.[31] |. u8 64) in k let decodePoint (u:serialized_point) = (nat_from_bytes_le u % pow2 255) % prime let encodePoint (p:proj_point) : Tot serialized_point = let x, z = p in let p = x /% z in nat_to_bytes_le 32 p let add_and_double q nq nqp1 = let x_1, z_1 = q in let x_2, z_2 = nq in let x_3, z_3 = nqp1 in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let c = x_3 +% z_3 in let d = x_3 -% z_3 in let da = d *% a in let cb = c *% b in let x_3 = da +% cb in let z_3 = da -% cb in let aa = a *% a in let bb = b *% b in let x_3 = x_3 *% x_3 in let z_3 = z_3 *% z_3 in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in let z_3 = z_3 *% x_1 in (x_2, z_2), (x_3, z_3) let double nq = let x_2, z_2 = nq in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let aa = a *% a in let bb = b *% b in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in x_2, z_2 let cswap2 (sw:uint64) (nq:proj_point) (nqp1:proj_point) = let open Lib.RawIntTypes in if uint_to_nat sw = 1 then (nqp1, nq) else (nq, nqp1) let ladder_step (k:scalar) (q:proj_point) (i:nat{i < 251}) (nq, nqp1, swap) = let bit = ith_bit k (253-i) in let sw = swap ^. bit in let nq, nqp1 = cswap2 sw nq nqp1 in let nq, nqp1 = add_and_double q nq nqp1 in (nq, nqp1, bit) let montgomery_ladder (init:elem) (k:scalar) : Tot proj_point = let q = (init, one) in let nq = (one, zero) in let nqp1 = (init, one) in // bit 255 is 0 and bit 254 is 1 let nq,nqp1 = cswap2 (u64 1) nq nqp1 in let nq,nqp1 = add_and_double q nq nqp1 in let swap = u64 1 in // bits 253-3 depend on scalar let nq,nqp1,swap = Lib.LoopCombinators.repeati 251 (ladder_step k q) (nq, nqp1, swap) in let nq,nqp1 = cswap2 swap nq nqp1 in // bits 2-0 are 0 let nq = double nq in let nq = double nq in let nq = double nq in nq

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.Lemmas.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.RawIntTypes.fsti.checked", "Lib.NatMod.fsti.checked", "Lib.LoopCombinators.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "FStar.UInt8.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.List.Tot.fst.checked" ], "interface_file": false, "source_file": "Spec.Curve25519.fst" }

[ { "abbrev": false, "full_module": "Spec.Curve25519.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Lib.ByteSequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Spec", "short_module": null }, { "abbrev": false, "full_module": "Spec", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

k: Spec.Curve25519.scalar -> u81: Spec.Curve25519.serialized_point -> Spec.Curve25519.serialized_point

Prims.Tot

[ "total" ]

[]

[ "Spec.Curve25519.scalar", "Spec.Curve25519.serialized_point", "Spec.Curve25519.encodePoint", "Spec.Curve25519.proj_point", "Spec.Curve25519.montgomery_ladder", "Prims.int", "Spec.Curve25519.decodePoint" ]

[]

false

true

false

let scalarmult (k: scalar) (u: serialized_point) : Tot serialized_point =

let u = decodePoint u in let res = montgomery_ladder u k in encodePoint res

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_unsigned_u64

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_unsigned_u64:bounded_unsigned FStar.UInt64.t

instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 152, "start_col": 0, "start_line": 147 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () }

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_unsigned FStar.UInt64.t

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_unsigned", "FStar.UInt64.t", "Pulse.Lib.BoundedIntegers.bounded_int_u64", "Pulse.Lib.BoundedIntegers.bounded_int", "FStar.UInt64.__uint_to_t" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_unsigned_u64:bounded_unsigned FStar.UInt64.t =

{ base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () }

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_int_pos

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_int_pos:bounded_int pos

instance bounded_int_pos : bounded_int pos = { fits = (fun x -> x > 0); v = pos_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 197, "start_col": 0, "start_line": 187 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y //Again, parser doesn't allow using (-) let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y //this work and resolved to int, because of the 1 let add_nat_1 (x:nat) = x + 1 //But, to add two nats, this fails, since typeclass resolution doesn't consider subtyping [@@expect_failure] let add_nat (x y:nat) = x + y let nat_as_int (x:nat) : int = x instance bounded_int_nat : bounded_int nat = { fits = (fun x -> x >= 0); v = nat_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } //with an instance for nat this works let add_nat (x y:nat) = x + y //but we should find a way to make it work with refinement, otherwise we'll need instances for pos etc. too let pos_as_int (x:pos) : int = x

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_int Prims.pos

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_int", "Pulse.Lib.BoundedIntegers.fits_t", "Prims.int", "Prims.b2t", "Prims.op_GreaterThan", "Prims.prop", "Pulse.Lib.BoundedIntegers.pos_as_int", "Prims.op_Addition", "Prims.op_Subtraction", "Prims.op_LessThan", "Prims.bool", "Prims.op_Equality", "Prims.op_LessThanOrEqual", "Prims.op_Modulus" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_int_pos:bounded_int pos =

{ fits = (fun x -> x > 0); v = pos_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); ( - ) = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () }

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_int_u64

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_int_u64:bounded_int FStar.UInt64.t

instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 145, "start_col": 0, "start_line": 135 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () }

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_int FStar.UInt64.t

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_int", "FStar.UInt64.t", "Prims.int", "Prims.l_and", "Prims.b2t", "Pulse.Lib.BoundedIntegers.op_Less_Equals", "Pulse.Lib.BoundedIntegers.bounded_int_int", "Prims.prop", "FStar.UInt64.v", "FStar.UInt64.uint_to_t", "FStar.UInt64.add", "FStar.UInt64.sub", "FStar.UInt64.op_Less_Hat", "Prims.bool", "Prims.op_Equality", "Prims.op_LessThan", "FStar.UInt64.op_Less_Equals_Hat", "Prims.op_LessThanOrEqual", "FStar.UInt64.op_Percent_Hat" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_int_u64:bounded_int FStar.UInt64.t =

{ fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); ( - ) = (fun x y -> FStar.UInt64.sub x y); ( < ) = (let open FStar.UInt64 in fun x y -> x <^ y); ( <= ) = (let open FStar.UInt64 in fun x y -> x <=^ y); ( % ) = (let open FStar.UInt64 in fun x y -> x %^ y); properties = () }

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.sub_u32

val sub_u32 : x: FStar.UInt32.t -> y: FStar.UInt32.t{Pulse.Lib.BoundedIntegers.ok Pulse.Lib.BoundedIntegers.op_Subtraction x y} -> FStar.UInt32.t

let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 82, "end_line": 159, "start_col": 0, "start_line": 159 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

x: FStar.UInt32.t -> y: FStar.UInt32.t{Pulse.Lib.BoundedIntegers.ok Pulse.Lib.BoundedIntegers.op_Subtraction x y} -> FStar.UInt32.t

Prims.Tot

[ "total" ]

[]

[ "FStar.UInt32.t", "Pulse.Lib.BoundedIntegers.ok", "Pulse.Lib.BoundedIntegers.bounded_int_u32", "Pulse.Lib.BoundedIntegers.op_Subtraction", "Prims.int", "Pulse.Lib.BoundedIntegers.bounded_int_int" ]

[]

false

let sub_u32 (x: FStar.UInt32.t) (y: FStar.UInt32.t{ok op_Subtraction x y}) =

x - y

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_unsigned_size_t

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_unsigned_size_t:bounded_unsigned FStar.SizeT.t

instance bounded_unsigned_size_t : bounded_unsigned FStar.SizeT.t = { base = TC.solve; max_bound = 0xffffsz; static_max_bound = false; properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 219, "start_col": 0, "start_line": 214 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y //Again, parser doesn't allow using (-) let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y //this work and resolved to int, because of the 1 let add_nat_1 (x:nat) = x + 1 //But, to add two nats, this fails, since typeclass resolution doesn't consider subtyping [@@expect_failure] let add_nat (x y:nat) = x + y let nat_as_int (x:nat) : int = x instance bounded_int_nat : bounded_int nat = { fits = (fun x -> x >= 0); v = nat_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } //with an instance for nat this works let add_nat (x y:nat) = x + y //but we should find a way to make it work with refinement, otherwise we'll need instances for pos etc. too let pos_as_int (x:pos) : int = x instance bounded_int_pos : bounded_int pos = { fits = (fun x -> x > 0); v = pos_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } // Using a fits predicate as the bounds check allows this class to also accomodate SizeT open FStar.SizeT instance bounded_int_size_t : bounded_int FStar.SizeT.t = { fits = (fun x -> x >= 0 /\ FStar.SizeT.fits x); v = (fun x -> FStar.SizeT.v x); u = (fun x -> FStar.SizeT.uint_to_t x); ( + ) = (fun x y -> FStar.SizeT.add x y); op_Subtraction = (fun x y -> FStar.SizeT.sub x y); ( < ) = (fun x y -> FStar.SizeT.(x <^ y)); ( <= ) = (fun x y -> FStar.SizeT.(x <=^ y)); ( % ) = (fun x y -> FStar.SizeT.(x %^ y)); properties = (); }

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": false, "full_module": "FStar.SizeT", "short_module": null }, { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_unsigned FStar.SizeT.t

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_unsigned", "FStar.SizeT.t", "Pulse.Lib.BoundedIntegers.bounded_int_size_t", "Pulse.Lib.BoundedIntegers.bounded_int", "FStar.SizeT.__uint_to_t" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_unsigned_size_t:bounded_unsigned FStar.SizeT.t =

{ base = TC.solve; max_bound = 0xffffsz; static_max_bound = false; properties = () }

false

Hacl.Spec.Karatsuba.Lemmas.fst

Hacl.Spec.Karatsuba.Lemmas.lemma_middle_karatsuba

val lemma_middle_karatsuba: a0:nat -> a1:nat -> b0:nat -> b1:nat -> Lemma (let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in t45 == a0 * b1 + a1 * b0)

let lemma_middle_karatsuba a0 a1 b0 b1 = let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in match (s0, s1) with | (Positive, Positive) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a0 - a1) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b0 b1 } a0 * b0 + a1 * b1 - ((a0 - a1) * b0 - (a0 - a1) * b1); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b0; Math.Lemmas.distributivity_sub_left a0 a1 b1 } a0 * b0 + a1 * b1 - (a0 * b0 - a1 * b0 - (a0 * b1 - a1 * b1)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Negative) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a1 - a0) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b1 b0 } a0 * b0 + a1 * b1 - ((a1 - a0) * b1 - (a1 - a0) * b0); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b1; Math.Lemmas.distributivity_sub_left a1 a0 b0 } a0 * b0 + a1 * b1 - (a1 * b1 - a0 * b1 - (a1 * b0 - a0 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Positive, Negative) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a0 - a1) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b1 b0 } a0 * b0 + a1 * b1 + ((a0 - a1) * b1 - (a0 - a1) * b0); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b1; Math.Lemmas.distributivity_sub_left a0 a1 b0 } a0 * b0 + a1 * b1 + (a0 * b1 - a1 * b1 - (a0 * b0 - a1 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Positive) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a1 - a0) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b0 b1 } a0 * b0 + a1 * b1 + ((a1 - a0) * b0 - (a1 - a0) * b1); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b0; Math.Lemmas.distributivity_sub_left a1 a0 b1 } a0 * b0 + a1 * b1 + (a1 * b0 - a0 * b0 - (a1 * b1 - a0 * b1)); (==) { } a1 * b0 + a0 * b1; }

{ "file_name": "code/bignum/Hacl.Spec.Karatsuba.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 6, "end_line": 111, "start_col": 0, "start_line": 54 }

module Hacl.Spec.Karatsuba.Lemmas open FStar.Mul open Lib.IntTypes #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" type sign = | Positive | Negative let abs (a:nat) (b:nat) : nat = if a b:nat -> Pure (tuple2 sign nat) (requires True) (ensures fun (s, res) -> res == abs a b /\ s == (if a aLen:nat{aLen % 2 = 0} -> Lemma (let p = pow2 (aLen / 2 * pbits) in p * p == pow2 (pbits * aLen)) let lemma_double_p pbits aLen = let p = pow2 (aLen / 2 * pbits) in calc (==) { p * p; (==) { Math.Lemmas.pow2_plus (aLen / 2 * pbits) (aLen / 2 * pbits) } pow2 (aLen / 2 * pbits + aLen / 2 * pbits); (==) { Math.Lemmas.distributivity_add_left (aLen / 2) (aLen / 2) pbits } pow2 ((aLen / 2 * 2) * pbits); (==) { Math.Lemmas.lemma_div_exact aLen 2 } pow2 (aLen * pbits); } val lemma_bn_halves: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a:nat{a < pow2 (pbits * aLen)} -> Lemma (let p = pow2 (aLen / 2 * pbits) in a / p a1:nat -> b0:nat -> b1:nat -> Lemma (let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in t45 == a0 * b1 + a1 * b0)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "Lib.IntTypes.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked", "FStar.Calc.fsti.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Karatsuba.Lemmas.fst" }

[ { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

a0: Prims.nat -> a1: Prims.nat -> b0: Prims.nat -> b1: Prims.nat -> FStar.Pervasives.Lemma (ensures (let _ = Hacl.Spec.Karatsuba.Lemmas.sign_abs a0 a1 in (let FStar.Pervasives.Native.Mktuple2 #_ #_ s0 t0 = _ in let _ = Hacl.Spec.Karatsuba.Lemmas.sign_abs b0 b1 in (let FStar.Pervasives.Native.Mktuple2 #_ #_ s1 t1 = _ in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = (match s0 = s1 with | true -> t01 - t23 | _ -> t01 + t23) <: Prims.int in t45 == a0 * b1 + a1 * b0) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.nat", "Hacl.Spec.Karatsuba.Lemmas.sign", "FStar.Pervasives.Native.Mktuple2", "FStar.Calc.calc_finish", "Prims.int", "Prims.eq2", "Prims.op_Subtraction", "Prims.op_Addition", "FStar.Mul.op_Star", "Prims.Cons", "FStar.Preorder.relation", "Prims.Nil", "Prims.unit", "FStar.Calc.calc_step", "FStar.Calc.calc_init", "FStar.Calc.calc_pack", "Prims.squash", "FStar.Math.Lemmas.distributivity_sub_right", "FStar.Math.Lemmas.distributivity_sub_left", "Prims.op_Equality", "Prims.bool", "FStar.Pervasives.Native.tuple2", "Hacl.Spec.Karatsuba.Lemmas.sign_abs" ]

[]

false

true

false

let lemma_middle_karatsuba a0 a1 b0 b1 =

let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in match (s0, s1) with | Positive, Positive -> calc ( == ) { t01 - t23; ( == ) { () } a0 * b0 + a1 * b1 - (a0 - a1) * (b0 - b1); ( == ) { Math.Lemmas.distributivity_sub_right (a0 - a1) b0 b1 } a0 * b0 + a1 * b1 - ((a0 - a1) * b0 - (a0 - a1) * b1); ( == ) { (Math.Lemmas.distributivity_sub_left a0 a1 b0; Math.Lemmas.distributivity_sub_left a0 a1 b1) } a0 * b0 + a1 * b1 - (a0 * b0 - a1 * b0 - (a0 * b1 - a1 * b1)); ( == ) { () } a1 * b0 + a0 * b1; } | Negative, Negative -> calc ( == ) { t01 - t23; ( == ) { () } a0 * b0 + a1 * b1 - (a1 - a0) * (b1 - b0); ( == ) { Math.Lemmas.distributivity_sub_right (a1 - a0) b1 b0 } a0 * b0 + a1 * b1 - ((a1 - a0) * b1 - (a1 - a0) * b0); ( == ) { (Math.Lemmas.distributivity_sub_left a1 a0 b1; Math.Lemmas.distributivity_sub_left a1 a0 b0) } a0 * b0 + a1 * b1 - (a1 * b1 - a0 * b1 - (a1 * b0 - a0 * b0)); ( == ) { () } a1 * b0 + a0 * b1; } | Positive, Negative -> calc ( == ) { t01 + t23; ( == ) { () } a0 * b0 + a1 * b1 + (a0 - a1) * (b1 - b0); ( == ) { Math.Lemmas.distributivity_sub_right (a0 - a1) b1 b0 } a0 * b0 + a1 * b1 + ((a0 - a1) * b1 - (a0 - a1) * b0); ( == ) { (Math.Lemmas.distributivity_sub_left a0 a1 b1; Math.Lemmas.distributivity_sub_left a0 a1 b0) } a0 * b0 + a1 * b1 + (a0 * b1 - a1 * b1 - (a0 * b0 - a1 * b0)); ( == ) { () } a1 * b0 + a0 * b1; } | Negative, Positive -> calc ( == ) { t01 + t23; ( == ) { () } a0 * b0 + a1 * b1 + (a1 - a0) * (b0 - b1); ( == ) { Math.Lemmas.distributivity_sub_right (a1 - a0) b0 b1 } a0 * b0 + a1 * b1 + ((a1 - a0) * b0 - (a1 - a0) * b1); ( == ) { (Math.Lemmas.distributivity_sub_left a1 a0 b0; Math.Lemmas.distributivity_sub_left a1 a0 b1) } a0 * b0 + a1 * b1 + (a1 * b0 - a0 * b0 - (a1 * b1 - a0 * b1)); ( == ) { () } a1 * b0 + a0 * b1; }

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.size_t_plus_one

val size_t_plus_one : x: FStar.SizeT.t{x < 1024sz} -> FStar.SizeT.t

let size_t_plus_one (x:FStar.SizeT.t { x < 1024sz }) = x + 1sz

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 62, "end_line": 222, "start_col": 0, "start_line": 222 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y //Again, parser doesn't allow using (-) let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y //this work and resolved to int, because of the 1 let add_nat_1 (x:nat) = x + 1 //But, to add two nats, this fails, since typeclass resolution doesn't consider subtyping [@@expect_failure] let add_nat (x y:nat) = x + y let nat_as_int (x:nat) : int = x instance bounded_int_nat : bounded_int nat = { fits = (fun x -> x >= 0); v = nat_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } //with an instance for nat this works let add_nat (x y:nat) = x + y //but we should find a way to make it work with refinement, otherwise we'll need instances for pos etc. too let pos_as_int (x:pos) : int = x instance bounded_int_pos : bounded_int pos = { fits = (fun x -> x > 0); v = pos_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } // Using a fits predicate as the bounds check allows this class to also accomodate SizeT open FStar.SizeT instance bounded_int_size_t : bounded_int FStar.SizeT.t = { fits = (fun x -> x >= 0 /\ FStar.SizeT.fits x); v = (fun x -> FStar.SizeT.v x); u = (fun x -> FStar.SizeT.uint_to_t x); ( + ) = (fun x y -> FStar.SizeT.add x y); op_Subtraction = (fun x y -> FStar.SizeT.sub x y); ( < ) = (fun x y -> FStar.SizeT.(x <^ y)); ( <= ) = (fun x y -> FStar.SizeT.(x <=^ y)); ( % ) = (fun x y -> FStar.SizeT.(x %^ y)); properties = (); } instance bounded_unsigned_size_t : bounded_unsigned FStar.SizeT.t = { base = TC.solve; max_bound = 0xffffsz; static_max_bound = false; properties = () }

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": false, "full_module": "FStar.SizeT", "short_module": null }, { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

x: FStar.SizeT.t{x < 1024sz} -> FStar.SizeT.t

Prims.Tot

[ "total" ]

[]

[ "FStar.SizeT.t", "Prims.b2t", "Pulse.Lib.BoundedIntegers.op_Less", "Pulse.Lib.BoundedIntegers.bounded_int_size_t", "FStar.SizeT.__uint_to_t", "Pulse.Lib.BoundedIntegers.op_Plus" ]

[]

false

let size_t_plus_one (x: FStar.SizeT.t{x < 1024sz}) =

x + 1sz

false

Vale.AES.GCM_s.fst

Vale.AES.GCM_s.compute_iv_BE_def

val compute_iv_BE_def (h_LE: quad32) (iv: supported_iv_LE) : quad32

let compute_iv_BE_def (h_LE:quad32) (iv:supported_iv_LE) : quad32 = if 8 * (length iv) = 96 then ( let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE ) else ( let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE )

{ "file_name": "vale/specs/crypto/Vale.AES.GCM_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 3, "end_line": 34, "start_col": 0, "start_line": 20 }

module Vale.AES.GCM_s open Vale.Def.Opaque_s open Vale.Def.Words_s open Vale.Def.Words.Seq_s open Vale.Def.Types_s open Vale.AES.AES_s open Vale.AES.GCTR_s open Vale.AES.GHash_s open FStar.Seq open FStar.Mul unfold type gcm_plain_LE = gctr_plain_LE unfold type gcm_auth_LE = gctr_plain_LE #reset-options "--z3rlimit 30" type supported_iv_LE:eqtype = iv:seq nat8 { 1 <= 8 * (length iv) /\ 8 * (length iv) < pow2_64 }

{ "checked_file": "/", "dependencies": [ "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Def.Opaque_s.fsti.checked", "Vale.AES.GHash_s.fst.checked", "Vale.AES.GCTR_s.fst.checked", "Vale.AES.AES_s.fst.checked", "prims.fst.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked" ], "interface_file": false, "source_file": "Vale.AES.GCM_s.fst" }

[ { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GCTR_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Seq_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Opaque_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h_LE: Vale.Def.Types_s.quad32 -> iv: Vale.AES.GCM_s.supported_iv_LE -> Vale.Def.Types_s.quad32

Prims.Tot

[ "total" ]

[]

[ "Vale.Def.Types_s.quad32", "Vale.AES.GCM_s.supported_iv_LE", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star", "FStar.Seq.Base.length", "Vale.Def.Types_s.nat8", "Vale.Def.Words_s.four", "Vale.Def.Words_s.nat32", "Vale.Def.Words_s.Mkfour", "Vale.Def.Types_s.nat32", "Vale.Def.Words_s.__proj__Mkfour__item__lo1", "Vale.Def.Words_s.__proj__Mkfour__item__hi2", "Vale.Def.Words_s.__proj__Mkfour__item__hi3", "Vale.Def.Types_s.reverse_bytes_quad32", "Vale.Def.Types_s.le_bytes_to_quad32", "Vale.AES.GCTR_s.pad_to_128_bits", "Prims.bool", "Vale.AES.GHash_s.ghash_LE", "FStar.Seq.Base.seq", "FStar.Seq.Base.append", "FStar.Seq.Base.create", "Vale.Def.Types_s.insert_nat64_def", "Vale.Def.Types_s.le_bytes_to_seq_quad32" ]

[]

false

true

false

let compute_iv_BE_def (h_LE: quad32) (iv: supported_iv_LE) : quad32 =

if 8 * (length iv) = 96 then (let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE) else (let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE)

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.bounded_int_nat

[@@ FStar.Tactics.Typeclasses.tcinstance] val bounded_int_nat:bounded_int nat

instance bounded_int_nat : bounded_int nat = { fits = (fun x -> x >= 0); v = nat_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); //can't write ( - ), it doesn't parse ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () }

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 1, "end_line": 180, "start_col": 0, "start_line": 170 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y //Again, parser doesn't allow using (-) let sub_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok op_Subtraction x y}) = x - y //this work and resolved to int, because of the 1 let add_nat_1 (x:nat) = x + 1 //But, to add two nats, this fails, since typeclass resolution doesn't consider subtyping [@@expect_failure] let add_nat (x y:nat) = x + y let nat_as_int (x:nat) : int = x

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

Pulse.Lib.BoundedIntegers.bounded_int Prims.nat

Prims.Tot

[ "total" ]

[]

[ "Pulse.Lib.BoundedIntegers.Mkbounded_int", "Pulse.Lib.BoundedIntegers.fits_t", "Prims.int", "Prims.b2t", "Prims.op_GreaterThanOrEqual", "Prims.prop", "Pulse.Lib.BoundedIntegers.nat_as_int", "Prims.op_Addition", "Prims.op_Subtraction", "Prims.op_LessThan", "Prims.bool", "Prims.op_Equality", "Prims.op_LessThanOrEqual", "Prims.op_Modulus" ]

[]

false

true

false

[@@ FStar.Tactics.Typeclasses.tcinstance] let bounded_int_nat:bounded_int nat =

{ fits = (fun x -> x >= 0); v = nat_as_int; u = (fun x -> x); ( + ) = (fun x y -> Prims.op_Addition x y); ( - ) = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () }

false

Spec.Curve25519.fst

Spec.Curve25519.secret_to_public

val secret_to_public: lbytes 32 -> lbytes 32

let secret_to_public kpriv = let basepoint = map secret basepoint_lseq in scalarmult kpriv basepoint

{ "file_name": "specs/Spec.Curve25519.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 28, "end_line": 142, "start_col": 0, "start_line": 140 }

module Spec.Curve25519 open FStar.Mul open Lib.IntTypes open Lib.Sequence open Lib.ByteSequence open Spec.Curve25519.Lemmas #set-options "--z3rlimit 30 --ifuel 0 --fuel 0" (* Field types and parameters *) let prime : pos = pow2 255 - 19 type elem = x:nat{x < prime} let zero : elem = 0 let one : elem = 1 let fadd (x:elem) (y:elem) : elem = (x + y) % prime let fsub (x:elem) (y:elem) : elem = (x - y) % prime let fmul (x:elem) (y:elem) : elem = (x * y) % prime let ( +% ) = fadd let ( -% ) = fsub let ( *% ) = fmul let fpow (x:elem) (b:nat) : elem = Lib.NatMod.pow_mod #prime x b let ( **% ) = fpow let finv (x:elem) : elem = x **% (prime - 2) let ( /% ) (x:elem) (y:elem) = x *% finv y (* Type aliases *) type scalar = lbytes 32 type serialized_point = lbytes 32 type proj_point = elem & elem let ith_bit (k:scalar) (i:nat{i < 256}) : uint64 = let q = i / 8 in let r = size (i % 8) in to_u64 ((k.[q] >>. r) &. u8 1) let decodeScalar (k:scalar) = let k : scalar = k.[0] <- (k.[0] &. u8 248) in let k : scalar = k.[31] <- (k.[31] &. u8 127) in let k : scalar = k.[31] <- (k.[31] |. u8 64) in k let decodePoint (u:serialized_point) = (nat_from_bytes_le u % pow2 255) % prime let encodePoint (p:proj_point) : Tot serialized_point = let x, z = p in let p = x /% z in nat_to_bytes_le 32 p let add_and_double q nq nqp1 = let x_1, z_1 = q in let x_2, z_2 = nq in let x_3, z_3 = nqp1 in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let c = x_3 +% z_3 in let d = x_3 -% z_3 in let da = d *% a in let cb = c *% b in let x_3 = da +% cb in let z_3 = da -% cb in let aa = a *% a in let bb = b *% b in let x_3 = x_3 *% x_3 in let z_3 = z_3 *% z_3 in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in let z_3 = z_3 *% x_1 in (x_2, z_2), (x_3, z_3) let double nq = let x_2, z_2 = nq in let a = x_2 +% z_2 in let b = x_2 -% z_2 in let aa = a *% a in let bb = b *% b in let e = aa -% bb in let e121665 = e *% 121665 in let aa_e121665 = e121665 +% aa in let x_2 = aa *% bb in let z_2 = e *% aa_e121665 in x_2, z_2 let cswap2 (sw:uint64) (nq:proj_point) (nqp1:proj_point) = let open Lib.RawIntTypes in if uint_to_nat sw = 1 then (nqp1, nq) else (nq, nqp1) let ladder_step (k:scalar) (q:proj_point) (i:nat{i < 251}) (nq, nqp1, swap) = let bit = ith_bit k (253-i) in let sw = swap ^. bit in let nq, nqp1 = cswap2 sw nq nqp1 in let nq, nqp1 = add_and_double q nq nqp1 in (nq, nqp1, bit) let montgomery_ladder (init:elem) (k:scalar) : Tot proj_point = let q = (init, one) in let nq = (one, zero) in let nqp1 = (init, one) in // bit 255 is 0 and bit 254 is 1 let nq,nqp1 = cswap2 (u64 1) nq nqp1 in let nq,nqp1 = add_and_double q nq nqp1 in let swap = u64 1 in // bits 253-3 depend on scalar let nq,nqp1,swap = Lib.LoopCombinators.repeati 251 (ladder_step k q) (nq, nqp1, swap) in let nq,nqp1 = cswap2 swap nq nqp1 in // bits 2-0 are 0 let nq = double nq in let nq = double nq in let nq = double nq in nq let scalarmult (k:scalar) (u:serialized_point) : Tot serialized_point = let u = decodePoint u in let res = montgomery_ladder u k in encodePoint res inline_for_extraction let basepoint_list : x:list byte_t{List.Tot.length x == 32} = [@inline_let] let l = [9uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy; 0uy] in assert_norm (List.Tot.length l == 32); l let basepoint_lseq : Lib.Sequence.lseq byte_t 32 = Lib.Sequence.of_list basepoint_list

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.Lemmas.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.RawIntTypes.fsti.checked", "Lib.NatMod.fsti.checked", "Lib.LoopCombinators.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "FStar.UInt8.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.List.Tot.fst.checked" ], "interface_file": false, "source_file": "Spec.Curve25519.fst" }

[ { "abbrev": false, "full_module": "Spec.Curve25519.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Lib.ByteSequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Spec", "short_module": null }, { "abbrev": false, "full_module": "Spec", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

kpriv: Lib.ByteSequence.lbytes 32 -> Lib.ByteSequence.lbytes 32

Prims.Tot

[ "total" ]

[]

[ "Lib.ByteSequence.lbytes", "Spec.Curve25519.scalarmult", "Lib.Sequence.lseq", "Lib.IntTypes.int_t", "Lib.IntTypes.U8", "Lib.IntTypes.SEC", "Prims.l_Forall", "Prims.nat", "Prims.l_imp", "Prims.b2t", "Prims.op_LessThan", "Prims.eq2", "Lib.Sequence.index", "Lib.IntTypes.secret", "Lib.IntTypes.PUB", "Spec.Curve25519.basepoint_lseq", "Lib.Sequence.map", "Lib.IntTypes.uint_t" ]

[]

false

let secret_to_public kpriv =

let basepoint = map secret basepoint_lseq in scalarmult kpriv basepoint

false

Hacl.Spec.Karatsuba.Lemmas.fst

Hacl.Spec.Karatsuba.Lemmas.karatsuba

val karatsuba: pbits:pos // pbits = bits t -> aLen:nat -> a:nat{a < pow2 (pbits * aLen)} -> b:nat{b < pow2 (pbits * aLen)} -> Tot (res:nat{res == a * b}) (decreases aLen)

let rec karatsuba pbits aLen a b = if aLen < 16 || aLen % 2 = 1 then a * b else begin let aLen2 = aLen / 2 in let p = pow2 (aLen2 * pbits) in let a0 = a % p in let a1 = a / p in let b0 = b % p in let b1 = b / p in lemma_bn_halves pbits aLen a; lemma_bn_halves pbits aLen b; let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = karatsuba pbits aLen2 t0 t1 in assert (t23 == t0 * t1); let r01 = karatsuba pbits aLen2 a0 b0 in assert (r01 == a0 * b0); let r23 = karatsuba pbits aLen2 a1 b1 in assert (r23 == a1 * b1); let t01 = r01 + r23 in assert (t01 == a0 * b0 + a1 * b1); let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in lemma_middle_karatsuba a0 a1 b0 b1; assert (t45 == a0 * b1 + a1 * b0); let res = r23 * pow2 (pbits * aLen) + t45 * p + r01 in lemma_karatsuba pbits aLen a0 a1 b0 b1; res end

{ "file_name": "code/bignum/Hacl.Spec.Karatsuba.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 11, "end_line": 185, "start_col": 0, "start_line": 160 }

module Hacl.Spec.Karatsuba.Lemmas open FStar.Mul open Lib.IntTypes #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" type sign = | Positive | Negative let abs (a:nat) (b:nat) : nat = if a b:nat -> Pure (tuple2 sign nat) (requires True) (ensures fun (s, res) -> res == abs a b /\ s == (if a aLen:nat{aLen % 2 = 0} -> Lemma (let p = pow2 (aLen / 2 * pbits) in p * p == pow2 (pbits * aLen)) let lemma_double_p pbits aLen = let p = pow2 (aLen / 2 * pbits) in calc (==) { p * p; (==) { Math.Lemmas.pow2_plus (aLen / 2 * pbits) (aLen / 2 * pbits) } pow2 (aLen / 2 * pbits + aLen / 2 * pbits); (==) { Math.Lemmas.distributivity_add_left (aLen / 2) (aLen / 2) pbits } pow2 ((aLen / 2 * 2) * pbits); (==) { Math.Lemmas.lemma_div_exact aLen 2 } pow2 (aLen * pbits); } val lemma_bn_halves: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a:nat{a < pow2 (pbits * aLen)} -> Lemma (let p = pow2 (aLen / 2 * pbits) in a / p a1:nat -> b0:nat -> b1:nat -> Lemma (let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in t45 == a0 * b1 + a1 * b0) let lemma_middle_karatsuba a0 a1 b0 b1 = let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in match (s0, s1) with | (Positive, Positive) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a0 - a1) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b0 b1 } a0 * b0 + a1 * b1 - ((a0 - a1) * b0 - (a0 - a1) * b1); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b0; Math.Lemmas.distributivity_sub_left a0 a1 b1 } a0 * b0 + a1 * b1 - (a0 * b0 - a1 * b0 - (a0 * b1 - a1 * b1)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Negative) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a1 - a0) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b1 b0 } a0 * b0 + a1 * b1 - ((a1 - a0) * b1 - (a1 - a0) * b0); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b1; Math.Lemmas.distributivity_sub_left a1 a0 b0 } a0 * b0 + a1 * b1 - (a1 * b1 - a0 * b1 - (a1 * b0 - a0 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Positive, Negative) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a0 - a1) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b1 b0 } a0 * b0 + a1 * b1 + ((a0 - a1) * b1 - (a0 - a1) * b0); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b1; Math.Lemmas.distributivity_sub_left a0 a1 b0 } a0 * b0 + a1 * b1 + (a0 * b1 - a1 * b1 - (a0 * b0 - a1 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Positive) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a1 - a0) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b0 b1 } a0 * b0 + a1 * b1 + ((a1 - a0) * b0 - (a1 - a0) * b1); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b0; Math.Lemmas.distributivity_sub_left a1 a0 b1 } a0 * b0 + a1 * b1 + (a1 * b0 - a0 * b0 - (a1 * b1 - a0 * b1)); (==) { } a1 * b0 + a0 * b1; } val lemma_karatsuba: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a0:nat -> a1:nat -> b0:nat -> b1:nat -> Lemma (let aLen2 = aLen / 2 in let p = pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in a1 * b1 * pow2 (pbits * aLen) + (a0 * b1 + a1 * b0) * p + a0 * b0 == a * b) #push-options "--z3rlimit 200" let lemma_karatsuba pbits aLen a0 a1 b0 b1 = let aLen2 = aLen / 2 in let p = pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in calc (==) { a * b; (==) { } (a1 * p + a0) * (b1 * p + b0); (==) { Math.Lemmas.distributivity_add_left (a1 * p) a0 (b1 * p + b0) } a1 * p * (b1 * p + b0) + a0 * (b1 * p + b0); (==) { Math.Lemmas.distributivity_add_right (a1 * p) (b1 * p) b0; Math.Lemmas.distributivity_add_right a0 (b1 * p) b0 } a1 * p * (b1 * p) + a1 * p * b0 + a0 * (b1 * p) + a0 * b0; (==) { Math.Lemmas.paren_mul_right a0 b1 p } a1 * p * (b1 * p) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 p (b1 * p); Math.Lemmas.swap_mul b1 p; Math.Lemmas.paren_mul_right p p b1; Math.Lemmas.swap_mul b1 (p * p) } a1 * (b1 * (p * p)) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 b1 (p * p) } a1 * b1 * (p * p) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { lemma_double_p pbits aLen } a1 * b1 * pow2 (pbits * aLen) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 p b0; Math.Lemmas.swap_mul b0 p; Math.Lemmas.paren_mul_right a1 b0 p } a1 * b1 * pow2 (pbits * aLen) + a1 * b0 * p + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.distributivity_add_left (a1 * b0) (a0 * b1) p } a1 * b1 * pow2 (pbits * aLen) + (a1 * b0 + a0 * b1) * p + a0 * b0; } #pop-options val karatsuba: pbits:pos // pbits = bits t -> aLen:nat -> a:nat{a < pow2 (pbits * aLen)} -> b:nat{b < pow2 (pbits * aLen)} -> Tot (res:nat{res == a * b}) (decreases aLen)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "Lib.IntTypes.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked", "FStar.Calc.fsti.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Karatsuba.Lemmas.fst" }

[ { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

pbits: Prims.pos -> aLen: Prims.nat -> a: Prims.nat{a < Prims.pow2 (pbits * aLen)} -> b: Prims.nat{b < Prims.pow2 (pbits * aLen)} -> Prims.Tot (res: Prims.nat{res == a * b})

Prims.Tot

[ "total", "" ]

[]

[ "Prims.pos", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "Prims.pow2", "FStar.Mul.op_Star", "Prims.op_BarBar", "Prims.op_Equality", "Prims.int", "Prims.op_Modulus", "Prims.bool", "Hacl.Spec.Karatsuba.Lemmas.sign", "Prims.unit", "Hacl.Spec.Karatsuba.Lemmas.lemma_karatsuba", "Prims.op_Addition", "Prims._assert", "Prims.eq2", "Hacl.Spec.Karatsuba.Lemmas.lemma_middle_karatsuba", "Prims.op_Subtraction", "Prims.op_Multiply", "Hacl.Spec.Karatsuba.Lemmas.karatsuba", "FStar.Pervasives.Native.tuple2", "Hacl.Spec.Karatsuba.Lemmas.sign_abs", "Hacl.Spec.Karatsuba.Lemmas.lemma_bn_halves", "Prims.op_Division" ]

[ "recursion" ]

false

let rec karatsuba pbits aLen a b =

if aLen < 16 || aLen % 2 = 1 then a * b else let aLen2 = aLen / 2 in let p = pow2 (aLen2 * pbits) in let a0 = a % p in let a1 = a / p in let b0 = b % p in let b1 = b / p in lemma_bn_halves pbits aLen a; lemma_bn_halves pbits aLen b; let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = karatsuba pbits aLen2 t0 t1 in assert (t23 == t0 * t1); let r01 = karatsuba pbits aLen2 a0 b0 in assert (r01 == a0 * b0); let r23 = karatsuba pbits aLen2 a1 b1 in assert (r23 == a1 * b1); let t01 = r01 + r23 in assert (t01 == a0 * b0 + a1 * b1); let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in lemma_middle_karatsuba a0 a1 b0 b1; assert (t45 == a0 * b1 + a1 * b0); let res = r23 * pow2 (pbits * aLen) + t45 * p + r01 in lemma_karatsuba pbits aLen a0 a1 b0 b1; res

false

Pulse.Lib.BoundedIntegers.fst

Pulse.Lib.BoundedIntegers.add_u32

val add_u32 : x: FStar.UInt32.t -> y: FStar.UInt32.t{Pulse.Lib.BoundedIntegers.ok Pulse.Lib.BoundedIntegers.op_Plus x y} -> FStar.UInt32.t

let add_u32 (x:FStar.UInt32.t) (y:FStar.UInt32.t { ok (+) x y }) = x + y

{ "file_name": "share/steel/examples/pulse/lib/Pulse.Lib.BoundedIntegers.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 72, "end_line": 156, "start_col": 0, "start_line": 156 }

(* Copyright 2023 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 Pulse.Lib.BoundedIntegers module TC = FStar.Tactics.Typeclasses let fits_t (fits:int -> prop) = x:int { fits x } class bounded_int (t:eqtype) = { fits: int -> prop; v : t -> GTot int; u : fits_t fits -> GTot t; ( + ) : (x:t -> y:t -> Pure t (requires fits (v x + v y)) (ensures fun z -> v z == v x + v y)); op_Subtraction : (x:t -> y:t -> Pure t (requires fits (v x - v y)) (ensures fun z -> v z == v x - v y)); ( < ) : (x:t -> y:t -> b:bool { b = (v x < v y)}); ( <= ) : (x:t -> y:t -> b:bool { b = (v x <= v y)}); ( % ) : (x:t -> y:t -> Pure t (requires v y > 0 /\ fits (v x % v y)) (ensures fun z -> v z == v x % v y)); [@@@TC.no_method] properties: squash ( (forall (x:t). {:pattern v x} fits (v x)) ) (* ...todo, add other ops **) } instance bounded_int_int : bounded_int int = { fits = (fun _ -> True); v = id; u = id; ( + ) = (fun x y -> Prims.op_Addition x y); op_Subtraction = (fun x y -> Prims.op_Subtraction x y); ( < ) = (fun x y -> Prims.op_LessThan x y); ( <= ) = (fun x y -> Prims.op_LessThanOrEqual x y); ( % ) = (fun x y -> Prims.op_Modulus x y); properties = () } class bounded_unsigned (t:eqtype) = { [@@@TC.no_method] base:bounded_int t; max_bound:t; [@@@TC.no_method] static_max_bound: bool; [@@@TC.no_method] properties: squash ( (forall (x:t). v x >= 0 /\ (static_max_bound ==> v x <= v max_bound)) /\ (forall (x:nat). x <= v max_bound ==> fits #t x) ) } instance bounded_from_bounded_unsigned (t:eqtype) (c:bounded_unsigned t) : bounded_int t = c.base let safe_add (#t:eqtype) {| c: bounded_unsigned t |} (x y : t) : o:option t { Some? o ==> v (Some?.v o) == v x + v y } = if c.static_max_bound then ( assert ( x <= max_bound); if (y <= max_bound - x) then Some (x + y) else None ) else ( if x <= max_bound then ( assert (fits #t (v (max_bound #t) - v x)); if (y <= max_bound - x) then Some (x + y) else None ) else None ) let safe_mod (#t:eqtype) {| c: bounded_unsigned t |} (x : t) (y : t) : Pure (option t) (requires v y > 0) (ensures fun o -> Some? o ==> v (Some?.v o) == v x % v y) = if c.static_max_bound then Some (x % y) else ( if y <= max_bound then ( assert (fits #t (v x % v y)); Some (x % y) ) else None ) let ok (#t:eqtype) {| c:bounded_int t |} (op: int -> int -> int) (x y:t) = c.fits (op (v x) (v y)) let add (#t:eqtype) {| bounded_int t |} (x:t) (y:t { ok (+) x y }) = x + y let add3 (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) z (x + y)}) = x + y + z //Writing the signature of bounded_int.(+) using Pure //allows this to work, since the type of (x+y) is not refined let add3_alt (#t:eqtype) {| bounded_int t |} (x:t) (y:t) (z:t { ok (+) x y /\ ok (+) (x + y) z}) = x + y + z instance bounded_int_u32 : bounded_int FStar.UInt32.t = { fits = (fun x -> 0 <= x /\ x < 4294967296); v = (fun x -> FStar.UInt32.v x); u = FStar.UInt32.uint_to_t; ( + ) = (fun x y -> FStar.UInt32.add x y); op_Subtraction = (fun x y -> FStar.UInt32.sub x y); ( < ) = FStar.UInt32.(fun x y -> x <^ y); ( <= ) = FStar.UInt32.(fun x y -> x <=^ y); ( % ) = FStar.UInt32.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u32 : bounded_unsigned FStar.UInt32.t = { base = TC.solve; max_bound = 0xfffffffful; static_max_bound = true; properties = () } instance bounded_int_u64 : bounded_int FStar.UInt64.t = { fits = (fun x -> 0 <= x /\ x <= 0xffffffffffffffff); v = (fun x -> FStar.UInt64.v x); u = FStar.UInt64.uint_to_t; ( + ) = (fun x y -> FStar.UInt64.add x y); op_Subtraction = (fun x y -> FStar.UInt64.sub x y); ( < ) = FStar.UInt64.(fun x y -> x <^ y); ( <= ) = FStar.UInt64.(fun x y -> x <=^ y); ( % ) = FStar.UInt64.(fun x y -> x %^ y); properties = () } instance bounded_unsigned_u64 : bounded_unsigned FStar.UInt64.t = { base = TC.solve; max_bound = 0xffffffffffffffffuL; static_max_bound = true; properties = () } let test (t:eqtype) {| _ : bounded_unsigned t |} (x:t) = v x

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Typeclasses.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Pulse.Lib.BoundedIntegers.fst" }

[ { "abbrev": true, "full_module": "FStar.Tactics.Typeclasses", "short_module": "TC" }, { "abbrev": false, "full_module": "Pulse.Lib", "short_module": null }, { "abbrev": false, "full_module": "Pulse.Lib", "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 } ]

{ "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" }

false

x: FStar.UInt32.t -> y: FStar.UInt32.t{Pulse.Lib.BoundedIntegers.ok Pulse.Lib.BoundedIntegers.op_Plus x y} -> FStar.UInt32.t

Prims.Tot

[ "total" ]

[]

[ "FStar.UInt32.t", "Pulse.Lib.BoundedIntegers.ok", "Pulse.Lib.BoundedIntegers.bounded_int_u32", "Pulse.Lib.BoundedIntegers.op_Plus", "Prims.int", "Pulse.Lib.BoundedIntegers.bounded_int_int" ]

[]

false

let add_u32 (x: FStar.UInt32.t) (y: FStar.UInt32.t{ok ( + ) x y}) =

x + y

false

Hacl.Spec.Karatsuba.Lemmas.fst

Hacl.Spec.Karatsuba.Lemmas.lemma_karatsuba

val lemma_karatsuba: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a0:nat -> a1:nat -> b0:nat -> b1:nat -> Lemma (let aLen2 = aLen / 2 in let p = pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in a1 * b1 * pow2 (pbits * aLen) + (a0 * b1 + a1 * b0) * p + a0 * b0 == a * b)

let lemma_karatsuba pbits aLen a0 a1 b0 b1 = let aLen2 = aLen / 2 in let p = pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in calc (==) { a * b; (==) { } (a1 * p + a0) * (b1 * p + b0); (==) { Math.Lemmas.distributivity_add_left (a1 * p) a0 (b1 * p + b0) } a1 * p * (b1 * p + b0) + a0 * (b1 * p + b0); (==) { Math.Lemmas.distributivity_add_right (a1 * p) (b1 * p) b0; Math.Lemmas.distributivity_add_right a0 (b1 * p) b0 } a1 * p * (b1 * p) + a1 * p * b0 + a0 * (b1 * p) + a0 * b0; (==) { Math.Lemmas.paren_mul_right a0 b1 p } a1 * p * (b1 * p) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 p (b1 * p); Math.Lemmas.swap_mul b1 p; Math.Lemmas.paren_mul_right p p b1; Math.Lemmas.swap_mul b1 (p * p) } a1 * (b1 * (p * p)) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 b1 (p * p) } a1 * b1 * (p * p) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { lemma_double_p pbits aLen } a1 * b1 * pow2 (pbits * aLen) + a1 * p * b0 + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.paren_mul_right a1 p b0; Math.Lemmas.swap_mul b0 p; Math.Lemmas.paren_mul_right a1 b0 p } a1 * b1 * pow2 (pbits * aLen) + a1 * b0 * p + a0 * b1 * p + a0 * b0; (==) { Math.Lemmas.distributivity_add_left (a1 * b0) (a0 * b1) p } a1 * b1 * pow2 (pbits * aLen) + (a1 * b0 + a0 * b1) * p + a0 * b0; }

{ "file_name": "code/bignum/Hacl.Spec.Karatsuba.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 4, "end_line": 150, "start_col": 0, "start_line": 122 }

module Hacl.Spec.Karatsuba.Lemmas open FStar.Mul open Lib.IntTypes #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" type sign = | Positive | Negative let abs (a:nat) (b:nat) : nat = if a b:nat -> Pure (tuple2 sign nat) (requires True) (ensures fun (s, res) -> res == abs a b /\ s == (if a aLen:nat{aLen % 2 = 0} -> Lemma (let p = pow2 (aLen / 2 * pbits) in p * p == pow2 (pbits * aLen)) let lemma_double_p pbits aLen = let p = pow2 (aLen / 2 * pbits) in calc (==) { p * p; (==) { Math.Lemmas.pow2_plus (aLen / 2 * pbits) (aLen / 2 * pbits) } pow2 (aLen / 2 * pbits + aLen / 2 * pbits); (==) { Math.Lemmas.distributivity_add_left (aLen / 2) (aLen / 2) pbits } pow2 ((aLen / 2 * 2) * pbits); (==) { Math.Lemmas.lemma_div_exact aLen 2 } pow2 (aLen * pbits); } val lemma_bn_halves: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a:nat{a < pow2 (pbits * aLen)} -> Lemma (let p = pow2 (aLen / 2 * pbits) in a / p a1:nat -> b0:nat -> b1:nat -> Lemma (let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in t45 == a0 * b1 + a1 * b0) let lemma_middle_karatsuba a0 a1 b0 b1 = let s0, t0 = sign_abs a0 a1 in let s1, t1 = sign_abs b0 b1 in let t23 = t0 * t1 in let t01 = a0 * b0 + a1 * b1 in let t45 = if s0 = s1 then t01 - t23 else t01 + t23 in match (s0, s1) with | (Positive, Positive) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a0 - a1) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b0 b1 } a0 * b0 + a1 * b1 - ((a0 - a1) * b0 - (a0 - a1) * b1); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b0; Math.Lemmas.distributivity_sub_left a0 a1 b1 } a0 * b0 + a1 * b1 - (a0 * b0 - a1 * b0 - (a0 * b1 - a1 * b1)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Negative) -> calc (==) { //t45 t01 - t23; (==) { } a0 * b0 + a1 * b1 - (a1 - a0) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b1 b0 } a0 * b0 + a1 * b1 - ((a1 - a0) * b1 - (a1 - a0) * b0); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b1; Math.Lemmas.distributivity_sub_left a1 a0 b0 } a0 * b0 + a1 * b1 - (a1 * b1 - a0 * b1 - (a1 * b0 - a0 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Positive, Negative) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a0 - a1) * (b1 - b0); (==) { Math.Lemmas.distributivity_sub_right (a0 - a1) b1 b0 } a0 * b0 + a1 * b1 + ((a0 - a1) * b1 - (a0 - a1) * b0); (==) { Math.Lemmas.distributivity_sub_left a0 a1 b1; Math.Lemmas.distributivity_sub_left a0 a1 b0 } a0 * b0 + a1 * b1 + (a0 * b1 - a1 * b1 - (a0 * b0 - a1 * b0)); (==) { } a1 * b0 + a0 * b1; } | (Negative, Positive) -> calc (==) { //t45 t01 + t23; (==) { } a0 * b0 + a1 * b1 + (a1 - a0) * (b0 - b1); (==) { Math.Lemmas.distributivity_sub_right (a1 - a0) b0 b1 } a0 * b0 + a1 * b1 + ((a1 - a0) * b0 - (a1 - a0) * b1); (==) { Math.Lemmas.distributivity_sub_left a1 a0 b0; Math.Lemmas.distributivity_sub_left a1 a0 b1 } a0 * b0 + a1 * b1 + (a1 * b0 - a0 * b0 - (a1 * b1 - a0 * b1)); (==) { } a1 * b0 + a0 * b1; } val lemma_karatsuba: pbits:pos -> aLen:nat{aLen % 2 = 0} -> a0:nat -> a1:nat -> b0:nat -> b1:nat -> Lemma (let aLen2 = aLen / 2 in let p = pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in a1 * b1 * pow2 (pbits * aLen) + (a0 * b1 + a1 * b0) * p + a0 * b0 == a * b)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "Lib.IntTypes.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked", "FStar.Calc.fsti.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Karatsuba.Lemmas.fst" }

[ { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Karatsuba", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 200, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

pbits: Prims.pos -> aLen: Prims.nat{aLen % 2 = 0} -> a0: Prims.nat -> a1: Prims.nat -> b0: Prims.nat -> b1: Prims.nat -> FStar.Pervasives.Lemma (ensures (let aLen2 = aLen / 2 in let p = Prims.pow2 (pbits * aLen2) in let a = a1 * p + a0 in let b = b1 * p + b0 in (a1 * b1) * Prims.pow2 (pbits * aLen) + (a0 * b1 + a1 * b0) * p + a0 * b0 == a * b))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.pos", "Prims.nat", "Prims.b2t", "Prims.op_Equality", "Prims.int", "Prims.op_Modulus", "FStar.Calc.calc_finish", "Prims.eq2", "FStar.Mul.op_Star", "Prims.op_Addition", "Prims.pow2", "Prims.Cons", "FStar.Preorder.relation", "Prims.Nil", "Prims.unit", "FStar.Calc.calc_step", "FStar.Calc.calc_init", "FStar.Calc.calc_pack", "Prims.squash", "FStar.Math.Lemmas.distributivity_add_left", "FStar.Math.Lemmas.distributivity_add_right", "FStar.Math.Lemmas.paren_mul_right", "FStar.Math.Lemmas.swap_mul", "Hacl.Spec.Karatsuba.Lemmas.lemma_double_p", "Prims.op_Division" ]

[]

false

true

false

let lemma_karatsuba pbits aLen a0 a1 b0 b1 =

false

Vale.AES.GCM_s.fst

Vale.AES.GCM_s.gcm_encrypt_LE_def

val gcm_encrypt_LE_def (alg: algorithm) (key: seq nat8) (iv: supported_iv_LE) (plain auth: seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32) (ensures fun (c, t) -> True)

let gcm_encrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (plain:seq nat8) (auth:seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32 ) (ensures fun (c, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let c = gctr_encrypt_LE (inc32 j0_BE 1) plain alg key_LE in // Sets the first 64-bit number to 8 * length plain, and the second to 8* length auth let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length plain) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits c) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (c, t)

{ "file_name": "vale/specs/crypto/Vale.AES.GCM_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 8, "end_line": 65, "start_col": 0, "start_line": 39 }

module Vale.AES.GCM_s open Vale.Def.Opaque_s open Vale.Def.Words_s open Vale.Def.Words.Seq_s open Vale.Def.Types_s open Vale.AES.AES_s open Vale.AES.GCTR_s open Vale.AES.GHash_s open FStar.Seq open FStar.Mul unfold type gcm_plain_LE = gctr_plain_LE unfold type gcm_auth_LE = gctr_plain_LE #reset-options "--z3rlimit 30" type supported_iv_LE:eqtype = iv:seq nat8 { 1 <= 8 * (length iv) /\ 8 * (length iv) < pow2_64 } let compute_iv_BE_def (h_LE:quad32) (iv:supported_iv_LE) : quad32 = if 8 * (length iv) = 96 then ( let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE ) else ( let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE ) [@"opaque_to_smt"] let compute_iv_BE = opaque_make compute_iv_BE_def irreducible let compute_iv_BE_reveal = opaque_revealer (`%compute_iv_BE) compute_iv_BE compute_iv_BE_def

{ "checked_file": "/", "dependencies": [ "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Def.Opaque_s.fsti.checked", "Vale.AES.GHash_s.fst.checked", "Vale.AES.GCTR_s.fst.checked", "Vale.AES.AES_s.fst.checked", "prims.fst.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked" ], "interface_file": false, "source_file": "Vale.AES.GCM_s.fst" }

[ { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GCTR_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Seq_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Opaque_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> iv: Vale.AES.GCM_s.supported_iv_LE -> plain: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> auth: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8 * FStar.Seq.Base.seq Vale.Def.Types_s.nat8)

Prims.Pure

[]

[ "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.Def.Types_s.nat8", "Vale.AES.GCM_s.supported_iv_LE", "FStar.Pervasives.Native.Mktuple2", "Vale.Def.Words_s.nat8", "Vale.AES.GCTR_s.gctr_encrypt_LE", "Vale.Def.Types_s.le_quad32_to_bytes", "Vale.Def.Types_s.quad32", "Vale.AES.GHash_s.ghash_LE", "FStar.Seq.Base.append", "FStar.Seq.Base.create", "Vale.Def.Types_s.le_bytes_to_seq_quad32", "Vale.AES.GCTR_s.pad_to_128_bits", "Vale.Def.Types_s.reverse_bytes_quad32", "Vale.Def.Types_s.insert_nat64_def", "Vale.Def.Words_s.Mkfour", "Vale.Def.Types_s.nat32", "FStar.Mul.op_Star", "FStar.Seq.Base.length", "Vale.AES.GCTR_s.inc32", "Vale.AES.GCM_s.compute_iv_BE", "Vale.AES.AES_s.aes_encrypt_LE", "Vale.Def.Words_s.nat32", "Vale.Def.Words.Seq_s.seq_nat8_to_seq_nat32_LE", "FStar.Pervasives.Native.tuple2", "Prims.l_and", "Vale.AES.AES_common_s.is_aes_key", "Prims.b2t", "Prims.op_LessThan", "Vale.Def.Words_s.pow2_32", "Prims.l_True" ]

[]

false

let gcm_encrypt_LE_def (alg: algorithm) (key: seq nat8) (iv: supported_iv_LE) (plain auth: seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32) (ensures fun (c, t) -> True) =

let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let c = gctr_encrypt_LE (inc32 j0_BE 1) plain alg key_LE in let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length plain) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits c) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (c, t)

false

Vale.AES.GCM_s.fst

Vale.AES.GCM_s.gcm_decrypt_LE_def

val gcm_decrypt_LE_def (alg: algorithm) (key: seq nat8) (iv: supported_iv_LE) (cipher auth tag: seq nat8) : Pure (seq nat8 & bool) (requires is_aes_key alg key /\ length cipher < pow2_32 /\ length auth < pow2_32) (ensures fun (p, t) -> True)

let gcm_decrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (cipher:seq nat8) (auth:seq nat8) (tag:seq nat8) : Pure (seq nat8 & bool) (requires is_aes_key alg key /\ length cipher < pow2_32 /\ length auth < pow2_32 ) (ensures fun (p, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let p = gctr_encrypt_LE (inc32 j0_BE 1) cipher alg key_LE in // TODO: Rename gctr_encrypt_LE to gctr_LE let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length cipher) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits cipher) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (p, t = tag)

{ "file_name": "vale/specs/crypto/Vale.AES.GCM_s.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 14, "end_line": 94, "start_col": 0, "start_line": 69 }

module Vale.AES.GCM_s open Vale.Def.Opaque_s open Vale.Def.Words_s open Vale.Def.Words.Seq_s open Vale.Def.Types_s open Vale.AES.AES_s open Vale.AES.GCTR_s open Vale.AES.GHash_s open FStar.Seq open FStar.Mul unfold type gcm_plain_LE = gctr_plain_LE unfold type gcm_auth_LE = gctr_plain_LE #reset-options "--z3rlimit 30" type supported_iv_LE:eqtype = iv:seq nat8 { 1 <= 8 * (length iv) /\ 8 * (length iv) < pow2_64 } let compute_iv_BE_def (h_LE:quad32) (iv:supported_iv_LE) : quad32 = if 8 * (length iv) = 96 then ( let iv_LE = le_bytes_to_quad32 (pad_to_128_bits iv) in let iv_BE = reverse_bytes_quad32 iv_LE in let j0_BE = Mkfour 1 iv_BE.lo1 iv_BE.hi2 iv_BE.hi3 in j0_BE ) else ( let padded_iv_quads = le_bytes_to_seq_quad32 (pad_to_128_bits iv) in let length_BE = insert_nat64_def (Mkfour 0 0 0 0) (8 * length iv) 0 in let length_LE = reverse_bytes_quad32 length_BE in let hash_input_LE = append padded_iv_quads (create 1 length_LE) in let hash_output_LE = ghash_LE h_LE hash_input_LE in reverse_bytes_quad32 hash_output_LE ) [@"opaque_to_smt"] let compute_iv_BE = opaque_make compute_iv_BE_def irreducible let compute_iv_BE_reveal = opaque_revealer (`%compute_iv_BE) compute_iv_BE compute_iv_BE_def // little-endian let gcm_encrypt_LE_def (alg:algorithm) (key:seq nat8) (iv:supported_iv_LE) (plain:seq nat8) (auth:seq nat8) : Pure (seq nat8 & seq nat8) (requires is_aes_key alg key /\ length plain < pow2_32 /\ length auth < pow2_32 ) (ensures fun (c, t) -> True) = let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let c = gctr_encrypt_LE (inc32 j0_BE 1) plain alg key_LE in // Sets the first 64-bit number to 8 * length plain, and the second to 8* length auth let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length plain) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits c) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (c, t) [@"opaque_to_smt"] let gcm_encrypt_LE = opaque_make gcm_encrypt_LE_def irreducible let gcm_encrypt_LE_reveal = opaque_revealer (`%gcm_encrypt_LE) gcm_encrypt_LE gcm_encrypt_LE_def

{ "checked_file": "/", "dependencies": [ "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Def.Opaque_s.fsti.checked", "Vale.AES.GHash_s.fst.checked", "Vale.AES.GCTR_s.fst.checked", "Vale.AES.AES_s.fst.checked", "prims.fst.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked" ], "interface_file": false, "source_file": "Vale.AES.GCM_s.fst" }

[ { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GCTR_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Seq_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Opaque_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 30, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> iv: Vale.AES.GCM_s.supported_iv_LE -> cipher: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> auth: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> tag: FStar.Seq.Base.seq Vale.Def.Types_s.nat8 -> Prims.Pure (FStar.Seq.Base.seq Vale.Def.Types_s.nat8 * Prims.bool)

Prims.Pure

[]

[ "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.Def.Types_s.nat8", "Vale.AES.GCM_s.supported_iv_LE", "FStar.Pervasives.Native.Mktuple2", "Prims.bool", "Prims.op_Equality", "Vale.Def.Words_s.nat8", "Vale.AES.GCTR_s.gctr_encrypt_LE", "Vale.Def.Types_s.le_quad32_to_bytes", "Vale.Def.Types_s.quad32", "Vale.AES.GHash_s.ghash_LE", "FStar.Seq.Base.append", "FStar.Seq.Base.create", "Vale.Def.Types_s.le_bytes_to_seq_quad32", "Vale.AES.GCTR_s.pad_to_128_bits", "Vale.Def.Types_s.reverse_bytes_quad32", "Vale.Def.Types_s.insert_nat64_def", "Vale.Def.Words_s.Mkfour", "Vale.Def.Types_s.nat32", "FStar.Mul.op_Star", "FStar.Seq.Base.length", "Vale.AES.GCTR_s.inc32", "Vale.AES.GCM_s.compute_iv_BE", "Vale.AES.AES_s.aes_encrypt_LE", "Vale.Def.Words_s.nat32", "Vale.Def.Words.Seq_s.seq_nat8_to_seq_nat32_LE", "FStar.Pervasives.Native.tuple2", "Prims.l_and", "Vale.AES.AES_common_s.is_aes_key", "Prims.b2t", "Prims.op_LessThan", "Vale.Def.Words_s.pow2_32", "Prims.l_True" ]

[]

false

let gcm_decrypt_LE_def (alg: algorithm) (key: seq nat8) (iv: supported_iv_LE) (cipher auth tag: seq nat8) : Pure (seq nat8 & bool) (requires is_aes_key alg key /\ length cipher < pow2_32 /\ length auth < pow2_32) (ensures fun (p, t) -> True) =

let key_LE = seq_nat8_to_seq_nat32_LE key in let h_LE = aes_encrypt_LE alg key_LE (Mkfour 0 0 0 0) in let j0_BE = compute_iv_BE h_LE iv in let p = gctr_encrypt_LE (inc32 j0_BE 1) cipher alg key_LE in let lengths_BE = insert_nat64_def (insert_nat64_def (Mkfour 0 0 0 0) (8 * length auth) 1) (8 * length cipher) 0 in let lengths_LE = reverse_bytes_quad32 lengths_BE in let zero_padded_c_LE = le_bytes_to_seq_quad32 (pad_to_128_bits cipher) in let zero_padded_a_LE = le_bytes_to_seq_quad32 (pad_to_128_bits auth) in let hash_input_LE = append zero_padded_a_LE (append zero_padded_c_LE (create 1 lengths_LE)) in let s_LE = ghash_LE h_LE hash_input_LE in let t = gctr_encrypt_LE j0_BE (le_quad32_to_bytes s_LE) alg key_LE in (p, t = tag)

false

Hacl.Spec.K256.Field52.Lemmas4.fst

Hacl.Spec.K256.Field52.Lemmas4.lemma_mul_ab

val lemma_mul_ab (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:nat) : Lemma (let sum0 = a0 * b0 in let sum1 = a0 * b1 + a1 * b0 in let sum2 = a0 * b2 + a1 * b1 + a2 * b0 in let sum3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0 in let sum4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0 in let sum5 = a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 in let sum6 = a2 * b4 + a3 * b3 + a4 * b2 in let sum7 = a3 * b4 + a4 * b3 in let sum8 = a4 * b4 in (a0 + a1 * pow52 + a2 * pow104 + a3 * pow156 + a4 * pow208) * (b0 + b1 * pow52 + b2 * pow104 + b3 * pow156 + b4 * pow208) = sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + pow2 260 * (sum5 + sum6 * pow2 52 + sum7 * pow2 104 + sum8 * pow2 156))

let lemma_mul_ab a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 = let sum0 = a0 * b0 in let sum1 = a0 * b1 + a1 * b0 in let sum2 = a0 * b2 + a1 * b1 + a2 * b0 in let sum3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0 in let sum4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0 in let sum5 = a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 in let sum6 = a2 * b4 + a3 * b3 + a4 * b2 in let sum7 = a3 * b4 + a4 * b3 in let sum8 = a4 * b4 in let b_sum = b0 + b1 * pow52 + b2 * pow104 + b3 * pow156 + b4 * pow208 in calc (==) { (a0 + a1 * pow52 + a2 * pow104 + a3 * pow156 + a4 * pow208) * b_sum; (==) { ML.lemma_distr5 a0 (a1 * pow52) (a2 * pow104) (a3 * pow156) (a4 * pow208) b_sum } a0 * b_sum + a1 * pow52 * b_sum + a2 * pow104 * b_sum + a3 * pow156 * b_sum + a4 * pow208 * b_sum; (==) { ML.lemma_distr5_pow52 a0 b0 b1 b2 b3 b4 } sum0 + a0 * b1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * pow52 * b_sum + a2 * pow104 * b_sum + a3 * pow156 * b_sum + a4 * pow208 * b_sum; (==) { ML.lemma_distr5_pow52_mul_pow a1 b0 b1 b2 b3 b4 52 } sum0 + a0 * b1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b0 * pow2 52 + a1 * b1 * pow2 104 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * pow104 * b_sum + a3 * pow156 * b_sum + a4 * pow208 * b_sum; (==) { ML.lemma_distr5_pow52_mul_pow a2 b0 b1 b2 b3 b4 104 } sum0 + a0 * b1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b0 * pow2 52 + a1 * b1 * pow2 104 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b0 * pow2 104 + a2 * b1 * pow2 156 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * pow156 * b_sum + a4 * pow208 * b_sum; (==) { ML.lemma_distr5_pow52_mul_pow a3 b0 b1 b2 b3 b4 156 } sum0 + a0 * b1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b0 * pow2 52 + a1 * b1 * pow2 104 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b0 * pow2 104 + a2 * b1 * pow2 156 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b0 * pow2 156 + a3 * b1 * pow2 208 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * pow208 * b_sum; (==) { ML.lemma_distr5_pow52_mul_pow a4 b0 b1 b2 b3 b4 208 } sum0 + a0 * b1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b0 * pow2 52 + a1 * b1 * pow2 104 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b0 * pow2 104 + a2 * b1 * pow2 156 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b0 * pow2 156 + a3 * b1 * pow2 208 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b0 * pow2 208 + a4 * b1 * pow2 260 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { Math.Lemmas.distributivity_add_left (a0 * b1) (a1 * b0) (pow2 52) } sum0 + sum1 * pow2 52 + a0 * b2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b1 * pow2 104 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b0 * pow2 104 + a2 * b1 * pow2 156 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b0 * pow2 156 + a3 * b1 * pow2 208 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b0 * pow2 208 + a4 * b1 * pow2 260 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { ML.lemma_distr5 (a0 * b2) (a1 * b1) (a2 * b0) 0 0 (pow2 104) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + a0 * b3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b2 * pow2 156 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b1 * pow2 156 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b0 * pow2 156 + a3 * b1 * pow2 208 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b0 * pow2 208 + a4 * b1 * pow2 260 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { ML.lemma_distr5 (a0 * b3) (a1 * b2) (a2 * b1) (a3 * b0) 0 (pow2 156) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + a0 * b4 * pow2 208 + a1 * b3 * pow2 208 + a1 * b4 * pow2 260 + a2 * b2 * pow2 208 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b1 * pow2 208 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b0 * pow2 208 + a4 * b1 * pow2 260 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { ML.lemma_distr5 (a0 * b4) (a1 * b3) (a2 * b2) (a3 * b1) (a4 * b0) (pow2 208) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + a1 * b4 * pow2 260 + a2 * b3 * pow2 260 + a2 * b4 * pow2 312 + a3 * b2 * pow2 260 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b1 * pow2 260 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { ML.lemma_distr5 (a1 * b4) (a2 * b3) (a3 * b2) (a4 * b1) 0 (pow2 260) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + sum5 * pow2 260 + a2 * b4 * pow2 312 + a3 * b3 * pow2 312 + a3 * b4 * pow2 364 + a4 * b2 * pow2 312 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { ML.lemma_distr5 (a2 * b4) (a3 * b3) (a4 * b2) 0 0 (pow2 312) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + sum5 * pow2 260 + sum6 * pow2 312 + a3 * b4 * pow2 364 + a4 * b3 * pow2 364 + a4 * b4 * pow2 416; (==) { Math.Lemmas.distributivity_add_left (a3 * b4) (a4 * b3) (pow2 364) } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + sum5 * pow2 260 + sum6 * pow2 312 + sum7 * pow2 364 + sum8 * pow2 416; (==) { ML.lemma_distr5_pow52_mul_pow 1 sum5 sum6 sum7 sum8 0 260 } sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + pow2 260 * (sum5 + sum6 * pow2 52 + sum7 * pow2 104 + sum8 * pow2 156); }

{ "file_name": "code/k256/Hacl.Spec.K256.Field52.Lemmas4.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 5, "end_line": 294, "start_col": 0, "start_line": 215 }

module Hacl.Spec.K256.Field52.Lemmas4 open FStar.Mul open Lib.IntTypes module S = Spec.K256 include Hacl.Spec.K256.Field52.Definitions include Hacl.Spec.K256.Field52 module ML = Hacl.Spec.K256.MathLemmas module LD = Hacl.Spec.K256.Field52.Definitions.Lemmas #set-options "--z3rlimit 100 --fuel 0 --ifuel 0" val lemma_nat_r432 (r2 r3 r4 c9 c11 d4 d11 t3 r:nat) : Lemma (requires r2 = c9 % pow2 52 /\ c11 = c9 / pow2 52 + r * pow2 12 * d11 + t3 /\ r3 = c11 % pow2 52 /\ r4 = c11 / pow2 52 + (d4 % pow2 52) % pow2 48) (ensures (r4 * pow2 52 + r3) * pow2 52 + r2 = c9 + r * d11 * pow2 64 + t3 * pow2 52 + (d4 % pow2 48) * pow2 104) let lemma_nat_r432 r2 r3 r4 c9 c11 d4 d11 t3 r = let k = d4 % pow2 48 in calc (==) { (r4 * pow2 52 + r3) * pow2 52 + r2; (==) { Math.Lemmas.pow2_modulo_modulo_lemma_1 d4 48 52 } ((c11 / pow2 52 + k) * pow2 52 + c11 % pow2 52) * pow2 52 + r2; (==) { ML.lemma_distr_eucl c11 k } (c9 / pow2 52 + r * pow2 12 * d11 + t3 + k * pow2 52) * pow2 52 + c9 % pow2 52; (==) { ML.lemma_distr_eucl c9 (r * pow2 12 * d11 + t3 + k * pow2 52) } c9 + (r * pow2 12 * d11 + t3 + k * pow2 52) * pow2 52; (==) { ML.lemma_distr_pow (r * pow2 12 * d11 + t3) k 52 52 } c9 + (r * pow2 12 * d11 + t3) * pow2 52 + k * pow2 104; (==) { ML.lemma_swap_mul3 r (pow2 12) d11 } c9 + (r * d11 * pow2 12 + t3) * pow2 52 + k * pow2 104; (==) { ML.lemma_distr_pow t3 (r * d11) 12 52 } c9 + r * d11 * pow2 64 + t3 * pow2 52 + k * pow2 104; } val lemma_nat_r4321 (r1 r2 r3 r4 c6 c9 c11 d4 d10 d11 t3 r sum2:nat) : Lemma (requires d11 = d10 / pow2 64 /\ r1 = c6 % pow2 52 /\ c9 = c6 / pow2 52 + sum2 + r * (d10 % pow2 64) /\ r2 = c9 % pow2 52 /\ c11 = c9 / pow2 52 + r * pow2 12 * d11 + t3 /\ r3 = c11 % pow2 52 /\ r4 = c11 / pow2 52 + (d4 % pow2 52) % pow2 48) (ensures ((r4 * pow2 52 + r3) * pow2 52 + r2) * pow2 52 + r1 = c6 + sum2 * pow2 52 + r * d10 * pow2 52 + t3 * pow2 104 + (d4 % pow2 48) * pow2 156) let lemma_nat_r4321 r1 r2 r3 r4 c6 c9 c11 d4 d10 d11 t3 r sum2 = let k = d4 % pow2 48 in let tmp1 = t3 * pow2 52 + k * pow2 104 in calc (==) { ((r4 * pow2 52 + r3) * pow2 52 + r2) * pow2 52 + r1; (==) { lemma_nat_r432 r2 r3 r4 c9 c11 d4 d11 t3 r } (c9 + r * d11 * pow2 64 + tmp1) * pow2 52 + r1; (==) { } (c6 / pow2 52 + sum2 + r * (d10 % pow2 64) + r * d11 * pow2 64 + tmp1) * pow2 52 + c6 % pow2 52; (==) { ML.lemma_distr_eucl_mul r d10 (pow2 64) } (c6 / pow2 52 + sum2 + r * d10 + tmp1) * pow2 52 + c6 % pow2 52; (==) { ML.lemma_distr_eucl c6 (sum2 + r * d10 + tmp1) } c6 + (sum2 + r * d10 + tmp1) * pow2 52; (==) { Math.Lemmas.distributivity_add_left (sum2 + r * d10) tmp1 (pow2 52) } c6 + (sum2 + r * d10) * pow2 52 + tmp1 * pow2 52; (==) { Math.Lemmas.distributivity_add_left sum2 (r * d10) (pow2 52) } c6 + sum2 * pow2 52 + r * d10 * pow2 52 + tmp1 * pow2 52; (==) { ML.lemma_distr_pow_pow t3 52 k 104 52 } c6 + sum2 * pow2 52 + r * d10 * pow2 52 + t3 * pow2 104 + k * pow2 156; } val lemma_nat_r43210 (r0 r1 r2 r3 r4 c3 c6 c9 c11 d4 d8 d10 d11 t3 r sum1 sum2 sum7:nat) : Lemma (requires d10 == d8 / pow2 52 + sum7 /\ r0 = c3 % pow2 52 /\ c6 = c3 / pow2 52 + sum1 + d8 % pow2 52 * r /\ d11 = d10 / pow2 64 /\ r1 = c6 % pow2 52 /\ c9 = c6 / pow2 52 + sum2 + r * (d10 % pow2 64) /\ r2 = c9 % pow2 52 /\ c11 = c9 / pow2 52 + r * pow2 12 * d11 + t3 /\ r3 = c11 % pow2 52 /\ r4 = c11 / pow2 52 + (d4 % pow2 52) % pow2 48) (ensures r0 + r1 * pow52 + r2 * pow104 + r3 * pow156 + r4 * pow208 = c3 + (sum1 + r * d8) * pow2 52 + (sum2 + r * sum7) * pow2 104 + t3 * pow2 156 + (d4 % pow2 48) * pow2 208) let lemma_nat_r43210 r0 r1 r2 r3 r4 c3 c6 c9 c11 d4 d8 d10 d11 t3 r sum1 sum2 sum7 = let k = d4 % pow2 48 in let tmp1 = sum2 * pow2 52 + t3 * pow2 104 + k * pow2 156 in calc (==) { // tmp1 * pow2 52 (sum2 * pow2 52 + t3 * pow2 104 + k * pow2 156) * pow2 52; (==) { ML.lemma_distr_pow (sum2 * pow2 52 + t3 * pow2 104) k 156 52 } (sum2 * pow2 52 + t3 * pow2 104) * pow2 52 + k * pow2 208; (==) { ML.lemma_distr_pow_pow sum2 52 t3 104 52 } sum2 * pow2 104 + t3 * pow2 156 + k * pow2 208; }; calc (==) { r0 + r1 * pow52 + r2 * pow104 + r3 * pow156 + r4 * pow208; (==) { ML.lemma_as_nat_horner r0 r1 r2 r3 r4 } (((r4 * pow2 52 + r3) * pow2 52 + r2) * pow2 52 + r1) * pow2 52 + r0; (==) { lemma_nat_r4321 r1 r2 r3 r4 c6 c9 c11 d4 d10 d11 t3 r sum2 } (c3 / pow2 52 + sum1 + d8 % pow2 52 * r + r * (d8 / pow2 52 + sum7) * pow2 52 + tmp1) * pow2 52 + c3 % pow2 52; (==) { ML.lemma_distr_eucl_mul_add r d8 sum7 (pow2 52) } (c3 / pow2 52 + sum1 + r * d8 + r * sum7 * pow2 52 + tmp1) * pow2 52 + c3 % pow2 52; (==) { ML.lemma_distr_eucl c3 (sum1 + r * d8 + r * sum7 * pow2 52 + tmp1) } c3 + (sum1 + r * d8 + r * sum7 * pow2 52 + tmp1) * pow2 52; (==) { ML.lemma_distr_pow (sum1 + r * d8 + tmp1) (r * sum7) 52 52 } c3 + (sum1 + r * d8 + tmp1) * pow2 52 + r * sum7 * pow2 104; (==) { Math.Lemmas.distributivity_add_left (sum1 + r * d8) tmp1 (pow2 52) } c3 + (sum1 + r * d8) * pow2 52 + sum2 * pow2 104 + t3 * pow2 156 + k * pow2 208 + r * sum7 * pow2 104; (==) { Math.Lemmas.distributivity_add_left sum2 (r * sum7) (pow2 104) } c3 + (sum1 + r * d8) * pow2 52 + (sum2 + r * sum7) * pow2 104 + t3 * pow2 156 + k * pow2 208; } val simplify_c3 (d4 r sum5:nat) : Lemma (requires r % pow2 4 = 0) (ensures (let k = (d4 / pow2 52 + sum5) % pow2 52 in ((d4 % pow2 52) / pow2 48 + k * pow2 4) * (r / pow2 4) == (d4 / pow2 48) * (r / pow2 4) + (k - (d4 / pow2 52)) * r)) let simplify_c3 d4 r sum5 = let k = (d4 / pow2 52 + sum5) % pow2 52 in calc (==) { //simplify c3 ((d4 % pow2 52) / pow2 48 + k * pow2 4) * (r / pow2 4); (==) { Math.Lemmas.pow2_modulo_division_lemma_1 d4 48 52 } ((d4 / pow2 48) % pow2 4 + k * pow2 4) * (r / pow2 4); (==) { Math.Lemmas.euclidean_division_definition (d4 / pow2 48) (pow2 4) } (d4 / pow2 48 - (d4 / pow2 48 / pow2 4) * pow2 4 + k * pow2 4) * (r / pow2 4); (==) { Math.Lemmas.division_multiplication_lemma d4 (pow2 48) (pow2 4); Math.Lemmas.pow2_plus 48 4 } (d4 / pow2 48 - (d4 / pow2 52) * pow2 4 + k * pow2 4) * (r / pow2 4); (==) { Math.Lemmas.distributivity_sub_left k (d4 / pow2 52) (pow2 4) } (d4 / pow2 48 + (k - d4 / pow2 52) * pow2 4) * (r / pow2 4); (==) { Math.Lemmas.distributivity_add_left (d4 / pow2 48) ((k - d4 / pow2 52) * pow2 4) (r / pow2 4) } (d4 / pow2 48) * (r / pow2 4) + (k - d4 / pow2 52) * pow2 4 * (r / pow2 4); (==) { Math.Lemmas.paren_mul_right (k - d4 / pow2 52) (pow2 4) (r / pow2 4); Math.Lemmas.div_exact_r r (pow2 4) } (d4 / pow2 48) * (r / pow2 4) + (k - d4 / pow2 52) * r; } val lemma_nat_r43210_mod_prime (c3 d4 d8 t3 r sum0 sum1 sum2 sum3 sum4 sum5 sum6 sum7 sum8: nat) : Lemma (requires r = 0x1000003D10 /\ d4 = (sum3 + r * (sum8 % pow2 64)) / pow2 52 + sum4 + r * pow2 12 * (sum8 / pow2 64) /\ t3 = (sum3 + r * (sum8 % pow2 64)) % pow2 52 /\ d8 = (d4 / pow2 52 + sum5) / pow2 52 + sum6 /\ c3 = sum0 + ((d4 % pow2 52) / pow2 48 + ((d4 / pow2 52 + sum5) % pow2 52) * pow2 4) * (r / pow2 4)) (ensures (c3 + (sum1 + r * d8) * pow2 52 + (sum2 + r * sum7) * pow2 104 + t3 * pow2 156 + (d4 % pow2 48) * pow2 208) % S.prime == (sum0 + sum5 * r + (sum1 + sum6 * r) * pow2 52 + (sum2 + r * sum7) * pow2 104 + (sum3 + r * sum8) * pow2 156 + sum4 * pow2 208) % S.prime) let lemma_nat_r43210_mod_prime c3 d4 d8 t3 r sum0 sum1 sum2 sum3 sum4 sum5 sum6 sum7 sum8 = let tmp2 = sum3 + r * (sum8 % pow2 64) in let tmp1 = d4 / pow2 52 + sum5 in let tmp0 = sum0 + (tmp1 % pow2 52 - d4 / pow2 52) * r in let d4mod = (d4 % pow2 48) * pow2 208 + (d4 / pow2 48) * 0x1000003D1 in calc (==) { c3 + (d4 % pow2 48) * pow2 208 + (sum1 + r * d8) * pow2 52; (==) { simplify_c3 d4 r sum5; assert_norm (0x1000003D10 / pow2 4 = 0x1000003D1) } d4mod + tmp0 + (sum1 + r * d8) * pow2 52; (==) { Math.Lemmas.distributivity_add_left sum1 (r * d8) (pow2 52) } d4mod + sum0 + (tmp1 % pow2 52 - d4 / pow2 52) * r + sum1 * pow2 52 + r * (tmp1 / pow2 52 + sum6) * pow2 52; (==) { Math.Lemmas.distributivity_sub_left (tmp1 % pow2 52) (d4 / pow2 52) r } d4mod + sum0 + (tmp1 % pow2 52) * r - d4 / pow2 52 * r + sum1 * pow2 52 + r * (tmp1 / pow2 52 + sum6) * pow2 52; (==) { ML.lemma_distr_eucl_mul_add r tmp1 sum6 (pow2 52) } d4mod + sum0 + r * (d4 / pow2 52 + sum5) - d4 / pow2 52 * r + sum1 * pow2 52 + r * sum6 * pow2 52; (==) { Math.Lemmas.distributivity_add_right r (d4 / pow2 52) sum5 } d4mod + sum0 + r * sum5 + sum1 * pow2 52 + r * sum6 * pow2 52; (==) { Math.Lemmas.distributivity_add_left sum1 (r * sum6) (pow2 52) } d4mod + sum0 + r * sum5 + (sum1 + r * sum6) * pow2 52; }; calc (==) { //t3 * pow2 156 + d4 * pow2 208; (tmp2 % pow2 52) * pow2 156 + (tmp2 / pow2 52 + sum4 + r * pow2 12 * (sum8 / pow2 64)) * pow2 208; (==) { ML.lemma_distr_pow (tmp2 % pow2 52) (tmp2 / pow2 52 + sum4 + r * pow2 12 * (sum8 / pow2 64)) 52 156 } (tmp2 % pow2 52 + (tmp2 / pow2 52 + sum4 + r * pow2 12 * (sum8 / pow2 64)) * pow2 52) * pow2 156; (==) { ML.lemma_distr_eucl_mul_add 1 tmp2 (sum4 + r * pow2 12 * (sum8 / pow2 64)) (pow2 52) } (tmp2 + (sum4 + r * pow2 12 * (sum8 / pow2 64)) * pow2 52) * pow2 156; (==) { ML.lemma_swap_mul3 r (pow2 12) (sum8 / pow2 64) } (tmp2 + (sum4 + r * (sum8 / pow2 64) * pow2 12) * pow2 52) * pow2 156; (==) { ML.lemma_distr_pow sum4 (r * (sum8 / pow2 64)) 12 52 } (sum3 + r * (sum8 % pow2 64) + sum4 * pow2 52 + r * (sum8 / pow2 64) * pow2 64) * pow2 156; (==) { ML.lemma_distr_eucl_mul r sum8 (pow2 64) } (sum3 + r * sum8 + sum4 * pow2 52) * pow2 156; (==) { ML.lemma_distr_pow (sum3 + r * sum8) sum4 52 156 } (sum3 + r * sum8) * pow2 156 + sum4 * pow2 208; }; LD.as_nat_mod_prime (sum0 + r * sum5) (sum1 + r * sum6) (sum2 + r * sum7) t3 d4 val lemma_mul_ab (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4:nat) : Lemma (let sum0 = a0 * b0 in let sum1 = a0 * b1 + a1 * b0 in let sum2 = a0 * b2 + a1 * b1 + a2 * b0 in let sum3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0 in let sum4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0 in let sum5 = a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 in let sum6 = a2 * b4 + a3 * b3 + a4 * b2 in let sum7 = a3 * b4 + a4 * b3 in let sum8 = a4 * b4 in (a0 + a1 * pow52 + a2 * pow104 + a3 * pow156 + a4 * pow208) * (b0 + b1 * pow52 + b2 * pow104 + b3 * pow156 + b4 * pow208) = sum0 + sum1 * pow2 52 + sum2 * pow2 104 + sum3 * pow2 156 + sum4 * pow2 208 + pow2 260 * (sum5 + sum6 * pow2 52 + sum7 * pow2 104 + sum8 * pow2 156))

{ "checked_file": "/", "dependencies": [ "Spec.K256.fst.checked", "prims.fst.checked", "Lib.IntTypes.fsti.checked", "Hacl.Spec.K256.MathLemmas.fst.checked", "Hacl.Spec.K256.Field52.Definitions.Lemmas.fst.checked", "Hacl.Spec.K256.Field52.Definitions.fst.checked", "Hacl.Spec.K256.Field52.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked", "FStar.Calc.fsti.checked" ], "interface_file": false, "source_file": "Hacl.Spec.K256.Field52.Lemmas4.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.K256.Field52.Definitions.Lemmas", "short_module": "LD" }, { "abbrev": true, "full_module": "Hacl.Spec.K256.MathLemmas", "short_module": "ML" }, { "abbrev": false, "full_module": "Hacl.Spec.K256.Field52", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.K256.Field52.Definitions", "short_module": null }, { "abbrev": true, "full_module": "Spec.K256", "short_module": "S" }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.K256.Field52", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.K256.Field52", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 100, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

a0: Prims.nat -> a1: Prims.nat -> a2: Prims.nat -> a3: Prims.nat -> a4: Prims.nat -> b0: Prims.nat -> b1: Prims.nat -> b2: Prims.nat -> b3: Prims.nat -> b4: Prims.nat -> FStar.Pervasives.Lemma (ensures (let sum0 = a0 * b0 in let sum1 = a0 * b1 + a1 * b0 in let sum2 = a0 * b2 + a1 * b1 + a2 * b0 in let sum3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0 in let sum4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0 in let sum5 = a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 in let sum6 = a2 * b4 + a3 * b3 + a4 * b2 in let sum7 = a3 * b4 + a4 * b3 in let sum8 = a4 * b4 in (a0 + a1 * Hacl.Spec.K256.Field52.Definitions.pow52 + a2 * Hacl.Spec.K256.Field52.Definitions.pow104 + a3 * Hacl.Spec.K256.Field52.Definitions.pow156 + a4 * Hacl.Spec.K256.Field52.Definitions.pow208) * (b0 + b1 * Hacl.Spec.K256.Field52.Definitions.pow52 + b2 * Hacl.Spec.K256.Field52.Definitions.pow104 + b3 * Hacl.Spec.K256.Field52.Definitions.pow156 + b4 * Hacl.Spec.K256.Field52.Definitions.pow208) = sum0 + sum1 * Prims.pow2 52 + sum2 * Prims.pow2 104 + sum3 * Prims.pow2 156 + sum4 * Prims.pow2 208 + Prims.pow2 260 * (sum5 + sum6 * Prims.pow2 52 + sum7 * Prims.pow2 104 + sum8 * Prims.pow2 156)))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.nat", "FStar.Calc.calc_finish", "Prims.int", "Prims.eq2", "FStar.Mul.op_Star", "Prims.op_Addition", "Hacl.Spec.K256.Field52.Definitions.pow52", "Hacl.Spec.K256.Field52.Definitions.pow104", "Hacl.Spec.K256.Field52.Definitions.pow156", "Hacl.Spec.K256.Field52.Definitions.pow208", "Prims.pow2", "Prims.Cons", "FStar.Preorder.relation", "Prims.Nil", "Prims.unit", "FStar.Calc.calc_step", "FStar.Calc.calc_init", "FStar.Calc.calc_pack", "Hacl.Spec.K256.MathLemmas.lemma_distr5", "Prims.squash", "Hacl.Spec.K256.MathLemmas.lemma_distr5_pow52", "Hacl.Spec.K256.MathLemmas.lemma_distr5_pow52_mul_pow", "FStar.Math.Lemmas.distributivity_add_left" ]

[]

false

true

false

let lemma_mul_ab a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 =

false

Steel.ST.C.Types.Base.fsti

Steel.ST.C.Types.Base.assert_null

val assert_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost unit opened (pts_to_or_null p v) (fun _ -> emp) (p == null _) (fun _ -> True)

let assert_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost unit opened (pts_to_or_null p v) (fun _ -> emp) (p == null _) (fun _ -> True) = rewrite (pts_to_or_null p v) emp

{ "file_name": "lib/steel/c/Steel.ST.C.Types.Base.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 34, "end_line": 135, "start_col": 0, "start_line": 124 }

module Steel.ST.C.Types.Base open Steel.ST.Util module P = Steel.FractionalPermission /// Helper to compose two permissions into one val prod_perm (p1 p2: P.perm) : Pure P.perm (requires True) (ensures (fun p -> ((p1 `P.lesser_equal_perm` P.full_perm /\ p2 `P.lesser_equal_perm` P.full_perm) ==> p `P.lesser_equal_perm` P.full_perm) /\ p.v == (let open FStar.Real in p1.v *. p2.v) )) [@@noextract_to "krml"] // proof-only val typedef (t: Type0) : Type0 inline_for_extraction [@@noextract_to "krml"] let typeof (#t: Type0) (td: typedef t) : Tot Type0 = t val fractionable (#t: Type0) (td: typedef t) (x: t) : GTot prop val mk_fraction (#t: Type0) (td: typedef t) (x: t) (p: P.perm) : Ghost t (requires (fractionable td x)) (ensures (fun y -> p `P.lesser_equal_perm` P.full_perm ==> fractionable td y)) val mk_fraction_full (#t: Type0) (td: typedef t) (x: t) : Lemma (requires (fractionable td x)) (ensures (mk_fraction td x P.full_perm == x)) [SMTPat (mk_fraction td x P.full_perm)] val mk_fraction_compose (#t: Type0) (td: typedef t) (x: t) (p1 p2: P.perm) : Lemma (requires (fractionable td x /\ p1 `P.lesser_equal_perm` P.full_perm /\ p2 `P.lesser_equal_perm` P.full_perm)) (ensures (mk_fraction td (mk_fraction td x p1) p2 == mk_fraction td x (p1 `prod_perm` p2))) val full (#t: Type0) (td: typedef t) (v: t) : GTot prop val uninitialized (#t: Type0) (td: typedef t) : Ghost t (requires True) (ensures (fun y -> full td y /\ fractionable td y)) val unknown (#t: Type0) (td: typedef t) : Ghost t (requires True) (ensures (fun y -> fractionable td y)) val full_not_unknown (#t: Type) (td: typedef t) (v: t) : Lemma (requires (full td v)) (ensures (~ (v == unknown td))) [SMTPat (full td v)] val mk_fraction_unknown (#t: Type0) (td: typedef t) (p: P.perm) : Lemma (ensures (mk_fraction td (unknown td) p == unknown td)) val mk_fraction_eq_unknown (#t: Type0) (td: typedef t) (v: t) (p: P.perm) : Lemma (requires (fractionable td v /\ mk_fraction td v p == unknown td)) (ensures (v == unknown td)) // To be extracted as: void* [@@noextract_to "krml"] // primitive val void_ptr : Type0 // To be extracted as: NULL [@@noextract_to "krml"] // primitive val void_null: void_ptr // To be extracted as: *t [@@noextract_to "krml"] // primitive val ptr_gen ([@@@unused] t: Type) : Type0 [@@noextract_to "krml"] // primitive val null_gen (t: Type) : Tot (ptr_gen t) val ghost_void_ptr_of_ptr_gen (#[@@@unused] t: Type) (x: ptr_gen t) : GTot void_ptr val ghost_ptr_gen_of_void_ptr (x: void_ptr) ([@@@unused] t: Type) : GTot (ptr_gen t) val ghost_void_ptr_of_ptr_gen_of_void_ptr (x: void_ptr) (t: Type) : Lemma (ghost_void_ptr_of_ptr_gen (ghost_ptr_gen_of_void_ptr x t) == x) [SMTPat (ghost_void_ptr_of_ptr_gen (ghost_ptr_gen_of_void_ptr x t))] val ghost_ptr_gen_of_void_ptr_of_ptr_gen (#t: Type) (x: ptr_gen t) : Lemma (ghost_ptr_gen_of_void_ptr (ghost_void_ptr_of_ptr_gen x) t == x) [SMTPat (ghost_ptr_gen_of_void_ptr (ghost_void_ptr_of_ptr_gen x) t)] inline_for_extraction [@@noextract_to "krml"] // primitive let ptr (#t: Type) (td: typedef t) : Tot Type0 = ptr_gen t inline_for_extraction [@@noextract_to "krml"] // primitive let null (#t: Type) (td: typedef t) : Tot (ptr td) = null_gen t inline_for_extraction [@@noextract_to "krml"] let ref (#t: Type) (td: typedef t) : Tot Type0 = (p: ptr td { ~ (p == null td) }) val pts_to (#t: Type) (#td: typedef t) (r: ref td) ([@@@smt_fallback] v: Ghost.erased t) : vprop let pts_to_or_null (#t: Type) (#td: typedef t) (p: ptr td) (v: Ghost.erased t) : vprop = if FStar.StrongExcludedMiddle.strong_excluded_middle (p == null _) then emp else pts_to p v [@@noextract_to "krml"] // primitive val is_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STAtomicBase bool false opened Unobservable (pts_to_or_null p v) (fun _ -> pts_to_or_null p v) (True) (fun res -> res == true <==> p == null _)

{ "checked_file": "/", "dependencies": [ "Steel.ST.Util.fsti.checked", "Steel.FractionalPermission.fst.checked", "prims.fst.checked", "FStar.StrongExcludedMiddle.fst.checked", "FStar.Real.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Ghost.fsti.checked" ], "interface_file": false, "source_file": "Steel.ST.C.Types.Base.fsti" }

[ { "abbrev": true, "full_module": "Steel.FractionalPermission", "short_module": "P" }, { "abbrev": false, "full_module": "Steel.ST.Util", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "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 } ]

{ "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" }

false

p: Steel.ST.C.Types.Base.ptr td -> Steel.ST.Effect.Ghost.STGhost Prims.unit

Steel.ST.Effect.Ghost.STGhost

[]

[ "Steel.Memory.inames", "Steel.ST.C.Types.Base.typedef", "FStar.Ghost.erased", "Steel.ST.C.Types.Base.ptr", "Steel.ST.Util.rewrite", "Steel.ST.C.Types.Base.pts_to_or_null", "Steel.Effect.Common.emp", "Prims.unit", "Steel.Effect.Common.vprop", "Prims.eq2", "Steel.ST.C.Types.Base.null", "Prims.l_True" ]

[]

false

true

false

let assert_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost unit opened (pts_to_or_null p v) (fun _ -> emp) (p == null _) (fun _ -> True) =

rewrite (pts_to_or_null p v) emp

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128

val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code

let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ())))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 50, "end_line": 42, "start_col": 0, "start_line": 35 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_code

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.InsVector.va_code_Vmr", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft128_1", "Vale.AES.PPC64LE.PolyOps.va_code_VPolyAnd", "Vale.PPC64LE.InsVector.va_code_Vcmpequw", "Vale.PPC64LE.InsVector.va_code_Vspltw", "Vale.AES.PPC64LE.PolyOps.va_code_VPolyAdd", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_code" ]

[]

false

true

false

let va_code_ShiftKey1_128 () =

(va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ())))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_gf128_power

val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool

let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ())))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 31, "end_line": 195, "start_col": 0, "start_line": 184 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_pbool

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_pbool_and", "Vale.PPC64LE.InsVector.va_codegen_success_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.PPC64LE.InsBasic.va_codegen_success_LoadImmShl64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Prims.op_Minus", "Vale.PPC64LE.InsVector.va_codegen_success_Mtvsrws", "Vale.PPC64LE.InsVector.va_codegen_success_Vsldoi", "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_128", "Vale.PPC64LE.Decls.va_ttrue", "Vale.PPC64LE.Decls.va_pbool" ]

[]

false

true

false

let va_codegen_success_ShiftKey1_gf128_power () =

(va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (- 15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (- 32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ())))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wp_ShiftKey1_128

val va_wp_ShiftKey1_128 (f: poly) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0

let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (())))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 85, "end_line": 144, "start_col": 0, "start_line": 132 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Vale.Math.Poly2_s.poly -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Type0

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Prims.l_and", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Prims.eq2", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.PPC64LE.Decls.va_get_vec", "Vale.Math.Poly2_s.monomial", "Vale.Math.Poly2_s.reverse", "Vale.Math.Poly2_s.shift", "Vale.Math.Poly2_s.add", "Prims.op_Minus", "Prims.l_Forall", "Vale.PPC64LE.Memory.quad32", "Prims.l_imp", "Vale.AES.GF128.shift_key_1", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.Decls.va_upd_vec" ]

[]

false

true

let va_wp_ShiftKey1_128 (f: poly) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0 =

(va_get_ok va_s0 /\ (let h:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let h1:Vale.Math.Poly2_s.poly = Vale.Math.Poly2_s.shift h 1 in let offset:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (- 1)) 127) /\ (forall (va_x_v1: quad32) (va_x_v2: quad32) (va_x_v3: quad32). let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let h:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let h1:Vale.Math.Poly2_s.poly = Vale.Math.Poly2_s.shift h 1 in let offset:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (())))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_128

val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool

let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ()))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 69, "end_line": 54, "start_col": 0, "start_line": 46 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_pbool

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_pbool_and", "Vale.PPC64LE.InsVector.va_codegen_success_Vmr", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_ShiftLeft128_1", "Vale.AES.PPC64LE.PolyOps.va_codegen_success_VPolyAnd", "Vale.PPC64LE.InsVector.va_codegen_success_Vcmpequw", "Vale.PPC64LE.InsVector.va_codegen_success_Vspltw", "Vale.AES.PPC64LE.PolyOps.va_codegen_success_VPolyAdd", "Vale.PPC64LE.Decls.va_ttrue", "Vale.PPC64LE.Decls.va_pbool" ]

[]

false

true

false

let va_codegen_success_ShiftKey1_128 () =

(va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ()))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wp_ShiftKey1_gf128_power

val va_wp_ShiftKey1_gf128_power (h: poly) (n: nat) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0

let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (())))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 21, "end_line": 281, "start_col": 0, "start_line": 272 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Type0

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Prims.nat", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Prims.l_and", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Prims.eq2", "Vale.AES.GHash_BE.g_power", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.PPC64LE.Decls.va_get_vec", "Prims.l_Forall", "Vale.PPC64LE.Memory.nat64", "Vale.PPC64LE.Memory.quad32", "Prims.l_imp", "Vale.AES.GHash_BE.gf128_power", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.PPC64LE.Decls.va_upd_reg" ]

[]

false

true

let va_wp_ShiftKey1_gf128_power (h: poly) (n: nat) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0 =

(va_get_ok va_s0 /\ (let hn:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10: nat64) (va_x_v1: quad32) (va_x_v2: quad32) (va_x_v3: quad32) (va_x_v4: quad32) (va_x_v5: quad32). let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let hn:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (())))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers

val va_code_Gf128_powers : va_dummy:unit -> Tot va_code

let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ())))))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 21, "end_line": 328, "start_col": 0, "start_line": 315 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_code

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.InsBasic.va_code_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Load128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.Arch.HeapTypes_s.Secret", "Vale.PPC64LE.InsVector.va_code_Vmr", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer", "Vale.AES.PPC64LE.GF128_Mul.va_code_Gf128MulRev128", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_code" ]

[]

false

true

false

let va_code_Gf128_powers () =

(va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index ( va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ())))))))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power

val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code

let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ()))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 18, "end_line": 180, "start_col": 0, "start_line": 171 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_code

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.InsVector.va_code_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.PPC64LE.InsBasic.va_code_LoadImmShl64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Prims.op_Minus", "Vale.PPC64LE.InsVector.va_code_Mtvsrws", "Vale.PPC64LE.InsVector.va_code_Vsldoi", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.Decls.va_code" ]

[]

false

true

false

let va_code_ShiftKey1_gf128_power () =

(va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (- 15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (- 32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ()))))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_codegen_success_Gf128_powers

val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool

let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ()))))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 42, "end_line": 347, "start_col": 0, "start_line": 332 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_dummy: Prims.unit -> Vale.PPC64LE.Decls.va_pbool

Prims.Tot

[ "total" ]

[]

[ "Prims.unit", "Vale.PPC64LE.Decls.va_pbool_and", "Vale.PPC64LE.InsBasic.va_codegen_success_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_codegen_success_Load128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.Arch.HeapTypes_s.Secret", "Vale.PPC64LE.InsVector.va_codegen_success_Vmr", "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_ShiftKey1_gf128_power", "Vale.PPC64LE.InsVector.va_codegen_success_Store128_byte16_buffer", "Vale.AES.PPC64LE.GF128_Mul.va_codegen_success_Gf128MulRev128", "Vale.PPC64LE.InsVector.va_codegen_success_Store128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_ttrue", "Vale.PPC64LE.Decls.va_pbool" ]

[]

false

true

false

let va_codegen_success_Gf128_powers () =

(va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ()))))))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_codegen_success_Keyhash_init

val va_codegen_success_Keyhash_init : alg:algorithm -> Tot va_pbool

let va_codegen_success_Keyhash_init alg = (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Gf128_powers ()) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ()))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 24, "end_line": 508, "start_col": 0, "start_line": 501 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b)) //-- //-- Keyhash_init [@ "opaque_to_smt" va_qattr] let va_code_Keyhash_init alg = (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ()))))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> Vale.PPC64LE.Decls.va_pbool

Prims.Tot

[ "total" ]

[]

[ "Vale.AES.AES_common_s.algorithm", "Vale.PPC64LE.Decls.va_pbool_and", "Vale.PPC64LE.InsMem.va_codegen_success_CreateHeaplets", "Vale.PPC64LE.InsVector.va_codegen_success_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.AES.va_codegen_success_AESEncryptBlock", "Vale.PPC64LE.InsBasic.va_codegen_success_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_codegen_success_Store128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.Arch.HeapTypes_s.Secret", "Vale.AES.PPC64LE.GF128_Init.va_codegen_success_Gf128_powers", "Vale.PPC64LE.InsMem.va_codegen_success_DestroyHeaplets", "Vale.PPC64LE.Decls.va_ttrue", "Vale.PPC64LE.Decls.va_pbool" ]

[]

false

true

false

let va_codegen_success_Keyhash_init alg =

(va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Gf128_powers ()) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ()))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_code_Keyhash_init

val va_code_Keyhash_init : alg:algorithm -> Tot va_code

let va_code_Keyhash_init alg = (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ()))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 29, "end_line": 498, "start_col": 0, "start_line": 492 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b)) //-- //-- Keyhash_init

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> Vale.PPC64LE.Decls.va_code

Prims.Tot

[ "total" ]

[]

[ "Vale.AES.AES_common_s.algorithm", "Vale.PPC64LE.Decls.va_Block", "Vale.PPC64LE.Decls.va_CCons", "Vale.PPC64LE.InsMem.va_code_CreateHeaplets", "Vale.PPC64LE.InsVector.va_code_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.AES.va_code_AESEncryptBlock", "Vale.PPC64LE.InsBasic.va_code_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.Arch.HeapTypes_s.Secret", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers", "Vale.PPC64LE.Decls.va_CNil", "Vale.PPC64LE.InsMem.va_code_DestroyHeaplets", "Vale.PPC64LE.Decls.va_code" ]

[]

false

true

false

let va_code_Keyhash_init alg =

(va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ()))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wp_Gf128_powers

val va_wp_Gf128_powers (h: poly) (hkeys_b: buffer128) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0

let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (())))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 98, "end_line": 459, "start_col": 0, "start_line": 440 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Type0

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Prims.l_and", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Vale.PPC64LE.Decls.validDstAddrs128", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.PPC64LE.Decls.va_get_reg", "Vale.PPC64LE.Decls.va_get_mem_layout", "Vale.Arch.HeapTypes_s.Secret", "Prims.eq2", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.Def.Types_s.reverse_bytes_quad32", "Vale.PPC64LE.Decls.buffer128_read", "Prims.l_Forall", "Vale.PPC64LE.InsBasic.vale_heap", "Vale.PPC64LE.Memory.nat64", "Vale.PPC64LE.Memory.quad32", "Prims.l_imp", "Vale.PPC64LE.Decls.modifies_mem", "Vale.PPC64LE.Decls.loc_buffer", "Vale.PPC64LE.Memory.vuint128", "Vale.AES.GHash_BE.gf128_power", "Vale.PPC64LE.Machine_s.quad32", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.Decls.va_upd_vec", "Vale.PPC64LE.Decls.va_upd_reg", "Vale.PPC64LE.Decls.va_upd_mem_heaplet", "Vale.PPC64LE.Decls.va_upd_mem" ]

[]

false

true

let va_wp_Gf128_powers (h: poly) (hkeys_b: buffer128) (va_s0: va_state) (va_k: (va_state -> unit -> Type0)) : Type0 =

(va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem: vale_heap) (va_x_heap1: vale_heap) (va_x_r10: nat64) (va_x_v0: quad32) (va_x_v1: quad32) (va_x_v2: quad32) (va_x_v3: quad32) (va_x_v4: quad32) (va_x_v5: quad32) (va_x_v6: quad32). let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))) )))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (())))

false

Steel.GhostMonotonicHigherReference.fst

Steel.GhostMonotonicHigherReference.intro_pure_full

val intro_pure_full (#opened #a #p #f: _) (r: ref a p) (v: a) (h: history a p {history_val h v f}) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v)

let intro_pure_full #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v) = intro_pure #_ #a #p #f r v h; intro_exists h (pts_to_body r f v)

{ "file_name": "lib/steel/Steel.GhostMonotonicHigherReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 38, "end_line": 66, "start_col": 0, "start_line": 58 }

(* Copyright 2020 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 Steel.GhostMonotonicHigherReference open FStar.Ghost open FStar.PCM open Steel.Memory open Steel.Effect.Atomic open Steel.Effect open Steel.GhostPCMReference open Steel.FractionalPermission open Steel.Preorder module Preorder = FStar.Preorder module Q = Steel.Preorder module M = Steel.Memory module PR = Steel.GhostPCMReference module A = Steel.Effect.Atomic open FStar.Real #set-options "--ide_id_info_off" let ref a p = PR.ref (history a p) pcm_history [@@__reduce__] let pts_to_body #a #p (r:ref a p) (f:perm) (v:a) (h:history a p) = PR.pts_to r h `star` pure (history_val h v f) let pts_to' (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v: a) = h_exists (pts_to_body r f v) let pts_to_sl r f v = hp_of (pts_to' r f v) let intro_pure #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to_body r f v h) = A.intro_pure (history_val h v f)

{ "checked_file": "/", "dependencies": [ "Steel.Preorder.fst.checked", "Steel.Memory.fsti.checked", "Steel.GhostPCMReference.fsti.checked", "Steel.FractionalPermission.fst.checked", "Steel.Effect.Atomic.fsti.checked", "Steel.Effect.fsti.checked", "prims.fst.checked", "FStar.Real.fsti.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.PCM.fst.checked", "FStar.Ghost.fsti.checked" ], "interface_file": true, "source_file": "Steel.GhostMonotonicHigherReference.fst" }

[ { "abbrev": false, "full_module": "FStar.Real", "short_module": null }, { "abbrev": true, "full_module": "Steel.Effect.Atomic", "short_module": "A" }, { "abbrev": true, "full_module": "Steel.GhostPCMReference", "short_module": "PR" }, { "abbrev": true, "full_module": "Steel.Memory", "short_module": "M" }, { "abbrev": true, "full_module": "Steel.Preorder", "short_module": "Q" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Preorder", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "Steel.GhostPCMReference", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "Steel", "short_module": null }, { "abbrev": false, "full_module": "Steel", "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 } ]

{ "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" }

false

r: Steel.GhostMonotonicHigherReference.ref a p -> v: a -> h: Steel.Preorder.history a p {Steel.Preorder.history_val h (FStar.Ghost.hide v) f} -> Steel.Effect.Atomic.SteelGhostT Prims.unit

Steel.Effect.Atomic.SteelGhostT

[]

[ "Steel.Memory.inames", "FStar.Preorder.preorder", "Steel.FractionalPermission.perm", "Steel.GhostMonotonicHigherReference.ref", "Steel.Preorder.history", "Steel.Preorder.history_val", "FStar.Ghost.hide", "Steel.Effect.Atomic.intro_exists", "Steel.GhostMonotonicHigherReference.pts_to_body", "Prims.unit", "Steel.GhostMonotonicHigherReference.intro_pure", "Steel.GhostPCMReference.pts_to", "Steel.Preorder.pcm_history", "Steel.GhostMonotonicHigherReference.pts_to", "Steel.Effect.Common.vprop" ]

[]

false

true

false

let intro_pure_full #opened #a #p #f (r: ref a p) (v: a) (h: history a p {history_val h v f}) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v) =

intro_pure #_ #a #p #f r v h; intro_exists h (pts_to_body r f v)

false

Steel.ST.Array.fst

Steel.ST.Array.pts_to_range_index

val pts_to_range_index (#elt: Type0) (#p: P.perm) (#s: Ghost.erased (Seq.seq elt)) (a: array elt) (i: Ghost.erased nat) (m: US.t) (j: Ghost.erased nat) : ST elt (pts_to_range a i j p s) (fun _ -> pts_to_range a i j p s) (i <= US.v m /\ US.v m < j) (fun res -> i <= US.v m /\ US.v m < j /\ Seq.length s == j - i /\ res == Seq.index s (US.v m - i) )

let pts_to_range_index #elt #p #s a i m j = pts_to_range_split a i (US.v m) j; let s1 = elim_exists () in let s2 = elim_exists () in elim_pure _; let ga' = pts_to_range_elim' a (US.v m) j p s2 in let a' = array_slice_impl a m j () in vpattern_rewrite #_ #(array elt) #ga' (fun ga' -> pts_to ga' _ _) a'; let res = index a' 0sz in pts_to_range_intro' a (US.v m) j p a' s2; pts_to_range_join a i (US.v m) j; vpattern_rewrite (pts_to_range a i j p) (Ghost.reveal s); return res

{ "file_name": "lib/steel/Steel.ST.Array.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 12, "end_line": 684, "start_col": 0, "start_line": 671 }

(* Copyright 2020, 2021, 2022 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 Steel.ST.Array module US = FStar.SizeT /// Lifting a value of universe 0 to universe 1. We use /// FStar.Universe, since FStar.Extraction.Krml is set to extract /// those functions to identity. inline_for_extraction [@@ noextract_to "krml"] let raise_t (t: Type0) : Type u#1 = FStar.Universe.raise_t t inline_for_extraction [@@noextract_to "krml"] let raise (#t: Type) (x: t) : Tot (raise_t t) = FStar.Universe.raise_val x inline_for_extraction [@@noextract_to "krml"] let lower (#t: Type) (x: raise_t t) : Tot t = FStar.Universe.downgrade_val x /// A map operation on sequences. Here we only need Ghost versions, /// because such sequences are only used in vprops or with their /// selectors. let rec seq_map (#t: Type u#a) (#t' : Type u#b) (f: (t -> GTot t')) (s: Seq.seq t) : Ghost (Seq.seq t') (requires True) (ensures (fun s' -> Seq.length s' == Seq.length s /\ (forall i . {:pattern (Seq.index s' i)} Seq.index s' i == f (Seq.index s i)) )) (decreases (Seq.length s)) = if Seq.length s = 0 then Seq.empty else Seq.cons (f (Seq.index s 0)) (seq_map f (Seq.slice s 1 (Seq.length s))) let seq_map_append (#t: Type u#a) (#t': Type u#b) (f: (t -> GTot t')) (s1 s2: Seq.seq t) : Lemma (seq_map f (s1 `Seq.append` s2) `Seq.equal` (seq_map f s1 `Seq.append` seq_map f s2)) = () let seq_map_raise_inj (#elt: Type0) (s1 s2: Seq.seq elt) : Lemma (requires (seq_map raise s1 == seq_map raise s2)) (ensures (s1 == s2)) [SMTPat (seq_map raise s1); SMTPat (seq_map raise s2)] = assert (seq_map lower (seq_map raise s1) `Seq.equal` s1); assert (seq_map lower (seq_map raise s2) `Seq.equal` s2) /// Implementation of the interface /// base, ptr, array, pts_to module H = Steel.ST.HigherArray let base_t elt = H.base_t (raise_t elt) let base_len b = H.base_len b let ptr elt = H.ptr (raise_t elt) let null_ptr elt = H.null_ptr (raise_t elt) let is_null_ptr p = H.is_null_ptr p let base p = H.base p let offset p = H.offset p let ptr_base_offset_inj p1 p2 = H.ptr_base_offset_inj p1 p2 let base_len_null_ptr elt = H.base_len_null_ptr (raise_t elt) let length_fits a = H.length_fits a let pts_to a p s = H.pts_to a p (seq_map raise s) let pts_to_length a s = H.pts_to_length a _ let h_array_eq' (#t: Type u#1) (a1 a2: H.array t) : Lemma (requires ( dfst a1 == dfst a2 /\ (Ghost.reveal (dsnd a1) <: nat) == Ghost.reveal (dsnd a2) )) (ensures ( a1 == a2 )) = () let pts_to_not_null #_ #t #p a s = let _ = H.pts_to_not_null #_ #_ #p a (seq_map raise s) in assert (a =!= H.null #(raise_t t)); Classical.move_requires (h_array_eq' a) (H.null #(raise_t t)); noop () let pts_to_inj a p1 s1 p2 s2 = H.pts_to_inj a p1 (seq_map raise s1) p2 (seq_map raise s2) /// Non-selector operations. let malloc x n = let res = H.malloc (raise x) n in assert (seq_map raise (Seq.create (US.v n) x) `Seq.equal` Seq.create (US.v n) (raise x)); rewrite (H.pts_to res _ _) (pts_to res _ _); return res let free #_ x = let s = elim_exists () in rewrite (pts_to x _ _) (H.pts_to x P.full_perm (seq_map raise s)); H.free x let share #_ #_ #x a p p1 p2 = rewrite (pts_to a _ _) (H.pts_to a p (seq_map raise x)); H.share a p p1 p2; rewrite (H.pts_to a p1 _) (pts_to a p1 x); rewrite (H.pts_to a p2 _) (pts_to a p2 x) let gather #_ #_ a #x1 p1 #x2 p2 = rewrite (pts_to a p1 _) (H.pts_to a p1 (seq_map raise x1)); rewrite (pts_to a p2 _) (H.pts_to a p2 (seq_map raise x2)); H.gather a p1 p2; rewrite (H.pts_to a _ _) (pts_to _ _ _) let index #_ #p a #s i = rewrite (pts_to a _ _) (H.pts_to a p (seq_map raise s)); let res = H.index a i in rewrite (H.pts_to _ _ _) (pts_to _ _ _); return (lower res) let upd #_ a #s i v = rewrite (pts_to a _ _) (H.pts_to a P.full_perm (seq_map raise s)); H.upd a i (raise v); assert (seq_map raise (Seq.upd s (US.v i) v) `Seq.equal` Seq.upd (seq_map raise s) (US.v i) (raise v)); rewrite (H.pts_to _ _ _) (pts_to _ _ _) let ghost_join #_ #_ #x1 #x2 #p a1 a2 h = rewrite (pts_to a1 _ _) (H.pts_to a1 p (seq_map raise x1)); rewrite (pts_to a2 _ _) (H.pts_to a2 p (seq_map raise x2)); H.ghost_join a1 a2 h; assert (seq_map raise (x1 `Seq.append` x2) `Seq.equal` (seq_map raise x1 `Seq.append` seq_map raise x2)); rewrite (H.pts_to _ _ _) (H.pts_to (merge a1 a2) p (seq_map raise (x1 `Seq.append` x2))); rewrite (H.pts_to _ _ _) (pts_to (merge a1 a2) _ _) let ptr_shift p off = H.ptr_shift p off let ghost_split #_ #_ #x #p a i = rewrite (pts_to a _ _) (H.pts_to a p (seq_map raise x)); let _ = H.ghost_split a i in //H.ghost_split a i; assert (seq_map raise (Seq.slice x 0 (US.v i)) `Seq.equal` Seq.slice (seq_map raise x) 0 (US.v i)); rewrite (H.pts_to (H.split_l a i) _ _) (H.pts_to (split_l a i) p (seq_map raise (Seq.slice x 0 (US.v i)))); rewrite (H.pts_to (split_l a i) _ _) (pts_to (split_l a i) _ _); assert (seq_map raise (Seq.slice x (US.v i) (Seq.length x)) `Seq.equal` Seq.slice (seq_map raise x) (US.v i) (Seq.length (seq_map raise x))); Seq.lemma_split x (US.v i); rewrite (H.pts_to (H.split_r a i) _ _) (H.pts_to (split_r a i) p (seq_map raise (Seq.slice x (US.v i) (Seq.length x)))); rewrite (H.pts_to (split_r a i) _ _) (pts_to (split_r a i) _ _) let memcpy a0 a1 l = H.memcpy a0 a1 l //////////////////////////////////////////////////////////////////////////////// // compare //////////////////////////////////////////////////////////////////////////////// module R = Steel.ST.Reference #push-options "--fuel 0 --ifuel 1 --z3rlimit_factor 2" let equal_up_to #t (s0: Seq.seq t) (s1: Seq.seq t) (v : option US.t) : prop = Seq.length s0 = Seq.length s1 /\ (match v with | None -> Ghost.reveal s0 =!= Ghost.reveal s1 | Some v -> US.v v <= Seq.length s0 /\ Seq.slice s0 0 (US.v v) `Seq.equal` Seq.slice s1 0 (US.v v)) let within_bounds (x:option US.t) (l:US.t) (b:Ghost.erased bool) : prop = if b then Some? x /\ US.(Some?.v x <^ l) else None? x \/ US.(Some?.v x >=^ l) let compare_inv (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (s0: Seq.seq t) (s1: Seq.seq t) (l:US.t) (ctr : R.ref (option US.t)) (b: bool) = pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` exists_ (fun (x:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm x `star` pure (equal_up_to s0 s1 x) `star` pure (within_bounds x l b)) let elim_compare_inv #o (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (#s0: Seq.seq t) (#s1: Seq.seq t) (l:US.t) (ctr : R.ref (option US.t)) (b: bool) : STGhostT (Ghost.erased (option US.t)) o (compare_inv a0 a1 s0 s1 l ctr b) (fun x -> let open US in pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` R.pts_to ctr Steel.FractionalPermission.full_perm x `star` pure (equal_up_to s0 s1 x) `star` pure (within_bounds x l b)) = let open US in assert_spinoff ((compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr b) == (pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` exists_ (fun (v:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm v `star` pure (equal_up_to s0 s1 v) `star` pure (within_bounds v l b)))); rewrite (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr b) (pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` exists_ (fun (v:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm v `star` pure (equal_up_to s0 s1 v) `star` pure (within_bounds v l b))); let _v = elim_exists () in _v let intro_compare_inv #o (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (#s0: Seq.seq t) (#s1: Seq.seq t) (l:US.t) (ctr : R.ref (option US.t)) (x: Ghost.erased (option US.t)) (b:bool { within_bounds x l b }) : STGhostT unit o (let open US in pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` R.pts_to ctr Steel.FractionalPermission.full_perm x `star` pure (equal_up_to s0 s1 x)) (fun _ -> compare_inv a0 a1 s0 s1 l ctr (Ghost.hide b)) = let open US in intro_pure (within_bounds x l (Ghost.hide b)); intro_exists_erased x (fun (x:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm x `star` pure (equal_up_to s0 s1 x) `star` pure (within_bounds x l (Ghost.hide b))); assert_norm ((compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr (Ghost.hide b)) == (pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` exists_ (fun (v:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm v `star` pure (equal_up_to s0 s1 v) `star` pure (within_bounds v l (Ghost.hide b))))); rewrite (pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` exists_ (fun (v:option US.t) -> R.pts_to ctr Steel.FractionalPermission.full_perm v `star` pure (equal_up_to s0 s1 v) `star` pure (within_bounds v l (Ghost.hide b)))) (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr (Ghost.hide b)) let intro_exists_compare_inv #o (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (#s0: Seq.seq t) (#s1: Seq.seq t) (l:US.t) (ctr : R.ref (option US.t)) (x: Ghost.erased (option US.t)) : STGhostT unit o (let open US in pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` R.pts_to ctr Steel.FractionalPermission.full_perm x `star` pure (equal_up_to s0 s1 x)) (fun _ -> exists_ (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr)) = let b : bool = match Ghost.reveal x with | None -> false | Some x -> US.(x <^ l) in assert (within_bounds x l b); intro_compare_inv #_ #_ #p0 #p1 a0 a1 #s0 #s1 l ctr x b; intro_exists _ (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr) let extend_equal_up_to_lemma (#t:Type0) (s0:Seq.seq t) (s1:Seq.seq t) (i:nat{ i < Seq.length s0 /\ Seq.length s0 == Seq.length s1 }) : Lemma (requires Seq.equal (Seq.slice s0 0 i) (Seq.slice s1 0 i) /\ Seq.index s0 i == Seq.index s1 i) (ensures Seq.equal (Seq.slice s0 0 (i + 1)) (Seq.slice s1 0 (i + 1))) = assert (forall k. k Seq.index s0 k == Seq.index (Seq.slice s0 0 i) k /\ Seq.index s1 k == Seq.index (Seq.slice s1 0 i) k) let extend_equal_up_to (#o:_) (#t:Type0) (#s0:Seq.seq t) (#s1:Seq.seq t) (len:US.t) (i:US.t{ Seq.length s0 == Seq.length s1 /\ US.(i <^ len) /\ US.v len == Seq.length s0 } ) : STGhost unit o (pure (equal_up_to s0 s1 (Some i))) (fun _ -> pure (equal_up_to s0 s1 (Some US.(i +^ 1sz)))) (requires Seq.index s0 (US.v i) == Seq.index s1 (US.v i)) (ensures fun _ -> True) = elim_pure _; extend_equal_up_to_lemma s0 s1 (US.v i); intro_pure (equal_up_to s0 s1 (Some US.(i +^ 1sz))) let extend_equal_up_to_neg (#o:_) (#t:Type0) (#s0:Seq.seq t) (#s1:Seq.seq t) (len:US.t) (i:US.t{ Seq.length s0 == Seq.length s1 /\ US.(i <^ len) /\ US.v len == Seq.length s0 } ) : STGhost unit o (pure (equal_up_to s0 s1 (Some i))) (fun _ -> pure (equal_up_to s0 s1 None)) (requires Seq.index s0 (US.v i) =!= Seq.index s1 (US.v i)) (ensures fun _ -> True) = elim_pure _; intro_pure _ let init_compare_inv #o (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (#s0: Seq.seq t) (#s1: Seq.seq t) (l:US.t) (ctr : R.ref (option US.t)) : STGhost unit o (let open US in pts_to a0 p0 s0 `star` pts_to a1 p1 s1 `star` R.pts_to ctr Steel.FractionalPermission.full_perm (Some 0sz)) (fun _ -> exists_ (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr)) (requires ( length a0 > 0 /\ length a0 == length a1 /\ US.v l == length a0 )) (ensures (fun _ -> True)) = pts_to_length a0 _; pts_to_length a1 _; intro_pure (equal_up_to s0 s1 (Ghost.hide (Some 0sz))); rewrite (R.pts_to ctr Steel.FractionalPermission.full_perm (Some 0sz)) (R.pts_to ctr Steel.FractionalPermission.full_perm (Ghost.hide (Some 0sz))); intro_exists_compare_inv a0 a1 l ctr (Ghost.hide (Some 0sz)) let compare_pts (#t:eqtype) (#p0 #p1:perm) (a0 a1:array t) (#s0: Ghost.erased (Seq.seq t)) (#s1: Ghost.erased (Seq.seq t)) (l:US.t) : ST bool (pts_to a0 p0 s0 `star` pts_to a1 p1 s1) (fun _ -> pts_to a0 p0 s0 `star` pts_to a1 p1 s1) (requires length a0 > 0 /\ length a0 == length a1 /\ US.v l == length a0 ) (ensures fun b -> b = (Ghost.reveal s0 = Ghost.reveal s1)) = pts_to_length a0 _; pts_to_length a1 _; let ctr = R.alloc (Some 0sz) in let cond () : STT bool (exists_ (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr)) (fun b -> compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr (Ghost.hide b)) = let _b = elim_exists () in let _ = elim_compare_inv _ _ _ _ _ in let x = R.read ctr in elim_pure (within_bounds _ _ _); match x with | None -> intro_compare_inv #_ #_ #p0 #p1 a0 a1 l ctr _ false; return false | Some x -> let res = US.(x <^ l) in intro_compare_inv #_ #_ #p0 #p1 a0 a1 l ctr _ res; return res in let body () : STT unit (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr (Ghost.hide true)) (fun _ -> exists_ (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr)) = let _i = elim_compare_inv _ _ _ _ _ in elim_pure (within_bounds _ _ _); let Some i = R.read ctr in assert_spinoff ((pure (equal_up_to s0 s1 _i)) == (pure (equal_up_to s0 s1 (Some i)))); rewrite (pure (equal_up_to s0 s1 _i)) (pure (equal_up_to s0 s1 (Some i))); let v0 = index a0 i in let v1 = index a1 i in if v0 = v1 then ( R.write ctr (Some US.(i +^ 1sz)); extend_equal_up_to l i; intro_exists_compare_inv #_ #_ #p0 #p1 a0 a1 l ctr (Ghost.hide (Some (US.(i +^ 1sz)))) ) else ( R.write ctr None; extend_equal_up_to_neg l i; intro_exists_compare_inv #_ #_ #p0 #p1 a0 a1 l ctr (Ghost.hide None) ) in init_compare_inv a0 a1 l ctr; Steel.ST.Loops.while_loop (compare_inv #_ #p0 #p1 a0 a1 s0 s1 l ctr) cond body; let _ = elim_compare_inv _ _ _ _ _ in elim_pure (equal_up_to _ _ _); let v = R.read ctr in R.free ctr; elim_pure (within_bounds _ _ _); match v with | None -> return false | Some _ -> return true let compare #t #p0 #p1 a0 a1 #s0 #s1 l = pts_to_length a0 _; pts_to_length a1 _; if l = 0sz then ( assert (Seq.equal s0 s1); return true ) else ( compare_pts a0 a1 l ) #pop-options let intro_fits_u32 () = H.intro_fits_u32 () let intro_fits_u64 () = H.intro_fits_u64 () let intro_fits_ptrdiff32 () = H.intro_fits_ptrdiff32 () let intro_fits_ptrdiff64 () = H.intro_fits_ptrdiff64 () let ptrdiff #_ #p0 #p1 #s0 #s1 a0 a1 = rewrite (pts_to a0 _ _) (H.pts_to a0 p0 (seq_map raise s0)); rewrite (pts_to a1 _ _) (H.pts_to a1 p1 (seq_map raise s1)); let res = H.ptrdiff a0 a1 in rewrite (H.pts_to a1 _ _) (pts_to a1 _ _); rewrite (H.pts_to a0 _ _) (pts_to a0 _ _); return res let array_slice (#elt: Type0) (a: array elt) (i j: nat) (sq: squash (i <= j /\ j <= length a)) : Ghost (array elt) (requires True) (ensures (fun a' -> length a' == j - i)) = length_fits a; split_l (split_r a (US.uint_to_t i)) (US.uint_to_t (j - i)) [@@__reduce__] let pts_to_range_body (#elt: Type0) (a: array elt) (i j: nat) (p: P.perm) (s: Seq.seq elt) (sq: squash (i <= j /\ j <= length a)) : Tot vprop = pts_to (array_slice a i j sq) p s let pts_to_range (#elt: Type0) (a: array elt) (i j: nat) (p: P.perm) ([@@@ smt_fallback ] s: Seq.seq elt) : Tot vprop = exists_ (pts_to_range_body a i j p s) let pts_to_range_intro' (#opened: _) (#elt: Type0) (a: array elt) (i j: nat) (p: P.perm) (a': array elt) (s: Seq.seq elt) : STGhost unit opened (pts_to a' p s) (fun _ -> pts_to_range a i j p s) (i <= j /\ j <= length a /\ a' == array_slice a i j () ) (fun _ -> True) = let sq : squash (i <= j /\ j <= length a) = () in rewrite (pts_to a' p s) (pts_to (array_slice a i j sq) p s); rewrite (exists_ (pts_to_range_body a i j p s)) (pts_to_range a i j p s) let pts_to_range_elim' (#opened: _) (#elt: Type0) (a: array elt) (i j: nat) (p: P.perm) (s: Seq.seq elt) : STGhost (Ghost.erased (array elt)) opened (pts_to_range a i j p s) (fun a' -> pts_to a' p s) True (fun a' -> i <= j /\ j <= length a /\ Ghost.reveal a' == array_slice a i j () ) = rewrite (pts_to_range a i j p s) (exists_ (pts_to_range_body a i j p s)); let _ = elim_exists () in vpattern_replace_erased (fun a' -> pts_to a' p s) let pts_to_range_prop a i j p s = let a' = pts_to_range_elim' a i j p s in pts_to_length a' s; pts_to_range_intro' a i j p a' s let pts_to_range_intro a p s = ptr_shift_zero (ptr_of a); pts_to_range_intro' a 0 (length a) p a s let pts_to_range_elim a p s = ptr_shift_zero (ptr_of a); let a' = pts_to_range_elim' a 0 (length a) p s in vpattern_rewrite (fun a' -> pts_to a' _ _) a let pts_to_range_split #_ #_ #p #s a i m j = length_fits a; pts_to_range_prop a i j p s; let a' = pts_to_range_elim' a i j p s in let mi = US.uint_to_t (m - i) in ptr_shift_add (ptr_of a) (US.uint_to_t i) mi; let _ = ghost_split a' mi in pts_to_range_intro' a m j p (split_r a' mi) _; pts_to_range_intro' a i m p (split_l a' mi) _; noop () let pts_to_range_join #_ #_ #p #s1 #s2 a i m j = length_fits a; pts_to_range_prop a i m p s1; pts_to_range_prop a m j p s2; let a1 = pts_to_range_elim' a i m p s1 in let a2 = pts_to_range_elim' a m j p s2 in ghost_join a1 a2 (); pts_to_range_intro' a i j p _ _ inline_for_extraction [@@noextract_to "krml"] let array_slice_impl (#elt: Type0) (a: array elt) (i: US.t) (j: Ghost.erased nat) (sq: squash (US.v i <= j /\ j <= length a)) : Pure (array elt) (requires True) (ensures (fun a' -> a' == array_slice a (US.v i) j sq)) = length_fits a; split_l (split_r a i) (US.uint_to_t (j - US.v i))

{ "checked_file": "/", "dependencies": [ "Steel.ST.Reference.fsti.checked", "Steel.ST.Loops.fsti.checked", "Steel.ST.HigherArray.fsti.checked", "Steel.FractionalPermission.fst.checked", "prims.fst.checked", "FStar.Universe.fsti.checked", "FStar.SizeT.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "Steel.ST.Array.fst" }

[ { "abbrev": true, "full_module": "Steel.ST.Reference", "short_module": "R" }, { "abbrev": true, "full_module": "Steel.ST.HigherArray", "short_module": "H" }, { "abbrev": true, "full_module": "FStar.SizeT", "short_module": "US" }, { "abbrev": false, "full_module": "Steel.ST.Util", "short_module": null }, { "abbrev": true, "full_module": "FStar.PtrdiffT", "short_module": "UP" }, { "abbrev": true, "full_module": "FStar.SizeT", "short_module": "US" }, { "abbrev": true, "full_module": "Steel.FractionalPermission", "short_module": "P" }, { "abbrev": false, "full_module": "Steel.ST", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST", "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 } ]

{ "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" }

false

a: Steel.ST.Array.array elt -> i: FStar.Ghost.erased Prims.nat -> m: FStar.SizeT.t -> j: FStar.Ghost.erased Prims.nat -> Steel.ST.Effect.ST elt

Steel.ST.Effect.ST

[]

[ "Steel.FractionalPermission.perm", "FStar.Ghost.erased", "FStar.Seq.Base.seq", "Steel.ST.Array.array", "Prims.nat", "FStar.SizeT.t", "Steel.ST.Util.return", "FStar.Ghost.hide", "FStar.Set.set", "Steel.Memory.iname", "FStar.Set.empty", "Steel.ST.Array.pts_to_range", "FStar.Ghost.reveal", "Steel.Effect.Common.vprop", "Prims.unit", "Steel.ST.Util.vpattern_rewrite", "FStar.Seq.Base.append", "Steel.ST.Array.pts_to_range_join", "FStar.SizeT.v", "Steel.ST.Array.pts_to_range_intro'", "Steel.ST.Array.index", "FStar.SizeT.__uint_to_t", "Steel.ST.Array.pts_to", "Steel.ST.Array.array_slice_impl", "Steel.ST.Array.pts_to_range_elim'", "Steel.ST.Util.elim_pure", "Prims.l_and", "Prims.b2t", "Prims.op_LessThanOrEqual", "Steel.ST.Array.length", "Prims.eq2", "Prims.int", "FStar.Seq.Base.length", "Prims.op_Subtraction", "FStar.Seq.Base.slice", "Steel.ST.Util.elim_exists", "Steel.Effect.Common.VStar", "Steel.ST.Util.pure", "Steel.ST.Util.exists_", "Steel.ST.Array.pts_to_range_split" ]

[]

false

true

false

let pts_to_range_index #elt #p #s a i m j =

pts_to_range_split a i (US.v m) j; let s1 = elim_exists () in let s2 = elim_exists () in elim_pure _; let ga' = pts_to_range_elim' a (US.v m) j p s2 in let a' = array_slice_impl a m j () in vpattern_rewrite #_ #(array elt) #ga' (fun ga' -> pts_to ga' _ _) a'; let res = index a' 0sz in pts_to_range_intro' a (US.v m) j p a' s2; pts_to_range_join a i (US.v m) j; vpattern_rewrite (pts_to_range a i j p) (Ghost.reveal s); return res

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_quick_ShiftKey1_128

val va_quick_ShiftKey1_128 (f: poly) : (va_quickCode unit (va_code_ShiftKey1_128 ()))

let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 57, "end_line": 165, "start_col": 0, "start_line": 163 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Vale.Math.Poly2_s.poly -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128 ())

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.QuickCode.va_QProc", "Prims.unit", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Prims.Nil", "Vale.AES.PPC64LE.GF128_Init.va_wp_ShiftKey1_128", "Vale.AES.PPC64LE.GF128_Init.va_wpProof_ShiftKey1_128", "Vale.PPC64LE.QuickCode.va_quickCode" ]

[]

false

let va_quick_ShiftKey1_128 (f: poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) =

(va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_quick_Gf128_powers

val va_quick_Gf128_powers (h: poly) (hkeys_b: buffer128) : (va_quickCode unit (va_code_Gf128_powers ()))

let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 71, "end_line": 487, "start_col": 0, "start_line": 483 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers ())

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.QuickCode.va_QProc", "Prims.unit", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Prims.Nil", "Vale.AES.PPC64LE.GF128_Init.va_wp_Gf128_powers", "Vale.AES.PPC64LE.GF128_Init.va_wpProof_Gf128_powers", "Vale.PPC64LE.QuickCode.va_quickCode" ]

[]

false

let va_quick_Gf128_powers (h: poly) (hkeys_b: buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) =

(va_QProc (va_code_Gf128_powers ()) ([ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem ]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_qcode_ShiftKey1_128

val va_qcode_ShiftKey1_128 (va_mods: va_mods_t) (f: poly) : (va_quickCode unit (va_code_ShiftKey1_128 ()))

let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (()))))))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 34, "end_line": 94, "start_col": 0, "start_line": 57 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ()))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_mods: Vale.PPC64LE.QuickCode.va_mods_t -> f: Vale.Math.Poly2_s.poly -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128 ())

Prims.Tot

[ "total" ]

[]

[ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsVector.va_code_Vmr", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.GF128_Mul.va_code_ShiftLeft128_1", "Vale.AES.PPC64LE.PolyOps.va_code_VPolyAnd", "Vale.PPC64LE.InsVector.va_code_Vcmpequw", "Vale.PPC64LE.InsVector.va_code_Vspltw", "Vale.AES.PPC64LE.PolyOps.va_code_VPolyAdd", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsVector.va_quick_Vmr", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.AES.PPC64LE.GF128_Mul.va_quick_ShiftLeft128_1", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.eq2", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.Math.Poly2.Bits_s.to_quad32", "Vale.Math.Poly2.mask", "Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask", "Prims.bool", "Vale.Math.Poly2_s.poly_index", "Vale.Math.Poly2_s.shift", "Prims.op_AmpAmp", "Prims.op_Subtraction", "Prims.op_GreaterThanOrEqual", "Vale.Math.Poly2.lemma_shift_define_i", "Vale.AES.PPC64LE.PolyOps.va_quick_VPolyAnd", "Vale.PPC64LE.InsVector.va_quick_Vcmpequw", "Prims.b2t", "Prims.op_LessThan", "Vale.Math.Poly2_s.degree", "Prims.op_Equality", "Vale.Def.Words_s.nat32", "Vale.Def.Words_s.__proj__Mkfour__item__hi3", "Vale.Math.Poly2.poly_and", "Vale.Math.Poly2_s.monomial", "Vale.AES.GF128.lemma_test_high_bit", "Vale.PPC64LE.InsVector.va_quick_Vspltw", "Vale.Def.Words_s.Mkfour", "Vale.Math.Poly2_s.zero", "Vale.Def.Words_s.four", "Vale.Math.Poly2.Words.lemma_quad32_zero", "Vale.Math.Poly2.ones", "Vale.Math.Poly2.Words.lemma_quad32_ones", "Prims.nat", "Vale.Math.Poly2.Lemmas.lemma_and_consts", "Vale.AES.PPC64LE.PolyOps.va_quick_VPolyAdd", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128" ]

[]

false

let va_qcode_ShiftKey1_128 (va_mods: va_mods_t) (f: poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) =

(qblock va_mods (fun (va_s: va_state) -> let va_old_s:va_state = va_s in let h:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let h1:Vale.Math.Poly2_s.poly = Vale.Math.Poly2_s.shift h 1 in let offset:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s: va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s: va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s: va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s: va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (()))))))))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_quick_ShiftKey1_gf128_power

val va_quick_ShiftKey1_gf128_power (h: poly) (n: nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ()))

let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 43, "end_line": 309, "start_col": 0, "start_line": 305 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power ())

Prims.Tot

[ "total" ]

[]

[ "Vale.Math.Poly2_s.poly", "Prims.nat", "Vale.PPC64LE.QuickCode.va_QProc", "Prims.unit", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Prims.Nil", "Vale.AES.PPC64LE.GF128_Init.va_wp_ShiftKey1_gf128_power", "Vale.AES.PPC64LE.GF128_Init.va_wpProof_ShiftKey1_gf128_power", "Vale.PPC64LE.QuickCode.va_quickCode" ]

[]

false

let va_quick_ShiftKey1_gf128_power (h: poly) (n: nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) =

(va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wpProof_ShiftKey1_gf128_power

val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g))))

let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 302, "start_col": 0, "start_line": 292 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel) * Prims.unit)

Prims.Ghost

[]

[ "Vale.Math.Poly2_s.poly", "Prims.nat", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Vale.PPC64LE.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Prims.Nil", "Prims._assert", "Vale.PPC64LE.Decls.va_state_eq", "Vale.PPC64LE.Decls.va_update_vec", "Vale.PPC64LE.Decls.va_update_reg", "Vale.PPC64LE.Decls.va_update_ok", "Vale.PPC64LE.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.PPC64LE.Machine_s.state", "Vale.AES.PPC64LE.GF128_Init.va_lemma_ShiftKey1_gf128_power", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power" ]

[]

false

let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k =

let va_sM, va_f0 = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))) )); va_lemma_norm_mods ([ va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10 ]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wpProof_Gf128_powers

val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))

let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 480, "start_col": 0, "start_line": 470 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

h: Vale.Math.Poly2_s.poly -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel) * Prims.unit)

Prims.Ghost

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Vale.PPC64LE.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Prims.Nil", "Prims._assert", "Vale.PPC64LE.Decls.va_state_eq", "Vale.PPC64LE.Decls.va_update_vec", "Vale.PPC64LE.Decls.va_update_reg", "Vale.PPC64LE.Decls.va_update_mem_heaplet", "Vale.PPC64LE.Decls.va_update_ok", "Vale.PPC64LE.Decls.va_update_mem", "Vale.PPC64LE.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.PPC64LE.Machine_s.state", "Vale.AES.PPC64LE.GF128_Init.va_lemma_Gf128_powers", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers" ]

[]

false

let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k =

let va_sM, va_f0 = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem ]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_qcode_Keyhash_init

val va_qcode_Keyhash_init (va_mods: va_mods_t) (alg: algorithm) (key: (seq nat32)) (roundkeys_b hkeys_b: buffer128) : (va_quickCode unit (va_code_Keyhash_init alg))

let va_qcode_Keyhash_init (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (roundkeys_b:buffer128) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Keyhash_init alg)) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_CreateHeaplets ([declare_buffer128 roundkeys_b 0 Secret Immutable; declare_buffer128 hkeys_b 1 Secret Mutable])) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 196 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (fun (va_s:va_state) _ -> va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 197 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_AESEncryptBlock alg (va_get_vec 0 va_s) key (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) roundkeys_b)) roundkeys_b) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 198 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 199 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> va_QBind va_range1 "***** PRECONDITION NOT MET AT line 201 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128_powers (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 0 va_s)) hkeys_b) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1 "***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) -> Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) (fun _ -> let (va_arg12:Vale.Def.Types_s.quad32) = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) in let (va_arg11:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) hkeys_b) in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hkeys_reqs_pub_priv va_arg11 va_arg12) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 60, "end_line": 545, "start_col": 0, "start_line": 511 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b)) //-- //-- Keyhash_init [@ "opaque_to_smt" va_qattr] let va_code_Keyhash_init alg = (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ())))))))))) [@ "opaque_to_smt" va_qattr] let va_codegen_success_Keyhash_init alg = (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Gf128_powers ()) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ()))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_mods: Vale.PPC64LE.QuickCode.va_mods_t -> alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.PPC64LE.Memory.nat32 -> roundkeys_b: Vale.PPC64LE.Memory.buffer128 -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_Keyhash_init alg)

Prims.Tot

[ "total" ]

[]

[ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.PPC64LE.Memory.nat32", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsMem.va_code_CreateHeaplets", "Vale.PPC64LE.InsVector.va_code_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.AES.PPC64LE.AES.va_code_AESEncryptBlock", "Vale.PPC64LE.InsBasic.va_code_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.Arch.HeapTypes_s.Secret", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers", "Vale.PPC64LE.Machine_s.Block", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.InsMem.va_code_DestroyHeaplets", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsMem.va_quick_CreateHeaplets", "Vale.Arch.HeapImpl.buffer_info", "Vale.PPC64LE.InsMem.declare_buffer128", "Vale.Arch.HeapImpl.Immutable", "Vale.Arch.HeapImpl.Mutable", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.InsVector.va_quick_Vspltisw", "Vale.AES.PPC64LE.AES.va_quick_AESEncryptBlock", "Vale.PPC64LE.Decls.va_get_vec", "Vale.Arch.Types.reverse_bytes_quad32_seq", "Vale.PPC64LE.Decls.buffer128_as_seq", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.PPC64LE.InsBasic.va_quick_LoadImm64", "Vale.PPC64LE.InsVector.va_quick_Store128_byte16_buffer_index", "Vale.AES.PPC64LE.GF128_Init.va_quick_Gf128_powers", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.PPC64LE.QuickCodes.va_qAssertSquash", "Vale.AES.AES_BE_s.is_aes_key_word", "Prims.squash", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.l_iff", "Vale.AES.OptPublic_BE.hkeys_reqs_pub", "Vale.AES.GHash_BE.hkeys_reqs_priv", "Vale.AES.GHash_BE.lemma_hkeys_reqs_pub_priv", "Vale.PPC64LE.InsMem.va_quick_DestroyHeaplets", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.Def.Types_s.quad32", "Vale.PPC64LE.Decls.s128", "Vale.AES.AES_BE_s.aes_encrypt_word", "Vale.Def.Words_s.Mkfour", "Vale.Def.Types_s.nat32", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GF128_Init.va_code_Keyhash_init" ]

[]

false

let va_qcode_Keyhash_init (va_mods: va_mods_t) (alg: algorithm) (key: (seq nat32)) (roundkeys_b hkeys_b: buffer128) : (va_quickCode unit (va_code_Keyhash_init alg)) =

(qblock va_mods (fun (va_s: va_state) -> let va_old_s:va_state = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_CreateHeaplets ([ declare_buffer128 roundkeys_b 0 Secret Immutable; declare_buffer128 hkeys_b 1 Secret Mutable ])) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 196 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (fun (va_s: va_state) _ -> va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 197 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_AESEncryptBlock alg (va_get_vec 0 va_s) key (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) roundkeys_b)) roundkeys_b) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 198 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 199 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s: va_state) _ -> va_QBind va_range1 "***** PRECONDITION NOT MET AT line 201 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128_powers (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 0 va_s)) hkeys_b) (fun (va_s: va_state) _ -> va_qAssertSquash va_range1 "***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" ((fun (alg_10591: Vale.AES.AES_common_s.algorithm) (key_10592: (FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) (input_10593: Vale.Def.Types_s.quad32) -> Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0 )) (fun _ -> let va_arg12:Vale.Def.Types_s.quad32 = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) in let va_arg11:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32 ) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) hkeys_b) in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GHash_BE.lemma_hkeys_reqs_pub_priv va_arg11 va_arg12) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wpProof_ShiftKey1_128

val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g))))

let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 160, "start_col": 0, "start_line": 153 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Vale.Math.Poly2_s.poly -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel) * Prims.unit)

Prims.Ghost

[]

[ "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Vale.PPC64LE.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Prims.Nil", "Prims._assert", "Vale.PPC64LE.Decls.va_state_eq", "Vale.PPC64LE.Decls.va_update_vec", "Vale.PPC64LE.Decls.va_update_ok", "Vale.PPC64LE.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.PPC64LE.Machine_s.state", "Vale.AES.PPC64LE.GF128_Init.va_lemma_ShiftKey1_128", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128" ]

[]

false

let va_wpProof_ShiftKey1_128 f va_s0 va_k =

let va_sM, va_f0 = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_qcode_ShiftKey1_gf128_power

val va_qcode_ShiftKey1_gf128_power (va_mods: va_mods_t) (h: poly) (n: nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ()))

let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (()))))))))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 25, "end_line": 239, "start_col": 0, "start_line": 198 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ())))))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_mods: Vale.PPC64LE.QuickCode.va_mods_t -> h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power ())

Prims.Tot

[ "total" ]

[]

[ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.Math.Poly2_s.poly", "Prims.nat", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsVector.va_code_Vspltisw", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.PPC64LE.InsBasic.va_code_LoadImmShl64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Prims.op_Minus", "Vale.PPC64LE.InsVector.va_code_Mtvsrws", "Vale.PPC64LE.InsVector.va_code_Vsldoi", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsVector.va_quick_Vspltisw", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.InsBasic.va_quick_LoadImmShl64", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.eq2", "Prims.int", "Vale.Def.Types_s.ishl", "Prims.op_Modulus", "Prims.op_Multiply", "Prims.pow2", "Vale.AES.Types_helpers.lemma_ishl_64", "Vale.PPC64LE.InsVector.va_quick_Mtvsrws", "Vale.PPC64LE.InsVector.va_quick_Vsldoi", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.Def.Words_s.Mkfour", "Vale.Def.Words_s.nat32", "Vale.Math.Poly2_s.monomial", "Vale.AES.GF128.lemma_gf128_high_bit", "Vale.Math.Poly2_s.reverse", "Vale.Math.Poly2_s.shift", "Vale.Math.Poly2_s.add", "Vale.AES.GF128_s.gf128_modulus_low_terms", "Vale.AES.GF128.lemma_gf128_low_shift_1", "Vale.AES.PPC64LE.GF128_Init.va_quick_ShiftKey1_128", "Vale.AES.GHash_BE.gf128_power", "Vale.AES.GF128.shift_key_1", "Vale.AES.GHash_BE.g_power", "Vale.AES.GHash_BE.lemma_gf128_power", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.Def.Words_s.nat64", "Vale.PPC64LE.Machine_s.pow2_64", "Vale.PPC64LE.Decls.va_get_vec", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power" ]

[]

false

let va_qcode_ShiftKey1_gf128_power (va_mods: va_mods_t) (h: poly) (n: nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) =

(qblock va_mods (fun (va_s: va_state) -> let va_old_s:va_state = va_s in let hn:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (- 15872)) (fun (va_s: va_state) _ -> let va_arg24:Vale.Def.Types_s.nat64 = (- 15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (- 32768)) (fun (va_s: va_state) _ -> let va_arg23:Vale.Def.Types_s.nat64 = (- 32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s: va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GF128.lemma_gf128_high_bit () ) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms ) (fun (va_s: va_state) _ -> let va_arg22:Prims.nat = n in let va_arg21:Vale.Math.Poly2_s.poly = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))) ))))))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_qcode_Gf128_powers

val va_qcode_Gf128_powers (va_mods: va_mods_t) (h: poly) (hkeys_b: buffer128) : (va_quickCode unit (va_code_Gf128_powers ()))

let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (()))))))))))))))))))

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 99, "end_line": 387, "start_col": 0, "start_line": 350 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ()))))))))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_mods: Vale.PPC64LE.QuickCode.va_mods_t -> h: Vale.Math.Poly2_s.poly -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers ())

Prims.Tot

[ "total" ]

[]

[ "Vale.PPC64LE.QuickCode.va_mods_t", "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.QuickCodes.qblock", "Prims.unit", "Prims.Cons", "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.InsBasic.va_code_LoadImm64", "Vale.PPC64LE.Decls.va_op_reg_opr_reg", "Vale.PPC64LE.InsVector.va_code_Load128_byte16_buffer_index", "Vale.PPC64LE.Decls.va_op_heaplet_mem_heaplet", "Vale.PPC64LE.Decls.va_op_vec_opr_vec", "Vale.Arch.HeapTypes_s.Secret", "Vale.PPC64LE.InsVector.va_code_Vmr", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer", "Vale.AES.PPC64LE.GF128_Mul.va_code_Gf128MulRev128", "Vale.PPC64LE.InsVector.va_code_Store128_byte16_buffer_index", "Prims.Nil", "Vale.PPC64LE.Machine_s.precode", "Vale.PPC64LE.Decls.ins", "Vale.PPC64LE.Decls.ocmp", "Vale.PPC64LE.Decls.va_state", "Vale.PPC64LE.QuickCodes.va_QSeq", "Vale.PPC64LE.QuickCodes.va_range1", "Vale.PPC64LE.InsBasic.va_quick_LoadImm64", "Vale.PPC64LE.QuickCodes.va_QBind", "Vale.PPC64LE.InsVector.va_quick_Load128_byte16_buffer_index", "Vale.PPC64LE.QuickCodes.va_qPURE", "Prims.pure_post", "Prims.l_and", "Prims.l_True", "Prims.l_Forall", "Prims.l_imp", "Prims.eq2", "Vale.AES.GHash_BE.g_power", "Vale.AES.GHash_BE.lemma_g_power_1", "Vale.PPC64LE.InsVector.va_quick_Vmr", "Vale.AES.PPC64LE.GF128_Init.va_quick_ShiftKey1_gf128_power", "Vale.PPC64LE.InsVector.va_quick_Store128_byte16_buffer", "Vale.AES.PPC64LE.GF128_Mul.va_quick_Gf128MulRev128", "Prims.op_Addition", "Vale.AES.GF128.op_Star_Tilde", "Vale.AES.GHash_BE.lemma_g_power_n", "Vale.PPC64LE.InsVector.va_quick_Store128_byte16_buffer_index", "Vale.PPC64LE.QuickCodes.va_QEmpty", "Vale.PPC64LE.QuickCodes.quickCodes", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCode.va_quickCode", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers" ]

[]

false

let va_qcode_Gf128_powers (va_mods: va_mods_t) (h: poly) (hkeys_b: buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) =

(qblock va_mods (fun (va_s: va_state) -> let va_old_s:va_state = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s: va_state) _ -> let va_arg18:Vale.Math.Poly2_s.poly = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s: va_state) _ -> let va_arg17:Vale.Math.Poly2_s.poly = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_: unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))) ))

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_lemma_ShiftKey1_128

val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))))

let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 16, "end_line": 129, "start_col": 0, "start_line": 114 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_b0: Vale.PPC64LE.Decls.va_code -> va_s0: Vale.PPC64LE.Decls.va_state -> f: Vale.Math.Poly2_s.poly -> Prims.Ghost (Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel)

Prims.Ghost

[]

[ "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_state", "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.QuickCodes.fuel", "Prims.unit", "FStar.Pervasives.Native.Mktuple2", "Vale.PPC64LE.Decls.va_fuel", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Prims.Nil", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.list", "Vale.PPC64LE.QuickCode.__proj__QProc__item__mods", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_128", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.tuple3", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCodes.va_wp_sound_code_norm", "Prims.l_and", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.QuickCodes.va_range1", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.PPC64LE.Decls.va_get_vec", "Vale.AES.GF128.shift_key_1", "Vale.Math.Poly2_s.shift", "Vale.PPC64LE.QuickCode.quickCode", "Vale.AES.PPC64LE.GF128_Init.va_qcode_ShiftKey1_128" ]

[]

false

let va_lemma_ShiftKey1_128 va_b0 va_s0 f =

let va_mods:va_mods_t = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let va_sM, va_fM, va_g = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let h:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let h1:Vale.Math.Poly2_s.poly = Vale.Math.Poly2_s.shift h 1 in let offset:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_wpProof_Keyhash_init

val va_wpProof_Keyhash_init : alg:algorithm -> key:(seq nat32) -> roundkeys_b:buffer128 -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Keyhash_init alg key roundkeys_b hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Keyhash_init alg) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))

let va_wpProof_Keyhash_init alg key roundkeys_b hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Keyhash_init (va_code_Keyhash_init alg) va_s0 alg key roundkeys_b hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_layout va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 586, "start_col": 0, "start_line": 574 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b)) //-- //-- Keyhash_init [@ "opaque_to_smt" va_qattr] let va_code_Keyhash_init alg = (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ())))))))))) [@ "opaque_to_smt" va_qattr] let va_codegen_success_Keyhash_init alg = (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Gf128_powers ()) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Keyhash_init (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (roundkeys_b:buffer128) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Keyhash_init alg)) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_CreateHeaplets ([declare_buffer128 roundkeys_b 0 Secret Immutable; declare_buffer128 hkeys_b 1 Secret Mutable])) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 196 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (fun (va_s:va_state) _ -> va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 197 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_AESEncryptBlock alg (va_get_vec 0 va_s) key (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) roundkeys_b)) roundkeys_b) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 198 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 199 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> va_QBind va_range1 "***** PRECONDITION NOT MET AT line 201 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128_powers (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 0 va_s)) hkeys_b) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1 "***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) -> Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) (fun _ -> let (va_arg12:Vale.Def.Types_s.quad32) = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) in let (va_arg11:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) hkeys_b) in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hkeys_reqs_pub_priv va_arg11 va_arg12) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))) [@"opaque_to_smt"] let va_lemma_Keyhash_init va_b0 va_s0 alg key roundkeys_b hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Keyhash_init va_mods alg key roundkeys_b hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Keyhash_init alg) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 165 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 189 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_buffer128 hkeys_b (va_get_mem va_s0) (va_get_mem va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 190 column 117 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM)

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.PPC64LE.Memory.nat32 -> roundkeys_b: Vale.PPC64LE.Memory.buffer128 -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> va_s0: Vale.PPC64LE.Decls.va_state -> va_k: (_: Vale.PPC64LE.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel) * Prims.unit)

Prims.Ghost

[]

[ "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.PPC64LE.Memory.nat32", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.Decls.va_state", "Prims.unit", "Vale.PPC64LE.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_mem_layout", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Prims.Nil", "Prims._assert", "Vale.PPC64LE.Decls.va_state_eq", "Vale.PPC64LE.Decls.va_update_vec", "Vale.PPC64LE.Decls.va_update_reg", "Vale.PPC64LE.Decls.va_update_mem_layout", "Vale.PPC64LE.Decls.va_update_mem_heaplet", "Vale.PPC64LE.Decls.va_update_ok", "Vale.PPC64LE.Decls.va_update_mem", "Vale.PPC64LE.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.PPC64LE.Machine_s.state", "Vale.AES.PPC64LE.GF128_Init.va_lemma_Keyhash_init", "Vale.AES.PPC64LE.GF128_Init.va_code_Keyhash_init" ]

[]

false

let va_wpProof_Keyhash_init alg key roundkeys_b hkeys_b va_s0 va_k =

let va_sM, va_f0 = va_lemma_Keyhash_init (va_code_Keyhash_init alg) va_s0 alg key roundkeys_b hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_layout va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))) ))))); va_lemma_norm_mods ([ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_mem ]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_lemma_ShiftKey1_gf128_power

val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))))

let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 16, "end_line": 269, "start_col": 0, "start_line": 254 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_b0: Vale.PPC64LE.Decls.va_code -> va_s0: Vale.PPC64LE.Decls.va_state -> h: Vale.Math.Poly2_s.poly -> n: Prims.nat -> Prims.Ghost (Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel)

Prims.Ghost

[]

[ "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_state", "Vale.Math.Poly2_s.poly", "Prims.nat", "Vale.PPC64LE.QuickCodes.fuel", "Prims.unit", "FStar.Pervasives.Native.Mktuple2", "Vale.PPC64LE.Decls.va_fuel", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Prims.Nil", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.list", "Vale.PPC64LE.QuickCode.__proj__QProc__item__mods", "Vale.AES.PPC64LE.GF128_Init.va_code_ShiftKey1_gf128_power", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.tuple3", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCodes.va_wp_sound_code_norm", "Prims.l_and", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.QuickCodes.va_range1", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.PPC64LE.Decls.va_get_vec", "Vale.AES.GHash_BE.gf128_power", "Vale.PPC64LE.QuickCode.quickCode", "Vale.AES.PPC64LE.GF128_Init.va_qcode_ShiftKey1_gf128_power" ]

[]

false

let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n =

let va_mods:va_mods_t = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let va_sM, va_fM, va_g = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let hn:Vale.Math.Poly2_s.poly = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([ va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok ]) va_sM va_s0; (va_sM, va_fM)

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_lemma_Gf128_powers

val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))

let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 16, "end_line": 437, "start_col": 0, "start_line": 411 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_b0: Vale.PPC64LE.Decls.va_code -> va_s0: Vale.PPC64LE.Decls.va_state -> h: Vale.Math.Poly2_s.poly -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> Prims.Ghost (Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel)

Prims.Ghost

[]

[ "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_state", "Vale.Math.Poly2_s.poly", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.QuickCodes.fuel", "Prims.unit", "FStar.Pervasives.Native.Mktuple2", "Vale.PPC64LE.Decls.va_fuel", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Prims.Nil", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.list", "Vale.PPC64LE.QuickCode.__proj__QProc__item__mods", "Vale.AES.PPC64LE.GF128_Init.va_code_Gf128_powers", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.tuple3", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCodes.va_wp_sound_code_norm", "Prims.l_and", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.QuickCodes.va_range1", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Vale.PPC64LE.Decls.modifies_mem", "Vale.PPC64LE.Decls.loc_buffer", "Vale.PPC64LE.Memory.vuint128", "Vale.PPC64LE.Decls.va_get_mem_heaplet", "Vale.Math.Poly2.Bits_s.of_quad32", "Vale.Def.Types_s.reverse_bytes_quad32", "Vale.PPC64LE.Decls.buffer128_read", "Vale.AES.GHash_BE.gf128_power", "Vale.PPC64LE.Machine_s.quad32", "Vale.PPC64LE.QuickCode.quickCode", "Vale.AES.PPC64LE.GF128_Init.va_qcode_Gf128_powers" ]

[]

false

let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b =

let va_mods:va_mods_t = [ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem ] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let va_sM, va_fM, va_g = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem ]) va_sM va_s0; (va_sM, va_fM)

false

Steel.ST.C.Types.UserStruct.fsti

Steel.ST.C.Types.UserStruct.unstruct_field_alt

val unstruct_field_alt (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (#v': Ghost.erased (sd.field_desc.fd_type field)) (r': ref (sd.field_desc.fd_typedef field)) : STGhost (Ghost.erased t) opened (((has_struct_field r field r') `star` (pts_to r v)) `star` (pts_to r' v')) (fun s' -> (has_struct_field r field r') `star` (pts_to r s')) (sd.get v field == unknown (sd.field_desc.fd_typedef field)) (fun s' -> Ghost.reveal s' == set sd v field v')

let unstruct_field_alt (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (#v': Ghost.erased (sd.field_desc.fd_type field)) (r': ref (sd.field_desc.fd_typedef field)) : STGhost (Ghost.erased t) opened (has_struct_field r field r' `star` pts_to r v `star` pts_to r' v') (fun s' -> has_struct_field r field r' `star` pts_to r s') ( sd.get v field == unknown (sd.field_desc.fd_typedef field) ) (fun s' -> Ghost.reveal s' == set sd v field v') = unstruct_field r field r'; _

{ "file_name": "lib/steel/c/Steel.ST.C.Types.UserStruct.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 3, "end_line": 216, "start_col": 0, "start_line": 199 }

module Steel.ST.C.Types.UserStruct open Steel.ST.Util open Steel.ST.C.Types.Struct.Aux module Set = FStar.Set (* This library allows the user to define their own struct type, with a constructor from field values, and a destructor to field values for each field. This may be necessary for recursive structs *) let set_def (#t: eqtype) (s: FStar.Set.set t) (x: t) : Tot bool = FStar.Set.mem x s noextract let nonempty_set (t: eqtype) = (s: Set.set t { exists x . set_def s x == true }) noextract let set_snoc // for associativity reasons (#t: eqtype) (q: FStar.Set.set t) (a: t) : Pure (nonempty_set t) (requires True) (ensures (fun s -> (forall (x: t). {:pattern FStar.Set.mem x s} FStar.Set.mem x s == (x = a || FStar.Set.mem x q)) )) = q `FStar.Set.union` FStar.Set.singleton a [@@noextract_to "krml"] let field_t (s: Set.set string) : Tot eqtype = (f: string { Set.mem f s }) [@@noextract_to "krml"; norm_field_attr] inline_for_extraction // for field_desc.fd_type noeq type struct_def (t: Type) = { fields: Set.set string; field_desc: field_description_gen_t (field_t fields); mk: ((f: field_t fields) -> Tot (field_desc.fd_type f)) -> Tot t; get: (t -> (f: field_t fields) -> Tot (field_desc.fd_type f)); get_mk: (phi: ((f: field_t fields) -> Tot (field_desc.fd_type f))) -> (f: field_t fields) -> Lemma (get (mk phi) f == phi f); extensionality: (x1: t) -> (x2: t) -> ((f: field_t fields) -> Lemma (get x1 f == get x2 f)) -> Lemma (x1 == x2); } let nonempty_set_nonempty_type (x: string) (s: Set.set string) : Lemma (requires (x `Set.mem` s)) (ensures (exists (x: field_t s) . True)) = Classical.exists_intro (fun (_: field_t s) -> True) x [@@noextract_to "krml"] let set_aux (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) (f': field_t sd.fields) : Tot (sd.field_desc.fd_type f') = if f = f' then v else sd.get x f' [@@noextract_to "krml"] let set (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) : Tot t = sd.mk (set_aux sd x f v) let get_set (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) (f' : field_t sd.fields) : Lemma (sd.get (set sd x f v) f' == (if f = f' then v else sd.get x f')) [SMTPat (sd.get (set sd x f v) f')] = sd.get_mk (set_aux sd x f v) f' [@@noextract_to "krml"] val struct_typedef (#t: Type) (sd: struct_def t) : Tot (typedef t) val has_struct_field (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : Tot vprop val has_struct_field_dup (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r') (fun _ -> has_struct_field r field r' `star` has_struct_field r field r') val has_struct_field_inj (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r1 r2: ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r1 `star` has_struct_field r field r2) (fun _ -> has_struct_field r field r1 `star` has_struct_field r field r2 `star` ref_equiv r1 r2) val has_struct_field_equiv_from (#opened: _) (#t: Type) (#sd: struct_def t) (r1: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) (r2: ref (struct_typedef sd)) : STGhostT unit opened (ref_equiv r1 r2 `star` has_struct_field r1 field r') (fun _ -> ref_equiv r1 r2 `star` has_struct_field r2 field r') val has_struct_field_equiv_to (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r1' r2': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (ref_equiv r1' r2' `star` has_struct_field r field r1') (fun _ -> ref_equiv r1' r2' `star` has_struct_field r field r2') val ghost_struct_field_focus (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r' `star` pts_to r v) (fun _ -> has_struct_field r field r' `star` pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to r' (sd.get v field)) val ghost_struct_field (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STGhostT (Ghost.erased (ref (sd.field_desc.fd_typedef field))) opened (pts_to r v) (fun r' -> has_struct_field r field r' `star` pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to r' (sd.get v field)) [@@noextract_to "krml"] // primitive val struct_field0 (#t: Type) (t': Type0) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (td': typedef t' { t' == sd.field_desc.fd_type field /\ td' == sd.field_desc.fd_typedef field }) : STT (ref td') (pts_to r v) (fun r' -> has_struct_field r field (coerce_eq () r') `star` pts_to r (set sd (Ghost.reveal v) field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to #_ #(sd.field_desc.fd_typedef field) (coerce_eq () r') (sd.get (Ghost.reveal v) field)) inline_for_extraction [@@noextract_to "krml"] // primitive let struct_field (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STT (ref #(norm norm_field_steps (sd.field_desc.fd_type field)) (sd.field_desc.fd_typedef field)) (pts_to r v) (fun r' -> pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to #(norm norm_field_steps (sd.field_desc.fd_type field)) r' (sd.get v field) `star` has_struct_field r field r') = struct_field0 (norm norm_field_steps (sd.field_desc.fd_type field)) r field (sd.field_desc.fd_typedef field) val unstruct_field (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (#v': Ghost.erased (sd.field_desc.fd_type field)) (r': ref (sd.field_desc.fd_typedef field)) : STGhost unit opened (has_struct_field r field r' `star` pts_to r v `star` pts_to r' v') (fun _ -> has_struct_field r field r' `star` pts_to r (set sd v field v')) ( sd.get v field == unknown (sd.field_desc.fd_typedef field) ) (fun _ -> True)

{ "checked_file": "/", "dependencies": [ "Steel.ST.Util.fsti.checked", "Steel.ST.C.Types.Struct.Aux.fsti.checked", "Steel.FractionalPermission.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "Steel.ST.C.Types.UserStruct.fsti" }

[ { "abbrev": true, "full_module": "FStar.Set", "short_module": "Set" }, { "abbrev": false, "full_module": "Steel.ST.C.Types.Struct.Aux", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.Util", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "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 } ]

{ "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" }

false

r: Steel.ST.C.Types.Base.ref (Steel.ST.C.Types.UserStruct.struct_typedef sd) -> field: Steel.ST.C.Types.UserStruct.field_t (Mkstruct_def?.fields sd) -> r': Steel.ST.C.Types.Base.ref (Mkfield_description_gen_t?.fd_typedef (Mkstruct_def?.field_desc sd) field) -> Steel.ST.Effect.Ghost.STGhost (FStar.Ghost.erased t)

Steel.ST.Effect.Ghost.STGhost

[]

[ "Steel.Memory.inames", "Steel.ST.C.Types.UserStruct.struct_def", "FStar.Ghost.erased", "Steel.ST.C.Types.Base.ref", "Steel.ST.C.Types.UserStruct.struct_typedef", "Steel.ST.C.Types.UserStruct.field_t", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__fields", "Steel.ST.C.Types.Struct.Aux.__proj__Mkfield_description_gen_t__item__fd_type", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__field_desc", "Steel.ST.C.Types.Struct.Aux.__proj__Mkfield_description_gen_t__item__fd_typedef", "FStar.Ghost.hide", "Steel.ST.C.Types.UserStruct.set", "FStar.Ghost.reveal", "Prims.unit", "Steel.ST.C.Types.UserStruct.unstruct_field", "Steel.Effect.Common.star", "Steel.ST.C.Types.UserStruct.has_struct_field", "Steel.ST.C.Types.Base.pts_to", "Steel.Effect.Common.vprop", "Prims.eq2", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__get", "Steel.ST.C.Types.Base.unknown", "Prims.l_True" ]

[]

false

true

false

let unstruct_field_alt (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (#v': Ghost.erased (sd.field_desc.fd_type field)) (r': ref (sd.field_desc.fd_typedef field)) : STGhost (Ghost.erased t) opened (((has_struct_field r field r') `star` (pts_to r v)) `star` (pts_to r' v')) (fun s' -> (has_struct_field r field r') `star` (pts_to r s')) (sd.get v field == unknown (sd.field_desc.fd_typedef field)) (fun s' -> Ghost.reveal s' == set sd v field v') =

unstruct_field r field r'; _

false

Steel.GhostMonotonicHigherReference.fst

Steel.GhostMonotonicHigherReference.alloc

val alloc (#opened: _) (#a:Type) (p:Preorder.preorder a) (v:a) : SteelGhostT (ref a p) opened emp (fun r -> pts_to r full_perm v)

let alloc #_ (#a:Type) (p:Preorder.preorder a) (v:a) = let h = Current [v] full_perm in assert (compatible pcm_history h h); let x : ref a p = alloc h in intro_pure_full x v h; x

{ "file_name": "lib/steel/Steel.GhostMonotonicHigherReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 5, "end_line": 73, "start_col": 0, "start_line": 68 }

(* Copyright 2020 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 Steel.GhostMonotonicHigherReference open FStar.Ghost open FStar.PCM open Steel.Memory open Steel.Effect.Atomic open Steel.Effect open Steel.GhostPCMReference open Steel.FractionalPermission open Steel.Preorder module Preorder = FStar.Preorder module Q = Steel.Preorder module M = Steel.Memory module PR = Steel.GhostPCMReference module A = Steel.Effect.Atomic open FStar.Real #set-options "--ide_id_info_off" let ref a p = PR.ref (history a p) pcm_history [@@__reduce__] let pts_to_body #a #p (r:ref a p) (f:perm) (v:a) (h:history a p) = PR.pts_to r h `star` pure (history_val h v f) let pts_to' (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v: a) = h_exists (pts_to_body r f v) let pts_to_sl r f v = hp_of (pts_to' r f v) let intro_pure #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to_body r f v h) = A.intro_pure (history_val h v f) let intro_pure_full #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v) = intro_pure #_ #a #p #f r v h; intro_exists h (pts_to_body r f v)

{ "checked_file": "/", "dependencies": [ "Steel.Preorder.fst.checked", "Steel.Memory.fsti.checked", "Steel.GhostPCMReference.fsti.checked", "Steel.FractionalPermission.fst.checked", "Steel.Effect.Atomic.fsti.checked", "Steel.Effect.fsti.checked", "prims.fst.checked", "FStar.Real.fsti.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.PCM.fst.checked", "FStar.Ghost.fsti.checked" ], "interface_file": true, "source_file": "Steel.GhostMonotonicHigherReference.fst" }

[ { "abbrev": false, "full_module": "FStar.Real", "short_module": null }, { "abbrev": true, "full_module": "Steel.Effect.Atomic", "short_module": "A" }, { "abbrev": true, "full_module": "Steel.GhostPCMReference", "short_module": "PR" }, { "abbrev": true, "full_module": "Steel.Memory", "short_module": "M" }, { "abbrev": true, "full_module": "Steel.Preorder", "short_module": "Q" }, { "abbrev": false, "full_module": "Steel.Preorder", "short_module": null }, { "abbrev": false, "full_module": "Steel.GhostPCMReference", "short_module": null }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "Steel", "short_module": null }, { "abbrev": false, "full_module": "Steel", "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 } ]

{ "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" }

false

p: FStar.Preorder.preorder a -> v: a -> Steel.Effect.Atomic.SteelGhostT (Steel.GhostMonotonicHigherReference.ref a p)

Steel.Effect.Atomic.SteelGhostT

[]

[ "Steel.Memory.inames", "FStar.Preorder.preorder", "Steel.GhostMonotonicHigherReference.ref", "Prims.unit", "Steel.GhostMonotonicHigherReference.intro_pure_full", "Steel.FractionalPermission.full_perm", "Steel.GhostPCMReference.alloc", "Steel.Preorder.history", "Steel.Preorder.pcm_history", "Steel.GhostPCMReference.ref", "Prims._assert", "FStar.PCM.compatible", "Steel.Preorder.Current", "Prims.Cons", "Prims.Nil" ]

[]

false

true

false

let alloc #_ (#a: Type) (p: Preorder.preorder a) (v: a) =

let h = Current [v] full_perm in assert (compatible pcm_history h h); let x:ref a p = alloc h in intro_pure_full x v h; x

false

Vale.AES.PPC64LE.GF128_Init.fst

Vale.AES.PPC64LE.GF128_Init.va_lemma_Keyhash_init

val va_lemma_Keyhash_init : va_b0:va_code -> va_s0:va_state -> alg:algorithm -> key:(seq nat32) -> roundkeys_b:buffer128 -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Keyhash_init alg) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Memory.is_initial_heap (va_get_mem_layout va_s0) (va_get_mem va_s0) /\ (alg = AES_128 \/ alg = AES_256) /\ Vale.PPC64LE.Decls.buffers_disjoint128 roundkeys_b hkeys_b /\ Vale.AES.AES_BE_s.is_aes_key_word alg key /\ Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem va_s0) roundkeys_b) == Vale.AES.AES_BE_s.key_to_round_keys_word alg key /\ Vale.PPC64LE.Decls.validSrcAddrs128 (va_get_mem va_s0) (va_get_reg 4 va_s0) roundkeys_b (Vale.AES.AES_common_s.nr alg + 1) (va_get_mem_layout va_s0) Secret /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_buffer128 hkeys_b (va_get_mem va_s0) (va_get_mem va_sM) /\ Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_layout va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))

let va_lemma_Keyhash_init va_b0 va_s0 alg key roundkeys_b hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Keyhash_init va_mods alg key roundkeys_b hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Keyhash_init alg) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 165 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 189 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_buffer128 hkeys_b (va_get_mem va_s0) (va_get_mem va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 190 column 117 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM)

{ "file_name": "obj/Vale.AES.PPC64LE.GF128_Init.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 16, "end_line": 570, "start_col": 0, "start_line": 550 }

module Vale.AES.PPC64LE.GF128_Init open Vale.Def.Words_s open Vale.Def.Words.Four_s open Vale.Def.Types_s open FStar.Seq open Vale.Arch.Types open Vale.Arch.HeapImpl open Vale.Math.Poly2_s open Vale.Math.Poly2 open Vale.Math.Poly2.Bits_s open Vale.Math.Poly2.Bits open Vale.Math.Poly2.Lemmas open Vale.AES.GF128_s open Vale.AES.GF128 open Vale.AES.GHash_BE open Vale.AES.AES_BE_s open Vale.AES.AES256_helpers_BE open Vale.AES.PPC64LE.AES open Vale.PPC64LE.Machine_s open Vale.PPC64LE.Memory open Vale.PPC64LE.State open Vale.PPC64LE.Decls open Vale.PPC64LE.InsBasic open Vale.PPC64LE.InsMem open Vale.PPC64LE.InsVector open Vale.PPC64LE.QuickCode open Vale.PPC64LE.QuickCodes open Vale.AES.PPC64LE.PolyOps open Vale.AES.PPC64LE.GF128_Mul open Vale.AES.OptPublic_BE //-- ShiftKey1_128 val va_code_ShiftKey1_128 : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_128 () = (va_Block (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CCons (va_code_ShiftLeft128_1 ()) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_CCons (va_code_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_CCons (va_code_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_CCons (va_code_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_CNil ()))))))))) val va_codegen_success_ShiftKey1_128 : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_128 () = (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_pbool_and (va_codegen_success_ShiftLeft128_1 ()) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_pbool_and (va_codegen_success_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (va_pbool_and (va_codegen_success_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (va_pbool_and (va_codegen_success_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_128 (va_mods:va_mods_t) (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 79 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 80 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftLeft128_1 h) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 81 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Bits.lemma_of_to_quad32_mask h1) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 82 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.lemma_shift_define_i h 1 128) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 84 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 85 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vcmpequw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 5)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 86 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_test_high_bit h) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 87 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltw (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) 0) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 88 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_zero ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 89 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Words.lemma_quad32_ones ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 92 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAnd (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 4)) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 93 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.Math.Poly2.Lemmas.lemma_and_consts ()) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 94 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_VPolyAdd (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 3)) (va_QEmpty (())))))))))))))))) val va_lemma_ShiftKey1_128 : va_b0:va_code -> va_s0:va_state -> f:poly -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_128 ()) va_s0 /\ va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) /\ va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0)))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_128 va_b0 va_s0 f = let (va_mods:va_mods_t) = [va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_128 va_mods f in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_128 ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 77 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_128 (f:poly) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 5 va_s0) == Vale.Math.Poly2_s.monomial 127 /\ offset == Vale.Math.Poly2_s.reverse (Vale.Math.Poly2_s.shift (Vale.Math.Poly2_s.add (Vale.Math.Poly2_s.monomial 128) f) (-1)) 127) /\ (forall (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) . let va_sM = va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 va_s0)) in va_get_ok va_sM /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in let (h1:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2_s.shift h 1 in let (offset:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GF128.shift_key_1 128 f h) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_128 : f:poly -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_128 f va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_128 f va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_128 (va_code_ShiftKey1_128 ()) va_s0 f in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_128 (f:poly) : (va_quickCode unit (va_code_ShiftKey1_128 ())) = (va_QProc (va_code_ShiftKey1_128 ()) ([va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1]) (va_wp_ShiftKey1_128 f) (va_wpProof_ShiftKey1_128 f)) //-- //-- ShiftKey1_gf128_power val va_code_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_ShiftKey1_gf128_power () = (va_Block (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 1) 0) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 2) 1) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_CCons (va_code_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_CCons (va_code_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_CCons (va_code_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_CCons (va_code_ShiftKey1_128 ()) (va_CNil ())))))))))))) val va_codegen_success_ShiftKey1_gf128_power : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_ShiftKey1_gf128_power () = (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 1) 0) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 2) 1) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (va_pbool_and (va_codegen_success_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_pbool_and (va_codegen_success_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (va_pbool_and (va_codegen_success_ShiftKey1_128 ()) (va_ttrue ()))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_ShiftKey1_gf128_power (va_mods:va_mods_t) (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s) in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 110 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 1) 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 111 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 2) 1) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 112 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-15872)) (fun (va_s:va_state) _ -> let (va_arg24:Vale.Def.Types_s.nat64) = (-15872) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 113 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg24 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 114 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 4) (va_op_reg_opr_reg 10)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 115 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImmShl64 (va_op_reg_opr_reg 10) (-32768)) (fun (va_s:va_state) _ -> let (va_arg23:Vale.Def.Types_s.nat64) = (-32768) `op_Modulus` pow2_64 in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 116 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.Types_helpers.lemma_ishl_64 va_arg23 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 117 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Mtvsrws (va_op_vec_opr_vec 5) (va_op_reg_opr_reg 10)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 118 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 1) 8) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 119 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 5) (va_op_vec_opr_vec 1) 12) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 120 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vsldoi (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 4) (va_op_vec_opr_vec 2) 4) (fun (va_s:va_state) _ -> va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 121 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_high_bit ()) (va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 122 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GF128.lemma_gf128_low_shift_1 ()) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 124 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_128 gf128_modulus_low_terms) (fun (va_s:va_state) _ -> let (va_arg22:Prims.nat) = n in let (va_arg21:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 125 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_gf128_power va_arg21 va_arg22) (va_QEmpty (())))))))))))))))))) val va_lemma_ShiftKey1_gf128_power : va_b0:va_code -> va_s0:va_state -> h:poly -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_ShiftKey1_gf128_power ()) va_s0 /\ va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) /\ va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0))))))))) [@"opaque_to_smt"] let va_lemma_ShiftKey1_gf128_power va_b0 va_s0 h n = let (va_mods:va_mods_t) = [va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok] in let va_qc = va_qcode_ShiftKey1_gf128_power va_mods h n in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_ShiftKey1_gf128_power ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 97 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in label va_range1 "***** POSTCONDITION NOT MET AT line 108 column 43 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10; va_Mod_ok]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_ShiftKey1_gf128_power (h:poly) (n:nat) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in hn == Vale.AES.GHash_BE.g_power h n) /\ (forall (va_x_r10:nat64) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) . let va_sM = va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_reg 10 va_x_r10 va_s0))))) in va_get_ok va_sM /\ (let (hn:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0) in Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) == Vale.AES.GHash_BE.gf128_power h n) ==> va_k va_sM (()))) val va_wpProof_ShiftKey1_gf128_power : h:poly -> n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_ShiftKey1_gf128_power h n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_ShiftKey1_gf128_power h n va_s0 va_k = let (va_sM, va_f0) = va_lemma_ShiftKey1_gf128_power (va_code_ShiftKey1_gf128_power ()) va_s0 h n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_reg 10 va_sM (va_update_ok va_sM va_s0)))))))); va_lemma_norm_mods ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_ShiftKey1_gf128_power (h:poly) (n:nat) : (va_quickCode unit (va_code_ShiftKey1_gf128_power ())) = (va_QProc (va_code_ShiftKey1_gf128_power ()) ([va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_reg 10]) (va_wp_ShiftKey1_gf128_power h n) (va_wpProof_ShiftKey1_gf128_power h n)) //-- //-- Gf128_powers val va_code_Gf128_powers : va_dummy:unit -> Tot va_code [@ "opaque_to_smt" va_qattr] let va_code_Gf128_powers () = (va_Block (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_CCons (va_code_Gf128MulRev128 ()) (va_CCons (va_code_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_CCons (va_code_ShiftKey1_gf128_power ()) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CNil ()))))))))))))))) val va_codegen_success_Gf128_powers : va_dummy:unit -> Tot va_pbool [@ "opaque_to_smt" va_qattr] let va_codegen_success_Gf128_powers () = (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_pbool_and (va_codegen_success_Gf128MulRev128 ()) (va_pbool_and (va_codegen_success_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_pbool_and (va_codegen_success_ShiftKey1_gf128_power ()) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_ttrue ())))))))))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Gf128_powers (va_mods:va_mods_t) (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 147 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 148 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Load128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> let (va_arg18:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 149 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_1 va_arg18) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 150 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 6) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 151 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 152 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 153 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) Secret hkeys_b 0) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 155 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 1) (va_op_vec_opr_vec 6)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 156 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 2) (va_op_vec_opr_vec 6)) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 157 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128MulRev128 ()) (fun (va_s:va_state) _ -> let (va_arg17:Vale.Math.Poly2_s.poly) = h in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 158 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_g_power_n va_arg17 1) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 159 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vmr (va_op_vec_opr_vec 3) (va_op_vec_opr_vec 1)) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 160 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_ShiftKey1_gf128_power h 2) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 161 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 16) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 162 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 1) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 1) (va_QEmpty (())))))))))))))))))) val va_lemma_Gf128_powers : va_b0:va_code -> va_s0:va_state -> h:poly -> hkeys_b:buffer128 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Gf128_powers ()) va_s0 /\ va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) /\ va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))) [@"opaque_to_smt"] let va_lemma_Gf128_powers va_b0 va_s0 h hkeys_b = let (va_mods:va_mods_t) = [va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem] in let va_qc = va_qcode_Gf128_powers va_mods h hkeys_b in let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Gf128_powers ()) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 128 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 141 column 61 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 142 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 143 column 96 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 145 column 84 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem]) va_sM va_s0; (va_sM, va_fM) [@ va_qattr] let va_wp_Gf128_powers (h:poly) (hkeys_b:buffer128) (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 = (va_get_ok va_s0 /\ Vale.PPC64LE.Decls.validDstAddrs128 (va_get_mem_heaplet 1 va_s0) (va_get_reg 3 va_s0) hkeys_b 3 (va_get_mem_layout va_s0) Secret /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0))) == h /\ (forall (va_x_mem:vale_heap) (va_x_heap1:vale_heap) (va_x_r10:nat64) (va_x_v0:quad32) (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v5:quad32) (va_x_v6:quad32) . let va_sM = va_upd_vec 6 va_x_v6 (va_upd_vec 5 va_x_v5 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2 (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 (va_upd_reg 10 va_x_r10 (va_upd_mem_heaplet 1 va_x_heap1 (va_upd_mem va_x_mem va_s0))))))))) in va_get_ok va_sM /\ Vale.PPC64LE.Decls.modifies_mem (Vale.PPC64LE.Decls.loc_buffer #Vale.PPC64LE.Memory.vuint128 hkeys_b) (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 0 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 1 /\ Vale.Math.Poly2.Bits_s.of_quad32 (Vale.Def.Types_s.reverse_bytes_quad32 (Vale.PPC64LE.Decls.buffer128_read hkeys_b 1 (va_get_mem_heaplet 1 va_sM))) == Vale.AES.GHash_BE.gf128_power h 2 /\ Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_sM) == Vale.PPC64LE.Decls.buffer128_read hkeys_b 2 (va_get_mem_heaplet 1 va_s0) ==> va_k va_sM (()))) val va_wpProof_Gf128_powers : h:poly -> hkeys_b:buffer128 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Gf128_powers h hkeys_b va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) [@"opaque_to_smt"] let va_wpProof_Gf128_powers h hkeys_b va_s0 va_k = let (va_sM, va_f0) = va_lemma_Gf128_powers (va_code_Gf128_powers ()) va_s0 h hkeys_b in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_vec 6 va_sM (va_update_vec 5 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_reg 10 va_sM (va_update_mem_heaplet 1 va_sM (va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))); va_lemma_norm_mods ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) [@ "opaque_to_smt" va_qattr] let va_quick_Gf128_powers (h:poly) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Gf128_powers ())) = (va_QProc (va_code_Gf128_powers ()) ([va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_heaplet 1; va_Mod_mem]) (va_wp_Gf128_powers h hkeys_b) (va_wpProof_Gf128_powers h hkeys_b)) //-- //-- Keyhash_init [@ "opaque_to_smt" va_qattr] let va_code_Keyhash_init alg = (va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Vspltisw (va_op_vec_opr_vec 0) 0) (va_CCons (va_code_AESEncryptBlock alg) (va_CCons (va_code_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_CCons (va_code_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_CCons (va_code_Gf128_powers ()) (va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_DestroyHeaplets ()) (va_CNil ())))))))))) [@ "opaque_to_smt" va_qattr] let va_codegen_success_Keyhash_init alg = (va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Vspltisw (va_op_vec_opr_vec 0) 0) (va_pbool_and (va_codegen_success_AESEncryptBlock alg) (va_pbool_and (va_codegen_success_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_pbool_and (va_codegen_success_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret) (va_pbool_and (va_codegen_success_Gf128_powers ()) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue ())))))))) [@ "opaque_to_smt" va_qattr] let va_qcode_Keyhash_init (va_mods:va_mods_t) (alg:algorithm) (key:(seq nat32)) (roundkeys_b:buffer128) (hkeys_b:buffer128) : (va_quickCode unit (va_code_Keyhash_init alg)) = (qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 192 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_CreateHeaplets ([declare_buffer128 roundkeys_b 0 Secret Immutable; declare_buffer128 hkeys_b 1 Secret Mutable])) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 196 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Vspltisw (va_op_vec_opr_vec 0) 0) (fun (va_s:va_state) _ -> va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 197 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_AESEncryptBlock alg (va_get_vec 0 va_s) key (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.buffer128_as_seq (va_get_mem_heaplet 0 va_s) roundkeys_b)) roundkeys_b) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 198 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_LoadImm64 (va_op_reg_opr_reg 10) 32) (va_QBind va_range1 "***** PRECONDITION NOT MET AT line 199 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Store128_byte16_buffer_index (va_op_heaplet_mem_heaplet 1) (va_op_vec_opr_vec 0) (va_op_reg_opr_reg 3) (va_op_reg_opr_reg 10) Secret hkeys_b 2) (fun (va_s:va_state) _ -> va_QBind va_range1 "***** PRECONDITION NOT MET AT line 201 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_Gf128_powers (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 0 va_s)) hkeys_b) (fun (va_s:va_state) _ -> va_qAssertSquash va_range1 "***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" ((fun (alg_10591:Vale.AES.AES_common_s.algorithm) (key_10592:(FStar.Seq.Base.seq Vale.Def.Types_s.nat32)) (input_10593:Vale.Def.Types_s.quad32) -> Vale.AES.AES_BE_s.is_aes_key_word alg_10591 key_10592) alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)) (fun _ -> let (va_arg12:Vale.Def.Types_s.quad32) = Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0) in let (va_arg11:(FStar.Seq.Base.seq Vale.Def.Types_s.quad32)) = Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem_heaplet 1 va_s) hkeys_b) in va_qPURE va_range1 "***** PRECONDITION NOT MET AT line 203 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (fun (_:unit) -> Vale.AES.GHash_BE.lemma_hkeys_reqs_pub_priv va_arg11 va_arg12) (va_QSeq va_range1 "***** PRECONDITION NOT MET AT line 205 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))))

{ "checked_file": "/", "dependencies": [ "Vale.PPC64LE.State.fsti.checked", "Vale.PPC64LE.QuickCodes.fsti.checked", "Vale.PPC64LE.QuickCode.fst.checked", "Vale.PPC64LE.Memory.fsti.checked", "Vale.PPC64LE.Machine_s.fst.checked", "Vale.PPC64LE.InsVector.fsti.checked", "Vale.PPC64LE.InsMem.fsti.checked", "Vale.PPC64LE.InsBasic.fsti.checked", "Vale.PPC64LE.Decls.fsti.checked", "Vale.Math.Poly2_s.fsti.checked", "Vale.Math.Poly2.Words.fsti.checked", "Vale.Math.Poly2.Lemmas.fsti.checked", "Vale.Math.Poly2.Bits_s.fsti.checked", "Vale.Math.Poly2.Bits.fsti.checked", "Vale.Math.Poly2.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Four_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.Arch.HeapImpl.fsti.checked", "Vale.AES.Types_helpers.fsti.checked", "Vale.AES.PPC64LE.PolyOps.fsti.checked", "Vale.AES.PPC64LE.GF128_Mul.fsti.checked", "Vale.AES.PPC64LE.AES.fsti.checked", "Vale.AES.OptPublic_BE.fsti.checked", "Vale.AES.GHash_BE.fsti.checked", "Vale.AES.GF128_s.fsti.checked", "Vale.AES.GF128.fsti.checked", "Vale.AES.AES_common_s.fst.checked", "Vale.AES.AES_BE_s.fst.checked", "Vale.AES.AES256_helpers_BE.fsti.checked", "prims.fst.checked", "FStar.Seq.Base.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": true, "source_file": "Vale.AES.PPC64LE.GF128_Init.fst" }

[ { "abbrev": false, "full_module": "Vale.AES.OptPublic_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.GF128_Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.PolyOps", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCodes", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsVector", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsMem", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.InsBasic", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.PPC64LE.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE.AES", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES256_helpers_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.AES_BE_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GHash_BE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.GF128_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Lemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2.Bits_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2", "short_module": null }, { "abbrev": false, "full_module": "Vale.Math.Poly2_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "FStar.Seq", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words.Four_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Words_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "short_module": null }, { "abbrev": false, "full_module": "Vale.AES.PPC64LE", "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 } ]

{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 0, "max_fuel": 1, "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": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

va_b0: Vale.PPC64LE.Decls.va_code -> va_s0: Vale.PPC64LE.Decls.va_state -> alg: Vale.AES.AES_common_s.algorithm -> key: FStar.Seq.Base.seq Vale.PPC64LE.Memory.nat32 -> roundkeys_b: Vale.PPC64LE.Memory.buffer128 -> hkeys_b: Vale.PPC64LE.Memory.buffer128 -> Prims.Ghost (Vale.PPC64LE.Decls.va_state * Vale.PPC64LE.Decls.va_fuel)

Prims.Ghost

[]

[ "Vale.PPC64LE.Decls.va_code", "Vale.PPC64LE.Decls.va_state", "Vale.AES.AES_common_s.algorithm", "FStar.Seq.Base.seq", "Vale.PPC64LE.Memory.nat32", "Vale.PPC64LE.Memory.buffer128", "Vale.PPC64LE.QuickCodes.fuel", "Prims.unit", "FStar.Pervasives.Native.Mktuple2", "Vale.PPC64LE.Decls.va_fuel", "Vale.PPC64LE.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.PPC64LE.QuickCode.mod_t", "Vale.PPC64LE.QuickCode.va_Mod_vec", "Vale.PPC64LE.QuickCode.va_Mod_reg", "Vale.PPC64LE.QuickCode.va_Mod_mem_layout", "Vale.PPC64LE.QuickCode.va_Mod_mem_heaplet", "Vale.PPC64LE.QuickCode.va_Mod_ok", "Vale.PPC64LE.QuickCode.va_Mod_mem", "Prims.Nil", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.list", "Vale.PPC64LE.QuickCode.__proj__QProc__item__mods", "Vale.AES.PPC64LE.GF128_Init.va_code_Keyhash_init", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.tuple3", "Vale.PPC64LE.Machine_s.state", "Vale.PPC64LE.QuickCodes.va_wp_sound_code_norm", "Prims.l_and", "Vale.PPC64LE.QuickCodes.label", "Vale.PPC64LE.QuickCodes.va_range1", "Prims.b2t", "Vale.PPC64LE.Decls.va_get_ok", "Vale.PPC64LE.Decls.modifies_buffer128", "Vale.PPC64LE.Decls.va_get_mem", "Vale.AES.OptPublic_BE.hkeys_reqs_pub", "Vale.Arch.Types.reverse_bytes_quad32_seq", "Vale.PPC64LE.Decls.s128", "Vale.AES.AES_BE_s.aes_encrypt_word", "Vale.Def.Words_s.Mkfour", "Vale.Def.Types_s.nat32", "Vale.PPC64LE.QuickCode.quickCode", "Vale.AES.PPC64LE.GF128_Init.va_qcode_Keyhash_init" ]

[]

false

let va_lemma_Keyhash_init va_b0 va_s0 alg key roundkeys_b hkeys_b =

let va_mods:va_mods_t = [ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem ] in let va_qc = va_qcode_Keyhash_init va_mods alg key roundkeys_b hkeys_b in let va_sM, va_fM, va_g = va_wp_sound_code_norm (va_code_Keyhash_init alg) va_qc va_s0 (fun va_s0 va_sM va_g -> let () = va_g in label va_range1 "***** POSTCONDITION NOT MET AT line 165 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (va_get_ok va_sM) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 189 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.PPC64LE.Decls.modifies_buffer128 hkeys_b (va_get_mem va_s0) (va_get_mem va_sM)) /\ label va_range1 "***** POSTCONDITION NOT MET AT line 190 column 117 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/crypto/aes/ppc64le/Vale.AES.PPC64LE.GF128_Init.vaf *****" (Vale.AES.OptPublic_BE.hkeys_reqs_pub (Vale.Arch.Types.reverse_bytes_quad32_seq (Vale.PPC64LE.Decls.s128 (va_get_mem va_sM) hkeys_b)) (Vale.AES.AES_BE_s.aes_encrypt_word alg key (Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 0 0 0)))) in assert_norm (va_qc.mods == va_mods); va_lemma_norm_mods ([ va_Mod_vec 6; va_Mod_vec 5; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0; va_Mod_reg 10; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_ok; va_Mod_mem ]) va_sM va_s0; (va_sM, va_fM)

false

Steel.ST.C.Types.UserStruct.fsti

Steel.ST.C.Types.UserStruct.struct_field

val struct_field (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STT (ref #(norm norm_field_steps (sd.field_desc.fd_type field)) (sd.field_desc.fd_typedef field)) (pts_to r v) (fun r' -> ((pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field)))) `star` (pts_to #(norm norm_field_steps (sd.field_desc.fd_type field)) r' (sd.get v field))) `star` (has_struct_field r field r'))

let struct_field (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STT (ref #(norm norm_field_steps (sd.field_desc.fd_type field)) (sd.field_desc.fd_typedef field)) (pts_to r v) (fun r' -> pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to #(norm norm_field_steps (sd.field_desc.fd_type field)) r' (sd.get v field) `star` has_struct_field r field r') = struct_field0 (norm norm_field_steps (sd.field_desc.fd_type field)) r field (sd.field_desc.fd_typedef field)

{ "file_name": "lib/steel/c/Steel.ST.C.Types.UserStruct.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 36, "end_line": 180, "start_col": 0, "start_line": 167 }

module Steel.ST.C.Types.UserStruct open Steel.ST.Util open Steel.ST.C.Types.Struct.Aux module Set = FStar.Set (* This library allows the user to define their own struct type, with a constructor from field values, and a destructor to field values for each field. This may be necessary for recursive structs *) let set_def (#t: eqtype) (s: FStar.Set.set t) (x: t) : Tot bool = FStar.Set.mem x s noextract let nonempty_set (t: eqtype) = (s: Set.set t { exists x . set_def s x == true }) noextract let set_snoc // for associativity reasons (#t: eqtype) (q: FStar.Set.set t) (a: t) : Pure (nonempty_set t) (requires True) (ensures (fun s -> (forall (x: t). {:pattern FStar.Set.mem x s} FStar.Set.mem x s == (x = a || FStar.Set.mem x q)) )) = q `FStar.Set.union` FStar.Set.singleton a [@@noextract_to "krml"] let field_t (s: Set.set string) : Tot eqtype = (f: string { Set.mem f s }) [@@noextract_to "krml"; norm_field_attr] inline_for_extraction // for field_desc.fd_type noeq type struct_def (t: Type) = { fields: Set.set string; field_desc: field_description_gen_t (field_t fields); mk: ((f: field_t fields) -> Tot (field_desc.fd_type f)) -> Tot t; get: (t -> (f: field_t fields) -> Tot (field_desc.fd_type f)); get_mk: (phi: ((f: field_t fields) -> Tot (field_desc.fd_type f))) -> (f: field_t fields) -> Lemma (get (mk phi) f == phi f); extensionality: (x1: t) -> (x2: t) -> ((f: field_t fields) -> Lemma (get x1 f == get x2 f)) -> Lemma (x1 == x2); } let nonempty_set_nonempty_type (x: string) (s: Set.set string) : Lemma (requires (x `Set.mem` s)) (ensures (exists (x: field_t s) . True)) = Classical.exists_intro (fun (_: field_t s) -> True) x [@@noextract_to "krml"] let set_aux (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) (f': field_t sd.fields) : Tot (sd.field_desc.fd_type f') = if f = f' then v else sd.get x f' [@@noextract_to "krml"] let set (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) : Tot t = sd.mk (set_aux sd x f v) let get_set (#t: Type) (sd: struct_def t) (x: t) (f: field_t sd.fields) (v: sd.field_desc.fd_type f) (f' : field_t sd.fields) : Lemma (sd.get (set sd x f v) f' == (if f = f' then v else sd.get x f')) [SMTPat (sd.get (set sd x f v) f')] = sd.get_mk (set_aux sd x f v) f' [@@noextract_to "krml"] val struct_typedef (#t: Type) (sd: struct_def t) : Tot (typedef t) val has_struct_field (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : Tot vprop val has_struct_field_dup (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r') (fun _ -> has_struct_field r field r' `star` has_struct_field r field r') val has_struct_field_inj (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r1 r2: ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r1 `star` has_struct_field r field r2) (fun _ -> has_struct_field r field r1 `star` has_struct_field r field r2 `star` ref_equiv r1 r2) val has_struct_field_equiv_from (#opened: _) (#t: Type) (#sd: struct_def t) (r1: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) (r2: ref (struct_typedef sd)) : STGhostT unit opened (ref_equiv r1 r2 `star` has_struct_field r1 field r') (fun _ -> ref_equiv r1 r2 `star` has_struct_field r2 field r') val has_struct_field_equiv_to (#opened: _) (#t: Type) (#sd: struct_def t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r1' r2': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (ref_equiv r1' r2' `star` has_struct_field r field r1') (fun _ -> ref_equiv r1' r2' `star` has_struct_field r field r2') val ghost_struct_field_focus (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (r': ref (sd.field_desc.fd_typedef field)) : STGhostT unit opened (has_struct_field r field r' `star` pts_to r v) (fun _ -> has_struct_field r field r' `star` pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to r' (sd.get v field)) val ghost_struct_field (#opened: _) (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STGhostT (Ghost.erased (ref (sd.field_desc.fd_typedef field))) opened (pts_to r v) (fun r' -> has_struct_field r field r' `star` pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to r' (sd.get v field)) [@@noextract_to "krml"] // primitive val struct_field0 (#t: Type) (t': Type0) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) (td': typedef t' { t' == sd.field_desc.fd_type field /\ td' == sd.field_desc.fd_typedef field }) : STT (ref td') (pts_to r v) (fun r' -> has_struct_field r field (coerce_eq () r') `star` pts_to r (set sd (Ghost.reveal v) field (unknown (sd.field_desc.fd_typedef field))) `star` pts_to #_ #(sd.field_desc.fd_typedef field) (coerce_eq () r') (sd.get (Ghost.reveal v) field))

{ "checked_file": "/", "dependencies": [ "Steel.ST.Util.fsti.checked", "Steel.ST.C.Types.Struct.Aux.fsti.checked", "Steel.FractionalPermission.fst.checked", "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "Steel.ST.C.Types.UserStruct.fsti" }

[ { "abbrev": true, "full_module": "FStar.Set", "short_module": "Set" }, { "abbrev": false, "full_module": "Steel.ST.C.Types.Struct.Aux", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.Util", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "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 } ]

{ "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" }

false

r: Steel.ST.C.Types.Base.ref (Steel.ST.C.Types.UserStruct.struct_typedef sd) -> field: Steel.ST.C.Types.UserStruct.field_t (Mkstruct_def?.fields sd) -> Steel.ST.Effect.STT (Steel.ST.C.Types.Base.ref (Mkfield_description_gen_t?.fd_typedef (Mkstruct_def?.field_desc sd) field))

Steel.ST.Effect.STT

[]

[ "Steel.ST.C.Types.UserStruct.struct_def", "FStar.Ghost.erased", "Steel.ST.C.Types.Base.ref", "Steel.ST.C.Types.UserStruct.struct_typedef", "Steel.ST.C.Types.UserStruct.field_t", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__fields", "Steel.ST.C.Types.UserStruct.struct_field0", "FStar.Pervasives.norm", "Steel.ST.C.Types.Base.norm_field_steps", "Steel.ST.C.Types.Struct.Aux.__proj__Mkfield_description_gen_t__item__fd_type", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__field_desc", "Steel.ST.C.Types.Struct.Aux.__proj__Mkfield_description_gen_t__item__fd_typedef", "Steel.ST.C.Types.Base.pts_to", "Steel.Effect.Common.star", "FStar.Ghost.hide", "Steel.ST.C.Types.UserStruct.set", "FStar.Ghost.reveal", "Steel.ST.C.Types.Base.unknown", "Steel.ST.C.Types.UserStruct.__proj__Mkstruct_def__item__get", "Steel.ST.C.Types.UserStruct.has_struct_field", "Steel.Effect.Common.vprop" ]

[]

false

true

false

let struct_field (#t: Type) (#sd: struct_def t) (#v: Ghost.erased t) (r: ref (struct_typedef sd)) (field: field_t sd.fields) : STT (ref #(norm norm_field_steps (sd.field_desc.fd_type field)) (sd.field_desc.fd_typedef field)) (pts_to r v) (fun r' -> ((pts_to r (set sd v field (unknown (sd.field_desc.fd_typedef field)))) `star` (pts_to #(norm norm_field_steps (sd.field_desc.fd_type field)) r' (sd.get v field))) `star` (has_struct_field r field r')) =

struct_field0 (norm norm_field_steps (sd.field_desc.fd_type field)) r field (sd.field_desc.fd_typedef field)

false

BinomialQueue.fst

BinomialQueue.is_priq

val is_priq : l: BinomialQueue.forest -> Prims.logical

let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 62, "end_line": 84, "start_col": 0, "start_line": 84 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest -> Prims.logical

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "Prims.l_and", "BinomialQueue.is_binomial_queue", "BinomialQueue.is_compact", "Prims.logical" ]

[]

false

true

let is_priq (l: forest) =

is_binomial_queue 1 l /\ is_compact l

false

BinomialQueue.fst

BinomialQueue.priq

val priq : Type0

let priq = l:forest{is_priq l}

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 30, "end_line": 88, "start_col": 0, "start_line": 88 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

Type0

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "BinomialQueue.is_priq" ]

[]

false

true

let priq =

l: forest{is_priq l}

false

BinomialQueue.fst

BinomialQueue.is_compact

val is_compact : l: BinomialQueue.forest -> Prims.logical

let is_compact (l:forest) = l == [] \/ Internal? (L.last l)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 59, "end_line": 82, "start_col": 0, "start_line": 82 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest -> Prims.logical

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "Prims.l_or", "Prims.eq2", "Prims.list", "BinomialQueue.tree", "Prims.Nil", "Prims.b2t", "BinomialQueue.uu___is_Internal", "FStar.List.Tot.Base.last", "Prims.logical" ]

[]

false

true

let is_compact (l: forest) =

l == [] \/ Internal? (L.last l)

false

BinomialQueue.fst

BinomialQueue.last_cons

val last_cons (#a: Type) (x: a) (l: list a) : Lemma (requires Cons? l) (ensures L.last (x :: l) == L.last l) [SMTPat (L.last (x :: l))]

let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 27, "end_line": 33, "start_col": 0, "start_line": 25 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

x: a -> l: Prims.list a -> FStar.Pervasives.Lemma (requires Cons? l) (ensures FStar.List.Tot.Base.last (x :: l) == FStar.List.Tot.Base.last l) [SMTPat (FStar.List.Tot.Base.last (x :: l))]

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.list", "BinomialQueue.last_cons", "Prims.unit", "Prims.b2t", "Prims.uu___is_Cons", "Prims.squash", "Prims.eq2", "FStar.List.Tot.Base.last", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat", "Prims.Nil" ]

[ "recursion" ]

false

true

false

let rec last_cons (#a: Type) (x: a) (l: list a) : Lemma (requires Cons? l) (ensures L.last (x :: l) == L.last l) [SMTPat (L.last (x :: l))] =

match l with | [_] -> () | _ :: tl -> last_cons x tl

false

BinomialQueue.fst

BinomialQueue.pow2heap_pred

val pow2heap_pred (d: nat) (upper_bound: key_t) (t: tree) : prop

let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 43, "end_line": 56, "start_col": 0, "start_line": 49 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.nat -> upper_bound: BinomialQueue.key_t -> t: BinomialQueue.tree -> Prims.prop

Prims.Tot

[ "total" ]

[]

[ "Prims.nat", "BinomialQueue.key_t", "BinomialQueue.tree", "Prims.eq2", "Prims.int", "Prims.l_and", "Prims.b2t", "Prims.op_LessThan", "Prims.op_LessThanOrEqual", "BinomialQueue.pow2heap_pred", "Prims.op_Subtraction", "Prims.prop" ]

[ "recursion" ]

false

true

let rec pow2heap_pred (d: nat) (upper_bound: key_t) (t: tree) : prop =

match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right

false

BinomialQueue.fst

BinomialQueue.is_pow2heap

val is_pow2heap (d: pos) (t: tree) : prop

let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 14, "end_line": 65, "start_col": 0, "start_line": 62 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> t: BinomialQueue.tree -> Prims.prop

Prims.Tot

[ "total" ]

[]

[ "Prims.pos", "BinomialQueue.tree", "BinomialQueue.key_t", "BinomialQueue.pow2heap_pred", "Prims.op_Subtraction", "Prims.l_False", "Prims.prop" ]

[]

false

true

let is_pow2heap (d: pos) (t: tree) : prop =

match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False

false

Steel.GhostMonotonicHigherReference.fst

Steel.GhostMonotonicHigherReference.elim_pure

val elim_pure (#a #uses #p #f: _) (r: ref a p) (v: a) (h: (history a p)) : SteelGhostT (_: unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> PR.pts_to r h)

let elim_pure #a #uses #p #f (r:ref a p) (v:a) (h:(history a p)) : SteelGhostT (_:unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> PR.pts_to r h) = let _ = extract_pure r v h in drop (pure (history_val h v f))

{ "file_name": "lib/steel/Steel.GhostMonotonicHigherReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 35, "end_line": 95, "start_col": 0, "start_line": 86 }

(* Copyright 2020 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 Steel.GhostMonotonicHigherReference open FStar.Ghost open FStar.PCM open Steel.Memory open Steel.Effect.Atomic open Steel.Effect open Steel.GhostPCMReference open Steel.FractionalPermission open Steel.Preorder module Preorder = FStar.Preorder module Q = Steel.Preorder module M = Steel.Memory module PR = Steel.GhostPCMReference module A = Steel.Effect.Atomic open FStar.Real #set-options "--ide_id_info_off" let ref a p = PR.ref (history a p) pcm_history [@@__reduce__] let pts_to_body #a #p (r:ref a p) (f:perm) (v:a) (h:history a p) = PR.pts_to r h `star` pure (history_val h v f) let pts_to' (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v: a) = h_exists (pts_to_body r f v) let pts_to_sl r f v = hp_of (pts_to' r f v) let intro_pure #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to_body r f v h) = A.intro_pure (history_val h v f) let intro_pure_full #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v) = intro_pure #_ #a #p #f r v h; intro_exists h (pts_to_body r f v) let alloc #_ (#a:Type) (p:Preorder.preorder a) (v:a) = let h = Current [v] full_perm in assert (compatible pcm_history h h); let x : ref a p = alloc h in intro_pure_full x v h; x let extract_pure #a #uses #p #f (r:ref a p) (v:a) (h:(history a p)) : SteelGhostT (_:unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> pts_to_body r f v h) = elim_pure (history_val h v f); A.intro_pure (history_val h v f)

{ "checked_file": "/", "dependencies": [ "Steel.Preorder.fst.checked", "Steel.Memory.fsti.checked", "Steel.GhostPCMReference.fsti.checked", "Steel.FractionalPermission.fst.checked", "Steel.Effect.Atomic.fsti.checked", "Steel.Effect.fsti.checked", "prims.fst.checked", "FStar.Real.fsti.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.PCM.fst.checked", "FStar.Ghost.fsti.checked" ], "interface_file": true, "source_file": "Steel.GhostMonotonicHigherReference.fst" }

[ { "abbrev": false, "full_module": "FStar.Real", "short_module": null }, { "abbrev": true, "full_module": "Steel.Effect.Atomic", "short_module": "A" }, { "abbrev": true, "full_module": "Steel.GhostPCMReference", "short_module": "PR" }, { "abbrev": true, "full_module": "Steel.Memory", "short_module": "M" }, { "abbrev": true, "full_module": "Steel.Preorder", "short_module": "Q" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Preorder", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "Steel.GhostPCMReference", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "Steel", "short_module": null }, { "abbrev": false, "full_module": "Steel", "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 } ]

{ "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" }

false

r: Steel.GhostMonotonicHigherReference.ref a p -> v: a -> h: Steel.Preorder.history a p -> Steel.Effect.Atomic.SteelGhostT (_: Prims.unit{Steel.Preorder.history_val h (FStar.Ghost.hide v) f})

Steel.Effect.Atomic.SteelGhostT

[]

[ "Steel.Memory.inames", "FStar.Preorder.preorder", "Steel.FractionalPermission.perm", "Steel.GhostMonotonicHigherReference.ref", "Steel.Preorder.history", "Steel.Effect.Atomic.drop", "Steel.Effect.Common.pure", "Steel.Preorder.history_val", "FStar.Ghost.hide", "Prims.unit", "Steel.GhostMonotonicHigherReference.extract_pure", "Steel.GhostMonotonicHigherReference.pts_to_body", "Steel.GhostPCMReference.pts_to", "Steel.Preorder.pcm_history", "Steel.Effect.Common.vprop" ]

[]

false

true

false

let elim_pure #a #uses #p #f (r: ref a p) (v: a) (h: (history a p)) : SteelGhostT (_: unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> PR.pts_to r h) =

let _ = extract_pure r v h in drop (pure (history_val h v f))

false

BinomialQueue.fst

BinomialQueue.empty

val empty : priq

let empty = []

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 14, "end_line": 90, "start_col": 0, "start_line": 90 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l}

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

BinomialQueue.priq

Prims.Tot

[ "total" ]

[]

[ "Prims.Nil", "BinomialQueue.tree" ]

[]

false

true

false

let empty =

[]

false

BinomialQueue.fst

BinomialQueue.is_binomial_queue

val is_binomial_queue (d: pos) (l: forest) : Tot prop (decreases l)

let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 66, "end_line": 77, "start_col": 0, "start_line": 71 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> l: BinomialQueue.forest -> Prims.Tot Prims.prop

Prims.Tot

[ "total", "" ]

[]

[ "Prims.pos", "BinomialQueue.forest", "Prims.l_True", "BinomialQueue.tree", "Prims.list", "Prims.l_and", "Prims.l_or", "Prims.b2t", "BinomialQueue.uu___is_Leaf", "BinomialQueue.is_pow2heap", "BinomialQueue.is_binomial_queue", "Prims.op_Addition", "Prims.prop" ]

[ "recursion" ]

false

true

let rec is_binomial_queue (d: pos) (l: forest) : Tot prop (decreases l) =

match l with | [] -> True | hd :: tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl

false

BinomialQueue.fst

BinomialQueue.mk_compact

val mk_compact (l: forest) : forest

let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 28, "end_line": 106, "start_col": 0, "start_line": 100 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest -> BinomialQueue.forest

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "Prims.Nil", "BinomialQueue.tree", "Prims.list", "BinomialQueue.all_leaf", "Prims.bool", "Prims.Cons", "BinomialQueue.mk_compact" ]

[ "recursion" ]

false

true

false

let rec mk_compact (l: forest) : forest =

match l with | [] -> [] | _ -> if all_leaf l then [] else let hd :: tl = l in hd :: (mk_compact tl)

false

BinomialQueue.fst

BinomialQueue.all_leaf

val all_leaf (l: forest{Cons? l}) : bool

let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 14, "end_line": 98, "start_col": 0, "start_line": 94 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest{Cons? l} -> Prims.bool

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "Prims.b2t", "Prims.uu___is_Cons", "BinomialQueue.tree", "Prims.list", "BinomialQueue.all_leaf", "Prims.bool" ]

[ "recursion" ]

false

let rec all_leaf (l: forest{Cons? l}) : bool =

match l with | [Leaf] -> true | Leaf :: tl -> all_leaf tl | _ -> false

false

BinomialQueue.fst

BinomialQueue.mk_compact_preserves_binomial_queue

val mk_compact_preserves_binomial_queue (d: pos) (l: forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))]

let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 61, "end_line": 130, "start_col": 0, "start_line": 120 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> l: BinomialQueue.forest -> FStar.Pervasives.Lemma (requires BinomialQueue.is_binomial_queue d l) (ensures BinomialQueue.is_binomial_queue d (BinomialQueue.mk_compact l)) (decreases l) [SMTPat (BinomialQueue.is_binomial_queue d (BinomialQueue.mk_compact l))]

FStar.Pervasives.Lemma

[ "lemma", "" ]

[]

[ "Prims.pos", "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.all_leaf", "Prims.bool", "BinomialQueue.mk_compact_preserves_binomial_queue", "Prims.op_Addition", "FStar.List.Tot.Base.tl", "Prims.unit", "BinomialQueue.is_binomial_queue", "Prims.squash", "BinomialQueue.mk_compact", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat", "Prims.prop", "Prims.Nil" ]

[ "recursion" ]

false

true

false

let rec mk_compact_preserves_binomial_queue (d: pos) (l: forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] =

match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l)

false

BinomialQueue.fst

BinomialQueue.mk_compact_correctness

val mk_compact_correctness (l: forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))]

let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 40, "end_line": 118, "start_col": 0, "start_line": 110 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest -> FStar.Pervasives.Lemma (ensures BinomialQueue.is_compact (BinomialQueue.mk_compact l)) [SMTPat (BinomialQueue.is_compact (BinomialQueue.mk_compact l))]

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.all_leaf", "Prims.bool", "BinomialQueue.mk_compact_correctness", "FStar.List.Tot.Base.tl", "Prims.unit", "Prims.l_True", "Prims.squash", "BinomialQueue.is_compact", "BinomialQueue.mk_compact", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat", "Prims.logical", "Prims.Nil" ]

[ "recursion" ]

false

true

false

let rec mk_compact_correctness (l: forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] =

match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l)

false

Duplex.PingPong.fst

Duplex.PingPong.pingpong

val pingpong:dprot

let pingpong : dprot = x <-- send int; y <-- recv (y:int{y > x}); done

{ "file_name": "share/steel/examples/steel/Duplex.PingPong.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 6, "end_line": 16, "start_col": 0, "start_line": 13 }

module Duplex.PingPong open FStar.PCM open Steel.Memory open Steel.Effect.Atomic open Steel.Effect open Steel.Channel.Protocol open Duplex.PCM //////////////////////////////////////////////////////////////////////////////// // An example ////////////////////////////////////////////////////////////////////////////////

{ "checked_file": "/", "dependencies": [ "Steel.Memory.fsti.checked", "Steel.Effect.Atomic.fsti.checked", "Steel.Effect.fsti.checked", "Steel.Channel.Protocol.fst.checked", "prims.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.PCM.fst.checked", "Duplex.PCM.fsti.checked" ], "interface_file": false, "source_file": "Duplex.PingPong.fst" }

[ { "abbrev": false, "full_module": "Duplex.PCM", "short_module": null }, { "abbrev": false, "full_module": "Steel.Channel.Protocol", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "Duplex", "short_module": null }, { "abbrev": false, "full_module": "Duplex", "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 } ]

{ "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" }

false

Duplex.PCM.dprot

Prims.Tot

[ "total" ]

[]

[ "Duplex.PCM.bind", "Prims.int", "Prims.unit", "Duplex.PCM.send", "Prims.b2t", "Prims.op_GreaterThan", "Duplex.PCM.recv", "Duplex.PCM.done", "Duplex.PCM.nl_protocol" ]

[]

false

true

false

let pingpong:dprot =

x <-- send int ; y <-- recv (y: int{y > x}) ; done

false

BinomialQueue.fst

BinomialQueue.smash

val smash (d: pos) (t1 t2: tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t)

let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 51, "end_line": 144, "start_col": 0, "start_line": 135 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> t1: BinomialQueue.tree -> t2: BinomialQueue.tree -> Prims.Pure BinomialQueue.tree

Prims.Pure

[]

[ "Prims.pos", "BinomialQueue.tree", "FStar.Pervasives.Native.Mktuple2", "BinomialQueue.key_t", "Prims.op_LessThanOrEqual", "BinomialQueue.Internal", "BinomialQueue.Leaf", "Prims.bool", "Prims.l_and", "BinomialQueue.is_pow2heap", "Prims.op_Addition" ]

[]

false

let smash (d: pos) (t1 t2: tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) =

match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf

false

BinomialQueue.fst

BinomialQueue.carry

val carry (d: pos) (q: forest) (t: tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q)

let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 11, "end_line": 160, "start_col": 0, "start_line": 150 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> q: BinomialQueue.forest -> t: BinomialQueue.tree -> Prims.Pure BinomialQueue.forest

Prims.Pure

[ "" ]

[]

[ "Prims.pos", "BinomialQueue.forest", "BinomialQueue.tree", "Prims.Cons", "Prims.Nil", "Prims.list", "BinomialQueue.Leaf", "BinomialQueue.carry", "Prims.op_Addition", "BinomialQueue.smash", "Prims.l_and", "BinomialQueue.is_binomial_queue", "BinomialQueue.is_pow2heap" ]

[ "recursion" ]

false

let rec carry (d: pos) (q: forest) (t: tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) =

match q with | [] -> [t] | Leaf :: tl -> t :: tl | hd :: tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf :: q

false

BinomialQueue.fst

BinomialQueue.insert

val insert : key_t -> priq -> priq

let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 14, "end_line": 198, "start_col": 0, "start_line": 196 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

x: BinomialQueue.key_t -> q: BinomialQueue.priq -> BinomialQueue.priq

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.key_t", "BinomialQueue.priq", "BinomialQueue.mk_compact", "BinomialQueue.forest", "BinomialQueue.carry", "BinomialQueue.Internal", "BinomialQueue.Leaf" ]

[]

false

true

false

let insert x q =

let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l

false

LListReverse.fst

LListReverse.llist_nil_is_null

val llist_nil_is_null (#opened: _) (l: Ghost.erased (list U64.t)) (p: ref llist_cell) : STGhost unit opened (llist l p) (fun _ -> llist l p) True (fun _ -> (p == null <==> Nil? l))

let llist_nil_is_null (#opened: _) (l: Ghost.erased (list U64.t)) (p: ref llist_cell) : STGhost unit opened (llist l p) (fun _ -> llist l p) True (fun _ -> (p == null <==> Nil? l)) = if Nil? l then begin rewrite (llist l p) (llist_nil p); let _ = gen_elim () in rewrite (llist_nil p) (llist l p) end else begin let a :: q = Ghost.reveal l in rewrite (llist l p) (llist_cons a (llist q) p); let _ = gen_elim () in pts_to_not_null p; rewrite (llist_cons a (llist q) p) (llist l p) end

{ "file_name": "share/steel/tests/krml/LListReverse.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 5, "end_line": 62, "start_col": 0, "start_line": 42 }

module LListReverse open Steel.ST.GenElim open Steel.ST.Reference open Steel.ST.Loops module U64 = FStar.UInt64 let main () = C.EXIT_SUCCESS // dummy for compilation noeq type llist_cell = { value: U64.t; next: ref llist_cell; } [@@__reduce__] let llist_nil (p: ref llist_cell) : Tot vprop = pure (p == null) [@@__reduce__] let llist_cons (a: U64.t) (llist: (ref llist_cell -> Tot vprop)) (p: ref llist_cell) : Tot vprop = exists_ (fun c -> pts_to p full_perm c `star` pure (c.value == a) `star` llist c.next ) let rec llist (l: Ghost.erased (list U64.t)) : Tot (ref llist_cell -> vprop) (decreases Ghost.reveal l) = match Ghost.reveal l with | [] -> llist_nil | a :: q -> llist_cons a (llist q)

{ "checked_file": "/", "dependencies": [ "Steel.ST.Reference.fsti.checked", "Steel.ST.Loops.fsti.checked", "Steel.ST.GenElim.fsti.checked", "prims.fst.checked", "FStar.UInt64.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.Ghost.fsti.checked", "C.fst.checked" ], "interface_file": false, "source_file": "LListReverse.fst" }

[ { "abbrev": true, "full_module": "FStar.UInt64", "short_module": "U64" }, { "abbrev": false, "full_module": "Steel.ST.Loops", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.Reference", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.GenElim", "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 } ]

{ "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": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

l: FStar.Ghost.erased (Prims.list FStar.UInt64.t) -> p: Steel.ST.Reference.ref LListReverse.llist_cell -> Steel.ST.Effect.Ghost.STGhost Prims.unit

Steel.ST.Effect.Ghost.STGhost

[]

[ "Steel.Memory.inames", "FStar.Ghost.erased", "Prims.list", "FStar.UInt64.t", "Steel.ST.Reference.ref", "LListReverse.llist_cell", "Prims.uu___is_Nil", "FStar.Ghost.reveal", "Steel.ST.Util.rewrite", "LListReverse.llist_nil", "LListReverse.llist", "Prims.unit", "Steel.ST.GenElim.gen_elim", "Steel.ST.Util.pure", "Prims.eq2", "Steel.ST.Reference.null", "Steel.Effect.Common.emp", "Steel.Effect.Common.vprop", "Prims.prop", "Prims.bool", "LListReverse.llist_cons", "FStar.Ghost.hide", "Steel.ST.Reference.pts_to_not_null", "Steel.FractionalPermission.full_perm", "Steel.ST.Util.exists_", "Steel.Effect.Common.VStar", "Steel.ST.Reference.pts_to", "LListReverse.__proj__Mkllist_cell__item__value", "LListReverse.__proj__Mkllist_cell__item__next", "Steel.Effect.Common.star", "Prims.l_and", "Prims.l_True", "Prims.l_iff", "Prims.b2t" ]

[]

false

true

false

let llist_nil_is_null (#opened: _) (l: Ghost.erased (list U64.t)) (p: ref llist_cell) : STGhost unit opened (llist l p) (fun _ -> llist l p) True (fun _ -> (p == null <==> Nil? l)) =

if Nil? l then (rewrite (llist l p) (llist_nil p); let _ = gen_elim () in rewrite (llist_nil p) (llist l p)) else let a :: q = Ghost.reveal l in rewrite (llist l p) (llist_cons a (llist q) p); let _ = gen_elim () in pts_to_not_null p; rewrite (llist_cons a (llist q) p) (llist l p)

false

BinomialQueue.fst

BinomialQueue.join

val join (d: pos) (p q: forest) (c: tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p)

let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q))

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 51, "end_line": 192, "start_col": 0, "start_line": 167 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> p: BinomialQueue.forest -> q: BinomialQueue.forest -> c: BinomialQueue.tree -> Prims.Pure BinomialQueue.forest

Prims.Pure

[ "" ]

[]

[ "Prims.pos", "BinomialQueue.forest", "BinomialQueue.tree", "FStar.Pervasives.Native.Mktuple3", "Prims.list", "BinomialQueue.carry", "Prims.Cons", "BinomialQueue.join", "Prims.op_Addition", "BinomialQueue.Leaf", "BinomialQueue.smash", "Prims.l_and", "BinomialQueue.is_binomial_queue", "Prims.l_or", "Prims.b2t", "BinomialQueue.uu___is_Leaf", "BinomialQueue.is_pow2heap" ]

[ "recursion" ]

false

let rec join (d: pos) (p q: forest) (c: tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) =

match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf :: tl_p, Leaf :: tl_q, _ -> c :: (join (d + 1) tl_p tl_q Leaf) | hd_p :: tl_p, Leaf :: tl_q, Leaf -> hd_p :: (join (d + 1) tl_p tl_q Leaf) | Leaf :: tl_p, hd_q :: tl_q, Leaf -> hd_q :: (join (d + 1) tl_p tl_q Leaf) | Leaf :: tl_p, hd_q :: tl_q, _ -> Leaf :: (join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p :: tl_p, Leaf :: tl_q, _ -> Leaf :: (join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p :: tl_p, hd_q :: tl_q, c -> c :: (join (d + 1) tl_p tl_q (smash d hd_p hd_q))

false

BinomialQueue.fst

BinomialQueue.repr

val repr (q:priq) (s:ms) : prop

let repr q s = repr_l q s

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 25, "end_line": 327, "start_col": 0, "start_line": 327 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

q: BinomialQueue.priq -> s: BinomialQueue.ms -> Prims.prop

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.priq", "BinomialQueue.ms", "BinomialQueue.repr_l", "Prims.prop" ]

[]

false

true

let repr q s =

repr_l q s

false

BinomialQueue.fst

BinomialQueue.heap_delete_max

val heap_delete_max (d: pos) (t: tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1)

let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 48, "end_line": 262, "start_col": 0, "start_line": 256 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> t: BinomialQueue.tree -> Prims.Pure BinomialQueue.priq

Prims.Pure

[]

[ "Prims.pos", "BinomialQueue.tree", "BinomialQueue.key_t", "BinomialQueue.unzip", "Prims.op_Subtraction", "BinomialQueue.priq", "BinomialQueue.is_pow2heap", "Prims.eq2", "Prims.int", "FStar.List.Tot.Base.length" ]

[]

false

let heap_delete_max (d: pos) (t: tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) =

match t with | Internal left k Leaf -> unzip (d - 1) k left

false

BinomialQueue.fst

BinomialQueue.keys_of_tree

val keys_of_tree (t: tree) : ms

let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right))

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 46, "end_line": 312, "start_col": 0, "start_line": 307 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

t: BinomialQueue.tree -> BinomialQueue.ms

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.tree", "BinomialQueue.ms_empty", "BinomialQueue.key_t", "BinomialQueue.ms_append", "BinomialQueue.keys_of_tree", "BinomialQueue.ms_cons", "BinomialQueue.ms" ]

[ "recursion" ]

false

true

false

let rec keys_of_tree (t: tree) : ms =

match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right))

false

BinomialQueue.fst

BinomialQueue.merge

val merge : priq -> priq -> priq

let merge p q = let l = join 1 p q Leaf in mk_compact l

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 14, "end_line": 303, "start_col": 0, "start_line": 301 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

p: BinomialQueue.priq -> q: BinomialQueue.priq -> BinomialQueue.priq

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.priq", "BinomialQueue.mk_compact", "BinomialQueue.forest", "BinomialQueue.join", "BinomialQueue.Leaf" ]

[]

false

true

false

let merge p q =

let l = join 1 p q Leaf in mk_compact l

false

BinomialQueue.fst

BinomialQueue.find_max

val find_max (max: option key_t) (q: forest) : Tot (option key_t) (decreases q)

let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 67, "end_line": 214, "start_col": 0, "start_line": 206 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

max: FStar.Pervasives.Native.option BinomialQueue.key_t -> q: BinomialQueue.forest -> Prims.Tot (FStar.Pervasives.Native.option BinomialQueue.key_t)

Prims.Tot

[ "total", "" ]

[]

[ "FStar.Pervasives.Native.option", "BinomialQueue.key_t", "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.find_max", "FStar.Pervasives.Native.Some", "Prims.op_LessThan", "Prims.bool" ]

[ "recursion" ]

false

true

false

let rec find_max (max: option key_t) (q: forest) : Tot (option key_t) (decreases q) =

false

BinomialQueue.fst

BinomialQueue.binomial_queue_append

val binomial_queue_append (d: pos) (q: forest) (t: tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q)

let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 45, "end_line": 230, "start_col": 0, "start_line": 222 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> q: BinomialQueue.forest -> t: BinomialQueue.tree -> FStar.Pervasives.Lemma (requires BinomialQueue.is_binomial_queue d q /\ BinomialQueue.is_pow2heap (FStar.List.Tot.Base.length q + d) t) (ensures BinomialQueue.is_binomial_queue d (q @ [t])) (decreases q)

FStar.Pervasives.Lemma

[ "lemma", "" ]

[]

[ "Prims.pos", "BinomialQueue.forest", "BinomialQueue.tree", "Prims.list", "BinomialQueue.binomial_queue_append", "Prims.op_Addition", "Prims.unit", "Prims.l_and", "BinomialQueue.is_binomial_queue", "BinomialQueue.is_pow2heap", "FStar.List.Tot.Base.length", "Prims.squash", "FStar.List.Tot.Base.append", "Prims.Cons", "Prims.Nil", "FStar.Pervasives.pattern" ]

[ "recursion" ]

false

true

false

let rec binomial_queue_append (d: pos) (q: forest) (t: tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) =

match q with | [] -> () | _ :: q -> binomial_queue_append (d + 1) q t

false

BinomialQueue.fst

BinomialQueue.keys

val keys (q: forest) : ms

let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 51, "end_line": 317, "start_col": 0, "start_line": 314 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right))

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

q: BinomialQueue.forest -> BinomialQueue.ms

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "BinomialQueue.ms_empty", "BinomialQueue.tree", "Prims.list", "BinomialQueue.ms_append", "BinomialQueue.keys_of_tree", "BinomialQueue.keys", "BinomialQueue.ms" ]

[ "recursion" ]

false

true

false

let rec keys (q: forest) : ms =

match q with | [] -> ms_empty | hd :: tl -> ms_append (keys_of_tree hd) (keys tl)

false

BinomialQueue.fst

BinomialQueue.unzip

val unzip (d: nat) (upper_bound: key_t) (t: tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d)

let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf]

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 37, "end_line": 252, "start_col": 0, "start_line": 240 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important?

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.nat -> upper_bound: BinomialQueue.key_t -> t: BinomialQueue.tree -> Prims.Pure BinomialQueue.priq

Prims.Pure

[]

[ "Prims.nat", "BinomialQueue.key_t", "BinomialQueue.tree", "Prims.Nil", "FStar.List.Tot.Base.append", "Prims.Cons", "BinomialQueue.Internal", "BinomialQueue.Leaf", "Prims.unit", "FStar.List.Tot.Properties.lemma_append_last", "FStar.List.Tot.Properties.append_length", "BinomialQueue.binomial_queue_append", "BinomialQueue.priq", "BinomialQueue.unzip", "Prims.op_Subtraction", "BinomialQueue.pow2heap_pred", "Prims.eq2", "FStar.List.Tot.Base.length" ]

[ "recursion" ]

false

let rec unzip (d: nat) (upper_bound: key_t) (t: tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) =

match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf]

false

BinomialQueue.fst

BinomialQueue.repr_t

val repr_t (t: tree) (l: ms) : prop

let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 32, "end_line": 320, "start_col": 0, "start_line": 319 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

t: BinomialQueue.tree -> l: BinomialQueue.ms -> Prims.prop

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.tree", "BinomialQueue.ms", "BinomialQueue.permutation", "BinomialQueue.keys_of_tree", "Prims.prop" ]

[]

false

true

let repr_t (t: tree) (l: ms) : prop =

permutation (keys_of_tree t) l

false

BinomialQueue.fst

BinomialQueue.delete_max

val delete_max : priq -> option (key_t & priq)

let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 26, "end_line": 297, "start_col": 0, "start_line": 290 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

q: BinomialQueue.priq -> FStar.Pervasives.Native.option (BinomialQueue.key_t * BinomialQueue.priq)

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.priq", "BinomialQueue.find_max", "FStar.Pervasives.Native.None", "BinomialQueue.key_t", "FStar.Pervasives.Native.tuple2", "BinomialQueue.forest", "FStar.Pervasives.Native.Some", "FStar.Pervasives.Native.Mktuple2", "BinomialQueue.mk_compact", "Prims.unit", "BinomialQueue.mk_compact_correctness", "BinomialQueue.join", "BinomialQueue.Leaf", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.tuple3", "BinomialQueue.delete_max_aux" ]

[]

false

true

false

let delete_max q =

match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r)

false

BinomialQueue.fst

BinomialQueue.repr_l

val repr_l (q: forest) (s: ms) : prop

let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 24, "end_line": 323, "start_col": 0, "start_line": 322 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

q: BinomialQueue.forest -> s: BinomialQueue.ms -> Prims.prop

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.forest", "BinomialQueue.ms", "BinomialQueue.permutation", "BinomialQueue.keys", "Prims.prop" ]

[]

false

true

let repr_l (q: forest) (s: ms) : prop =

permutation (keys q) s

false

BinomialQueue.fst

BinomialQueue.delete_max_aux

val delete_max_aux (m: key_t) (d: pos) (q: forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q)

let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 62, "end_line": 285, "start_col": 0, "start_line": 269 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) ///

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

m: BinomialQueue.key_t -> d: Prims.pos -> q: BinomialQueue.forest -> Prims.Pure ((BinomialQueue.key_t * BinomialQueue.forest) * BinomialQueue.priq)

Prims.Pure

[ "" ]

[]

[ "BinomialQueue.key_t", "Prims.pos", "BinomialQueue.forest", "FStar.Pervasives.Native.Mktuple3", "BinomialQueue.priq", "Prims.op_Addition", "Prims.Nil", "BinomialQueue.tree", "Prims.list", "Prims.Cons", "BinomialQueue.Leaf", "FStar.Pervasives.Native.tuple3", "BinomialQueue.delete_max_aux", "Prims.op_LessThan", "BinomialQueue.Internal", "Prims.bool", "BinomialQueue.heap_delete_max", "BinomialQueue.is_binomial_queue", "Prims.l_and", "Prims.b2t", "Prims.op_LessThanOrEqual" ]

[ "recursion" ]

false

let rec delete_max_aux (m: key_t) (d: pos) (q: forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) =

match q with | [] -> m + 1, [], [] | Leaf :: q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf :: q, new_q | Internal left x right :: q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right) :: q, new_q else x, Leaf :: q, heap_delete_max d (Internal left x right)

false

Steel.ST.C.Types.Base.fsti

Steel.ST.C.Types.Base.assert_not_null

val assert_not_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost (squash (~(p == null _))) opened (pts_to_or_null p v) (fun _ -> pts_to p v) (~(p == null _)) (fun _ -> True)

let assert_not_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost (squash (~ (p == null _))) opened (pts_to_or_null p v) (fun _ -> pts_to p v) (~ (p == null _)) (fun _ -> True) = rewrite (pts_to_or_null p v) (pts_to p v)

{ "file_name": "lib/steel/c/Steel.ST.C.Types.Base.fsti", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 43, "end_line": 148, "start_col": 0, "start_line": 137 }

module Steel.ST.C.Types.Base open Steel.ST.Util module P = Steel.FractionalPermission /// Helper to compose two permissions into one val prod_perm (p1 p2: P.perm) : Pure P.perm (requires True) (ensures (fun p -> ((p1 `P.lesser_equal_perm` P.full_perm /\ p2 `P.lesser_equal_perm` P.full_perm) ==> p `P.lesser_equal_perm` P.full_perm) /\ p.v == (let open FStar.Real in p1.v *. p2.v) )) [@@noextract_to "krml"] // proof-only val typedef (t: Type0) : Type0 inline_for_extraction [@@noextract_to "krml"] let typeof (#t: Type0) (td: typedef t) : Tot Type0 = t val fractionable (#t: Type0) (td: typedef t) (x: t) : GTot prop val mk_fraction (#t: Type0) (td: typedef t) (x: t) (p: P.perm) : Ghost t (requires (fractionable td x)) (ensures (fun y -> p `P.lesser_equal_perm` P.full_perm ==> fractionable td y)) val mk_fraction_full (#t: Type0) (td: typedef t) (x: t) : Lemma (requires (fractionable td x)) (ensures (mk_fraction td x P.full_perm == x)) [SMTPat (mk_fraction td x P.full_perm)] val mk_fraction_compose (#t: Type0) (td: typedef t) (x: t) (p1 p2: P.perm) : Lemma (requires (fractionable td x /\ p1 `P.lesser_equal_perm` P.full_perm /\ p2 `P.lesser_equal_perm` P.full_perm)) (ensures (mk_fraction td (mk_fraction td x p1) p2 == mk_fraction td x (p1 `prod_perm` p2))) val full (#t: Type0) (td: typedef t) (v: t) : GTot prop val uninitialized (#t: Type0) (td: typedef t) : Ghost t (requires True) (ensures (fun y -> full td y /\ fractionable td y)) val unknown (#t: Type0) (td: typedef t) : Ghost t (requires True) (ensures (fun y -> fractionable td y)) val full_not_unknown (#t: Type) (td: typedef t) (v: t) : Lemma (requires (full td v)) (ensures (~ (v == unknown td))) [SMTPat (full td v)] val mk_fraction_unknown (#t: Type0) (td: typedef t) (p: P.perm) : Lemma (ensures (mk_fraction td (unknown td) p == unknown td)) val mk_fraction_eq_unknown (#t: Type0) (td: typedef t) (v: t) (p: P.perm) : Lemma (requires (fractionable td v /\ mk_fraction td v p == unknown td)) (ensures (v == unknown td)) // To be extracted as: void* [@@noextract_to "krml"] // primitive val void_ptr : Type0 // To be extracted as: NULL [@@noextract_to "krml"] // primitive val void_null: void_ptr // To be extracted as: *t [@@noextract_to "krml"] // primitive val ptr_gen ([@@@unused] t: Type) : Type0 [@@noextract_to "krml"] // primitive val null_gen (t: Type) : Tot (ptr_gen t) val ghost_void_ptr_of_ptr_gen (#[@@@unused] t: Type) (x: ptr_gen t) : GTot void_ptr val ghost_ptr_gen_of_void_ptr (x: void_ptr) ([@@@unused] t: Type) : GTot (ptr_gen t) val ghost_void_ptr_of_ptr_gen_of_void_ptr (x: void_ptr) (t: Type) : Lemma (ghost_void_ptr_of_ptr_gen (ghost_ptr_gen_of_void_ptr x t) == x) [SMTPat (ghost_void_ptr_of_ptr_gen (ghost_ptr_gen_of_void_ptr x t))] val ghost_ptr_gen_of_void_ptr_of_ptr_gen (#t: Type) (x: ptr_gen t) : Lemma (ghost_ptr_gen_of_void_ptr (ghost_void_ptr_of_ptr_gen x) t == x) [SMTPat (ghost_ptr_gen_of_void_ptr (ghost_void_ptr_of_ptr_gen x) t)] inline_for_extraction [@@noextract_to "krml"] // primitive let ptr (#t: Type) (td: typedef t) : Tot Type0 = ptr_gen t inline_for_extraction [@@noextract_to "krml"] // primitive let null (#t: Type) (td: typedef t) : Tot (ptr td) = null_gen t inline_for_extraction [@@noextract_to "krml"] let ref (#t: Type) (td: typedef t) : Tot Type0 = (p: ptr td { ~ (p == null td) }) val pts_to (#t: Type) (#td: typedef t) (r: ref td) ([@@@smt_fallback] v: Ghost.erased t) : vprop let pts_to_or_null (#t: Type) (#td: typedef t) (p: ptr td) (v: Ghost.erased t) : vprop = if FStar.StrongExcludedMiddle.strong_excluded_middle (p == null _) then emp else pts_to p v [@@noextract_to "krml"] // primitive val is_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STAtomicBase bool false opened Unobservable (pts_to_or_null p v) (fun _ -> pts_to_or_null p v) (True) (fun res -> res == true <==> p == null _) let assert_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost unit opened (pts_to_or_null p v) (fun _ -> emp) (p == null _) (fun _ -> True) = rewrite (pts_to_or_null p v) emp

{ "checked_file": "/", "dependencies": [ "Steel.ST.Util.fsti.checked", "Steel.FractionalPermission.fst.checked", "prims.fst.checked", "FStar.StrongExcludedMiddle.fst.checked", "FStar.Real.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Ghost.fsti.checked" ], "interface_file": false, "source_file": "Steel.ST.C.Types.Base.fsti" }

[ { "abbrev": true, "full_module": "Steel.FractionalPermission", "short_module": "P" }, { "abbrev": false, "full_module": "Steel.ST.Util", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "short_module": null }, { "abbrev": false, "full_module": "Steel.ST.C.Types", "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 } ]

{ "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" }

false

p: Steel.ST.C.Types.Base.ptr td -> Steel.ST.Effect.Ghost.STGhost (Prims.squash (~(p == Steel.ST.C.Types.Base.null td)))

Steel.ST.Effect.Ghost.STGhost

[]

[ "Steel.Memory.inames", "Steel.ST.C.Types.Base.typedef", "FStar.Ghost.erased", "Steel.ST.C.Types.Base.ptr", "Steel.ST.Util.rewrite", "Steel.ST.C.Types.Base.pts_to_or_null", "Steel.ST.C.Types.Base.pts_to", "Prims.unit", "Prims.squash", "Prims.l_not", "Prims.eq2", "Steel.ST.C.Types.Base.null", "Steel.Effect.Common.vprop", "Prims.l_True" ]

[]

false

true

false

let assert_not_null (#t: Type) (#opened: _) (#td: typedef t) (#v: Ghost.erased t) (p: ptr td) : STGhost (squash (~(p == null _))) opened (pts_to_or_null p v) (fun _ -> pts_to p v) (~(p == null _)) (fun _ -> True) =

rewrite (pts_to_or_null p v) (pts_to p v)

false

BinomialQueue.fst

BinomialQueue.all_leaf_keys

val all_leaf_keys (l: forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty)

let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 32, "end_line": 418, "start_col": 0, "start_line": 412 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest{Cons? l} -> FStar.Pervasives.Lemma (requires Cons? l /\ BinomialQueue.all_leaf l) (ensures BinomialQueue.permutation (BinomialQueue.keys l) BinomialQueue.ms_empty)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.forest", "Prims.b2t", "Prims.uu___is_Cons", "BinomialQueue.tree", "Prims.list", "BinomialQueue.all_leaf_keys", "Prims.unit", "Prims.l_and", "BinomialQueue.all_leaf", "Prims.squash", "BinomialQueue.permutation", "BinomialQueue.keys", "BinomialQueue.ms_empty", "Prims.Nil", "FStar.Pervasives.pattern" ]

[ "recursion" ]

false

true

false

let rec all_leaf_keys (l: forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) =

match l with | [Leaf] -> () | Leaf :: tl -> all_leaf_keys tl

false

BinomialQueue.fst

BinomialQueue.compact_preserves_keys

val compact_preserves_keys (q: forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))]

let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 40, "end_line": 429, "start_col": 0, "start_line": 420 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

q: BinomialQueue.forest -> FStar.Pervasives.Lemma (ensures BinomialQueue.permutation (BinomialQueue.keys q) (BinomialQueue.keys (BinomialQueue.mk_compact q))) [SMTPat (BinomialQueue.keys (BinomialQueue.mk_compact q))]

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.all_leaf", "BinomialQueue.all_leaf_keys", "Prims.bool", "BinomialQueue.compact_preserves_keys", "FStar.List.Tot.Base.tl", "Prims.unit", "Prims.l_True", "Prims.squash", "BinomialQueue.permutation", "BinomialQueue.keys", "BinomialQueue.mk_compact", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat", "BinomialQueue.ms", "Prims.Nil" ]

[ "recursion" ]

false

true

false

let rec compact_preserves_keys (q: forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] =

match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q)

false

Steel.GhostMonotonicHigherReference.fst

Steel.GhostMonotonicHigherReference.extract_pure

val extract_pure (#a #uses #p #f: _) (r: ref a p) (v: a) (h: (history a p)) : SteelGhostT (_: unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> pts_to_body r f v h)

let extract_pure #a #uses #p #f (r:ref a p) (v:a) (h:(history a p)) : SteelGhostT (_:unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> pts_to_body r f v h) = elim_pure (history_val h v f); A.intro_pure (history_val h v f)

{ "file_name": "lib/steel/Steel.GhostMonotonicHigherReference.fst", "git_rev": "f984200f79bdc452374ae994a5ca837496476c41", "git_url": "https://github.com/FStarLang/steel.git", "project_name": "steel" }

{ "end_col": 36, "end_line": 84, "start_col": 0, "start_line": 75 }

(* Copyright 2020 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 Steel.GhostMonotonicHigherReference open FStar.Ghost open FStar.PCM open Steel.Memory open Steel.Effect.Atomic open Steel.Effect open Steel.GhostPCMReference open Steel.FractionalPermission open Steel.Preorder module Preorder = FStar.Preorder module Q = Steel.Preorder module M = Steel.Memory module PR = Steel.GhostPCMReference module A = Steel.Effect.Atomic open FStar.Real #set-options "--ide_id_info_off" let ref a p = PR.ref (history a p) pcm_history [@@__reduce__] let pts_to_body #a #p (r:ref a p) (f:perm) (v:a) (h:history a p) = PR.pts_to r h `star` pure (history_val h v f) let pts_to' (#a:Type) (#p:Preorder.preorder a) (r:ref a p) (f:perm) (v: a) = h_exists (pts_to_body r f v) let pts_to_sl r f v = hp_of (pts_to' r f v) let intro_pure #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to_body r f v h) = A.intro_pure (history_val h v f) let intro_pure_full #opened #a #p #f (r:ref a p) (v:a) (h:history a p { history_val h v f }) : SteelGhostT unit opened (PR.pts_to r h) (fun _ -> pts_to r f v) = intro_pure #_ #a #p #f r v h; intro_exists h (pts_to_body r f v) let alloc #_ (#a:Type) (p:Preorder.preorder a) (v:a) = let h = Current [v] full_perm in assert (compatible pcm_history h h); let x : ref a p = alloc h in intro_pure_full x v h; x

{ "checked_file": "/", "dependencies": [ "Steel.Preorder.fst.checked", "Steel.Memory.fsti.checked", "Steel.GhostPCMReference.fsti.checked", "Steel.FractionalPermission.fst.checked", "Steel.Effect.Atomic.fsti.checked", "Steel.Effect.fsti.checked", "prims.fst.checked", "FStar.Real.fsti.checked", "FStar.Preorder.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.PCM.fst.checked", "FStar.Ghost.fsti.checked" ], "interface_file": true, "source_file": "Steel.GhostMonotonicHigherReference.fst" }

[ { "abbrev": false, "full_module": "FStar.Real", "short_module": null }, { "abbrev": true, "full_module": "Steel.Effect.Atomic", "short_module": "A" }, { "abbrev": true, "full_module": "Steel.GhostPCMReference", "short_module": "PR" }, { "abbrev": true, "full_module": "Steel.Memory", "short_module": "M" }, { "abbrev": true, "full_module": "Steel.Preorder", "short_module": "Q" }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Preorder", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "Steel.GhostPCMReference", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": true, "full_module": "FStar.Preorder", "short_module": "Preorder" }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Atomic", "short_module": null }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "Steel.FractionalPermission", "short_module": null }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": false, "full_module": "FStar.PCM", "short_module": null }, { "abbrev": false, "full_module": "Steel", "short_module": null }, { "abbrev": false, "full_module": "Steel", "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 } ]

{ "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" }

false

r: Steel.GhostMonotonicHigherReference.ref a p -> v: a -> h: Steel.Preorder.history a p -> Steel.Effect.Atomic.SteelGhostT (_: Prims.unit{Steel.Preorder.history_val h (FStar.Ghost.hide v) f})

Steel.Effect.Atomic.SteelGhostT

[]

[ "Steel.Memory.inames", "FStar.Preorder.preorder", "Steel.FractionalPermission.perm", "Steel.GhostMonotonicHigherReference.ref", "Steel.Preorder.history", "Steel.Effect.Atomic.intro_pure", "Steel.Preorder.history_val", "FStar.Ghost.hide", "Prims.unit", "Steel.Effect.Atomic.elim_pure", "Steel.GhostMonotonicHigherReference.pts_to_body", "Steel.Effect.Common.vprop" ]

[]

false

true

false

let extract_pure #a #uses #p #f (r: ref a p) (v: a) (h: (history a p)) : SteelGhostT (_: unit{history_val h v f}) uses (pts_to_body r f v h) (fun _ -> pts_to_body r f v h) =

elim_pure (history_val h v f); A.intro_pure (history_val h v f)

false

BinomialQueue.fst

BinomialQueue.find_max_emp_repr_r

val find_max_emp_repr_r (l: forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty)

let rec find_max_emp_repr_r (l:forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty) = match l with | [] -> () | Leaf::tl -> find_max_emp_repr_r tl | (Internal _ k _)::tl -> find_max_some_is_some k tl

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 54, "end_line": 478, "start_col": 0, "start_line": 471 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl let find_max_emp_repr_l (l:priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) = match l with | [] -> () | _ -> last_key_in_keys l

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.forest -> FStar.Pervasives.Lemma (requires BinomialQueue.find_max FStar.Pervasives.Native.None l == FStar.Pervasives.Native.None) (ensures BinomialQueue.permutation (BinomialQueue.keys l) BinomialQueue.ms_empty)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.find_max_emp_repr_r", "BinomialQueue.key_t", "BinomialQueue.find_max_some_is_some", "Prims.unit", "Prims.eq2", "FStar.Pervasives.Native.option", "BinomialQueue.find_max", "FStar.Pervasives.Native.None", "Prims.squash", "BinomialQueue.permutation", "BinomialQueue.keys", "BinomialQueue.ms_empty", "Prims.Nil", "FStar.Pervasives.pattern" ]

[ "recursion" ]

false

true

false

let rec find_max_emp_repr_r (l: forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty) =

match l with | [] -> () | Leaf :: tl -> find_max_emp_repr_r tl | Internal _ k _ :: tl -> find_max_some_is_some k tl

false

BinomialQueue.fst

BinomialQueue.find_max_emp_repr_l

val find_max_emp_repr_l (l: priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None)

let find_max_emp_repr_l (l:priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) = match l with | [] -> () | _ -> last_key_in_keys l

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 27, "end_line": 469, "start_col": 0, "start_line": 463 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

l: BinomialQueue.priq -> FStar.Pervasives.Lemma (requires BinomialQueue.repr_l l BinomialQueue.ms_empty) (ensures BinomialQueue.find_max FStar.Pervasives.Native.None l == FStar.Pervasives.Native.None )

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.priq", "Prims.list", "BinomialQueue.tree", "BinomialQueue.last_key_in_keys", "Prims.unit", "BinomialQueue.repr_l", "BinomialQueue.ms_empty", "Prims.squash", "Prims.eq2", "FStar.Pervasives.Native.option", "BinomialQueue.key_t", "BinomialQueue.find_max", "FStar.Pervasives.Native.None", "Prims.Nil", "FStar.Pervasives.pattern" ]

[]

false

true

false

let find_max_emp_repr_l (l: priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) =

match l with | [] -> () | _ -> last_key_in_keys l

false

BinomialQueue.fst

BinomialQueue.find_max_some_is_some

val find_max_some_is_some (k: key_t) (l: forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l)

let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 30, "end_line": 461, "start_col": 0, "start_line": 452 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

k: BinomialQueue.key_t -> l: BinomialQueue.forest -> FStar.Pervasives.Lemma (ensures Some? (BinomialQueue.find_max (FStar.Pervasives.Native.Some k) l) /\ k <= Some?.v (BinomialQueue.find_max (FStar.Pervasives.Native.Some k) l)) (decreases l)

FStar.Pervasives.Lemma

[ "lemma", "" ]

[]

[ "BinomialQueue.key_t", "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.find_max_some_is_some", "Prims.op_LessThan", "Prims.bool", "Prims.unit", "Prims.l_True", "Prims.squash", "Prims.l_and", "Prims.b2t", "FStar.Pervasives.Native.uu___is_Some", "BinomialQueue.find_max", "FStar.Pervasives.Native.Some", "Prims.op_LessThanOrEqual", "FStar.Pervasives.Native.__proj__Some__item__v", "Prims.Nil", "FStar.Pervasives.pattern" ]

[ "recursion" ]

false

true

false

let rec find_max_some_is_some (k: key_t) (l: forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) =

match l with | [] -> () | Leaf :: tl -> find_max_some_is_some k tl | Internal _ k' _ :: tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl

false

BinomialQueue.fst

BinomialQueue.tree_root_is_max

val tree_root_is_max (d: pos) (t: tree) : Lemma (requires is_pow2heap d t) (ensures (let Internal left k Leaf = t in max k (keys_of_tree left).ms_elems))

let tree_root_is_max (d:pos) (t:tree) : Lemma (requires is_pow2heap d t) (ensures (let Internal left k Leaf = t in max k (keys_of_tree left).ms_elems)) = let Internal left k Leaf = t in tree_root_is_max_aux (d - 1) k left

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 37, "end_line": 555, "start_col": 0, "start_line": 548 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl let find_max_emp_repr_l (l:priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) = match l with | [] -> () | _ -> last_key_in_keys l let rec find_max_emp_repr_r (l:forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty) = match l with | [] -> () | Leaf::tl -> find_max_emp_repr_r tl | (Internal _ k _)::tl -> find_max_some_is_some k tl #push-options "--warn_error -271" let delete_max_none_repr p = let delete_max_none_repr_l (l:priq) : Lemma (requires l `repr` ms_empty) (ensures delete_max l == None) [SMTPat ()] = find_max_emp_repr_l l in let delete_max_none_repr_r (l:priq) : Lemma (requires delete_max l == None) (ensures l `repr` ms_empty) [SMTPat ()] = find_max_emp_repr_r l in () #pop-options let rec keys_append (l1 l2:forest) (ms1 ms2:ms) : Lemma (requires l1 `repr_l` ms1 /\ l2 `repr_l` ms2) (ensures (L.append l1 l2) `repr_l` (ms_append ms1 ms2)) = match l1 with | [] -> () | _::tl -> keys_append tl l2 (keys tl) ms2 let rec unzip_repr (d:nat) (upper_bound:key_t) (t:tree) (lt:ms) : Lemma (requires pow2heap_pred d upper_bound t /\ permutation (keys_of_tree t) lt) (ensures permutation lt (keys (unzip d upper_bound t))) (decreases t) = match t with | Leaf -> () | Internal left k right -> let q = unzip (d - 1) upper_bound right in unzip_repr (d - 1) upper_bound right (keys_of_tree right); keys_append q [Internal left k Leaf] (keys_of_tree right) (ms_append (keys_of_tree left) (ms_append (ms_singleton k) ms_empty)) let heap_delete_max_repr (d:pos) (t:tree) (lt:ms) : Lemma (requires is_pow2heap d t /\ t `repr_t` lt) (ensures ( let Internal left k Leaf = t in permutation lt (ms_append (ms_singleton k) (keys (heap_delete_max d t))))) = let Internal left k Leaf = t in unzip_repr (d - 1) k left (keys_of_tree left) let max (k:key_t) (s:S.set key_t) = forall (x:key_t). Set.mem x s ==> x <= k let rec tree_root_is_max_aux (d:nat) (upper_bound:key_t) (t:tree) : Lemma (requires pow2heap_pred d upper_bound t) (ensures max upper_bound (keys_of_tree t).ms_elems) (decreases t) = match t with | Leaf -> () | Internal left k right -> tree_root_is_max_aux (d - 1) k left; tree_root_is_max_aux (d - 1) upper_bound right

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

d: Prims.pos -> t: BinomialQueue.tree -> FStar.Pervasives.Lemma (requires BinomialQueue.is_pow2heap d t) (ensures (let _ = t in (let BinomialQueue.Internal left k BinomialQueue.Leaf = _ in BinomialQueue.max k (Mkms?.ms_elems (BinomialQueue.keys_of_tree left))) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Prims.pos", "BinomialQueue.tree", "BinomialQueue.key_t", "BinomialQueue.tree_root_is_max_aux", "Prims.op_Subtraction", "Prims.unit", "BinomialQueue.is_pow2heap", "Prims.squash", "BinomialQueue.max", "BinomialQueue.__proj__Mkms__item__ms_elems", "BinomialQueue.keys_of_tree", "Prims.Nil", "FStar.Pervasives.pattern" ]

[]

false

true

false

let tree_root_is_max (d: pos) (t: tree) : Lemma (requires is_pow2heap d t) (ensures (let Internal left k Leaf = t in max k (keys_of_tree left).ms_elems)) =

let Internal left k Leaf = t in tree_root_is_max_aux (d - 1) k left

false

BinomialQueue.fst

BinomialQueue.max

val max : k: BinomialQueue.key_t -> s: FStar.Set.set BinomialQueue.key_t -> Prims.logical

let max (k:key_t) (s:S.set key_t) = forall (x:key_t). Set.mem x s ==> x <= k

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 42, "end_line": 534, "start_col": 0, "start_line": 533 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl let find_max_emp_repr_l (l:priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) = match l with | [] -> () | _ -> last_key_in_keys l let rec find_max_emp_repr_r (l:forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty) = match l with | [] -> () | Leaf::tl -> find_max_emp_repr_r tl | (Internal _ k _)::tl -> find_max_some_is_some k tl #push-options "--warn_error -271" let delete_max_none_repr p = let delete_max_none_repr_l (l:priq) : Lemma (requires l `repr` ms_empty) (ensures delete_max l == None) [SMTPat ()] = find_max_emp_repr_l l in let delete_max_none_repr_r (l:priq) : Lemma (requires delete_max l == None) (ensures l `repr` ms_empty) [SMTPat ()] = find_max_emp_repr_r l in () #pop-options let rec keys_append (l1 l2:forest) (ms1 ms2:ms) : Lemma (requires l1 `repr_l` ms1 /\ l2 `repr_l` ms2) (ensures (L.append l1 l2) `repr_l` (ms_append ms1 ms2)) = match l1 with | [] -> () | _::tl -> keys_append tl l2 (keys tl) ms2 let rec unzip_repr (d:nat) (upper_bound:key_t) (t:tree) (lt:ms) : Lemma (requires pow2heap_pred d upper_bound t /\ permutation (keys_of_tree t) lt) (ensures permutation lt (keys (unzip d upper_bound t))) (decreases t) = match t with | Leaf -> () | Internal left k right -> let q = unzip (d - 1) upper_bound right in unzip_repr (d - 1) upper_bound right (keys_of_tree right); keys_append q [Internal left k Leaf] (keys_of_tree right) (ms_append (keys_of_tree left) (ms_append (ms_singleton k) ms_empty)) let heap_delete_max_repr (d:pos) (t:tree) (lt:ms) : Lemma (requires is_pow2heap d t /\ t `repr_t` lt) (ensures ( let Internal left k Leaf = t in permutation lt (ms_append (ms_singleton k) (keys (heap_delete_max d t))))) = let Internal left k Leaf = t in unzip_repr (d - 1) k left (keys_of_tree left)

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

k: BinomialQueue.key_t -> s: FStar.Set.set BinomialQueue.key_t -> Prims.logical

Prims.Tot

[ "total" ]

[]

[ "BinomialQueue.key_t", "FStar.Set.set", "Prims.l_Forall", "Prims.l_imp", "Prims.b2t", "FStar.Set.mem", "Prims.op_LessThanOrEqual", "Prims.logical" ]

[]

false

true

let max (k: key_t) (s: S.set key_t) =

forall (x: key_t). Set.mem x s ==> x <= k

false

BinomialQueue.fst

BinomialQueue.insert_repr

val insert_repr (x:key_t) (q:priq) (s:ms) : Lemma (requires q `repr` s) (ensures insert x q `repr` (ms_cons x s))

let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x)

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 58, "end_line": 434, "start_col": 0, "start_line": 433 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

x: BinomialQueue.key_t -> q: BinomialQueue.priq -> s: BinomialQueue.ms -> FStar.Pervasives.Lemma (requires BinomialQueue.repr q s) (ensures BinomialQueue.repr (BinomialQueue.insert x q) (BinomialQueue.ms_cons x s))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "BinomialQueue.key_t", "BinomialQueue.priq", "BinomialQueue.ms", "BinomialQueue.carry_repr", "BinomialQueue.Internal", "BinomialQueue.Leaf", "BinomialQueue.ms_singleton", "Prims.unit" ]

[]

true

false

true

false

let insert_repr x q s =

carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x)

false

BinomialQueue.fst

BinomialQueue.find_max_mem_keys

val find_max_mem_keys (kopt: option key_t) (q: forest) : Lemma (ensures find_max kopt q == kopt \/ (let kopt = find_max kopt q in Some? kopt /\ S.mem (Some?.v kopt) (keys q).ms_elems)) (decreases q)

let rec find_max_mem_keys (kopt:option key_t) (q:forest) : Lemma (ensures find_max kopt q == kopt \/ (let kopt = find_max kopt q in Some? kopt /\ S.mem (Some?.v kopt) (keys q).ms_elems)) (decreases q) = match q with | [] -> () | Leaf::q -> find_max_mem_keys kopt q | (Internal _ k _)::q -> match kopt with | None -> find_max_mem_keys (Some k) q | Some k' -> let k = if k' < k then k else k' in find_max_mem_keys (Some k) q

{ "file_name": "examples/data_structures/BinomialQueue.fst", "git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }

{ "end_col": 34, "end_line": 605, "start_col": 0, "start_line": 589 }

(* Copyright 2022 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. Authors: Aseem Rastogi *) module BinomialQueue module L = FStar.List.Tot /// Some auxiliary lemmas let rec last_cons (#a:Type) (x:a) (l:list a) : Lemma (requires Cons? l) (ensures L.last (x::l) == L.last l) [SMTPat (L.last (x::l))] = match l with | [_] -> () | _::tl -> last_cons x tl /// We will maintain the priority queue as a forest type tree = | Leaf : tree | Internal : tree -> key_t -> tree -> tree /// Tree t is a complete binary tree of depth d /// /// All its keys are <= upper_bound /// /// If the left subtree is non-empty, /// its root is maximum in its subtree let rec pow2heap_pred (d:nat) (upper_bound:key_t) (t:tree) : prop = match t with | Leaf -> d == 0 | Internal left k right -> 0 < d /\ k <= upper_bound /\ pow2heap_pred (d - 1) k left /\ pow2heap_pred (d - 1) upper_bound right /// A power-2-heap of depth d is an Internal tree whose right child is a Leaf, /// and left child is a complete binary tree satisfying pow2heap_pred /// with upper bound as the key k let is_pow2heap (d:pos) (t:tree) : prop = match t with | Internal left k Leaf -> pow2heap_pred (d - 1) k left | _ -> False /// A list of trees is a binomial queue starting with depth d if: type forest = list tree let rec is_binomial_queue (d:pos) (l:forest) : Tot prop (decreases l) = match l with | [] -> True | hd::tl -> (Leaf? hd \/ is_pow2heap d hd) /\ is_binomial_queue (d + 1) tl /// We will also keep the binomial queue in a compact form, /// truncating unnecessary empty trees from the forest let is_compact (l:forest) = l == [] \/ Internal? (L.last l) let is_priq (l:forest) = is_binomial_queue 1 l /\ is_compact l /// The main priq type let priq = l:forest{is_priq l} let empty = [] /// We define a function to compact a forest let rec all_leaf (l:forest{Cons? l}) : bool = match l with | [Leaf] -> true | Leaf::tl -> all_leaf tl | _ -> false let rec mk_compact (l:forest) : forest = match l with | [] -> [] | _ -> if all_leaf l then [] else let hd::tl = l in hd::(mk_compact tl) /// Correctness of mk_compact let rec mk_compact_correctness (l:forest) : Lemma (is_compact (mk_compact l)) [SMTPat (is_compact (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_correctness (L.tl l) let rec mk_compact_preserves_binomial_queue (d:pos) (l:forest) : Lemma (requires is_binomial_queue d l) (ensures is_binomial_queue d (mk_compact l)) (decreases l) [SMTPat (is_binomial_queue d (mk_compact l))] = match l with | [] -> () | _ -> if all_leaf l then () else mk_compact_preserves_binomial_queue (d + 1) (L.tl l) /// smash is a key function combining two power of 2 heaps of depth d /// into a power of 2 heap of depth (d + 1) let smash (d:pos) (t1:tree) (t2:tree) : Pure tree (requires is_pow2heap d t1 /\ is_pow2heap d t2) (ensures fun t -> is_pow2heap (d + 1) t) = match t1, t2 with | Internal left1 k1 Leaf, Internal left2 k2 Leaf -> if k1 <= k2 then Internal (Internal left1 k1 left2) k2 Leaf else Internal (Internal left2 k2 left1) k1 Leaf /// carry adds t to q, preserving the binomial queue relation /// /// It has a nice symmetery to carry in binary arithmetic let rec carry (d:pos) (q:forest) (t:tree) : Pure forest (requires is_binomial_queue d q /\ is_pow2heap d t) (ensures fun q -> is_binomial_queue d q) (decreases q) = match q with | [] -> [t] | Leaf::tl -> t::tl | hd::tl -> let q = carry (d + 1) tl (smash d hd t) in Leaf::q /// join combines two trees p and q, with the carry c, /// preserving the binomial queue relation /// /// It has a nice symmetry to binary addition let rec join (d:pos) (p q:forest) (c:tree) : Pure forest (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c)) (ensures fun q -> is_binomial_queue d q) (decreases L.length p) = match p, q, c with | [], _, Leaf -> q | _, [], Leaf -> p | [], _, _ -> carry d q c | _, [], _ -> carry d p c | Leaf::tl_p, Leaf::tl_q, _ -> c::(join (d + 1) tl_p tl_q Leaf) | hd_p::tl_p, Leaf::tl_q, Leaf -> hd_p::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, Leaf -> hd_q::(join (d + 1) tl_p tl_q Leaf) | Leaf::tl_p, hd_q::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_q c)) | hd_p::tl_p, Leaf::tl_q, _ -> Leaf::(join (d + 1) tl_p tl_q (smash d hd_p c)) | hd_p::tl_p, hd_q::tl_q, c -> c::(join (d + 1) tl_p tl_q (smash d hd_p hd_q)) /// insert is just carry of (Internal Leaf x Leaf) to q let insert x q = let l = carry 1 q (Internal Leaf x Leaf) in mk_compact l /// Towards delete max /// find_max with the current max as max let rec find_max (max:option key_t) (q:forest) : Tot (option key_t) (decreases q) = match q with | [] -> max | Leaf::q -> find_max max q | (Internal _ k _)::q -> match max with | None -> find_max (Some k) q | Some max -> find_max (if max < k then Some k else Some max) q /// If q is a binomial queue starting at depth d, /// and t is a power of 2 heap of depth (d + length q) /// /// Then appending t to q is also a binomial queue let rec binomial_queue_append (d:pos) (q:forest) (t:tree) : Lemma (requires is_binomial_queue d q /\ is_pow2heap (L.length q + d) t) (ensures is_binomial_queue d (L.append q [t])) (decreases q) = match q with | [] -> () | _::q -> binomial_queue_append (d + 1) q t /// unzip splits the tree t along its right spine /// /// See https://www.cs.princeton.edu/~appel/BQ.pdf /// /// The upper bound is only needed to show we return a priq, /// may be it's not important? let rec unzip (d:nat) (upper_bound:key_t) (t:tree) : Pure priq (requires pow2heap_pred d upper_bound t) (ensures fun q -> L.length q == d) = match t with | Leaf -> [] | Internal left k right -> let q = unzip (d - 1) upper_bound right in binomial_queue_append 1 q (Internal left k Leaf); L.append_length q [Internal left k Leaf]; L.lemma_append_last q [Internal left k Leaf]; L.append q [Internal left k Leaf] /// Delete root of t, and unzip it let heap_delete_max (d:pos) (t:tree) : Pure priq (requires is_pow2heap d t) (ensures fun q -> L.length q == d - 1) = match t with | Internal left k Leaf -> unzip (d - 1) k left /// Take the first tree in q whose root is >= m, /// delete its root and unzip it, /// return (the deleted root, q with that tree replaces with Leaf, unzipped forest) /// let rec delete_max_aux (m:key_t) (d:pos) (q:forest) : Pure (key_t & forest & priq) (requires is_binomial_queue d q) (ensures fun (x, q, _) -> m <= x /\ is_binomial_queue d q) (decreases q) = match q with | [] -> m + 1, [], [] // this case won't arise // we could strengthen preconditions | Leaf::q -> let x, q, new_q = delete_max_aux m (d + 1) q in x, Leaf::q, new_q | (Internal left x right)::q -> if x < m then let y, q, new_q = delete_max_aux m (d + 1) q in y, (Internal left x right)::q, new_q else x, Leaf::q, heap_delete_max d (Internal left x right) /// delete_max finds the maximum key in the forest, /// deletes it from its tree, and joins the remaining forests let delete_max q = match find_max None q with | None -> None | Some m -> let x, q, new_q = delete_max_aux m 1 q in let r = join 1 q new_q Leaf in mk_compact_correctness r; Some (x, mk_compact r) /// merge is just join with Leaf as the carry let merge p q = let l = join 1 p q Leaf in mk_compact l /// Towards defining repr let rec keys_of_tree (t:tree) : ms = match t with | Leaf -> ms_empty | Internal left k right -> ms_append (keys_of_tree left) (ms_cons k (keys_of_tree right)) let rec keys (q:forest) : ms = match q with | [] -> ms_empty | hd::tl -> ms_append (keys_of_tree hd) (keys tl) let repr_t (t:tree) (l:ms) : prop = permutation (keys_of_tree t) l let repr_l (q:forest) (s:ms) : prop = permutation (keys q) s /// The main repr predicate saying s is a permutation of (keys q) let repr q s = repr_l q s let empty_repr _ = () /// Correctness of carry and join let smash_repr (d:pos) (t1 t2:tree) (l1 l2:ms) : Lemma (requires is_pow2heap d t1 /\ is_pow2heap d t2 /\ t1 `repr_t` l1 /\ t2 `repr_t` l2) (ensures smash d t1 t2 `repr_t` (ms_append l1 l2)) = () let rec carry_repr (d:pos) (q:forest) (t:tree) (lq lt:ms) : Lemma (requires is_binomial_queue d q /\ is_pow2heap d t /\ q `repr_l` lq /\ t `repr_t` lt) (ensures carry d q t `repr_l` ms_append lq lt) (decreases q) = match q with | [] -> () | Leaf::_ -> () | hd::tl -> smash_repr d hd t (keys_of_tree hd) (keys_of_tree t); carry_repr (d + 1) tl (smash d hd t) (keys tl) (ms_append (keys_of_tree hd) (keys_of_tree t)) #push-options "--z3rlimit 50 --fuel 1 --ifuel 1" let rec join_repr (d:pos) (p q:forest) (c:tree) (lp lq lc:ms) : Lemma (requires is_binomial_queue d p /\ is_binomial_queue d q /\ (Leaf? c \/ is_pow2heap d c) /\ p `repr_l` lp /\ q `repr_l` lq /\ c `repr_t` lc) (ensures join d p q c `repr_l` ms_append lp (ms_append lq lc)) (decreases p) = match p, q, c with | [], _, Leaf | _, [], Leaf -> () | [], _, _ -> carry_repr d q c lq lc | _, [], _ -> carry_repr d p c lp lc | Leaf::tl_p, Leaf::tl_q, _ -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | hd_p::tl_p, Leaf::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, Leaf -> join_repr (d + 1) tl_p tl_q Leaf (keys tl_p) (keys tl_q) ms_empty | Leaf::tl_p, hd_q::tl_q, _ -> smash_repr d hd_q c (keys_of_tree hd_q) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_q c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_q) (keys_of_tree c)) | hd_p::tl_p, Leaf::tl_q, _ -> smash_repr d hd_p c (keys_of_tree hd_p) (keys_of_tree c); join_repr (d + 1) tl_p tl_q (smash d hd_p c) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree c)) | hd_p::tl_p, hd_q::tl_q, c -> smash_repr d hd_p hd_q (keys_of_tree hd_p) (keys_of_tree hd_q); join_repr (d + 1) tl_p tl_q (smash d hd_p hd_q) (keys tl_p) (keys tl_q) (ms_append (keys_of_tree hd_p) (keys_of_tree hd_q)) #pop-options /// mk_compact preserves keys let rec all_leaf_keys (l:forest{Cons? l}) : Lemma (requires Cons? l /\ all_leaf l) (ensures permutation (keys l) ms_empty) = match l with | [Leaf] -> () | Leaf::tl -> all_leaf_keys tl let rec compact_preserves_keys (q:forest) : Lemma (permutation (keys q) (keys (mk_compact q))) [SMTPat (keys (mk_compact q))] = match q with | [] -> () | _ -> if all_leaf q then all_leaf_keys q else compact_preserves_keys (L.tl q) /// insert and merge correctness follows from carry and joinx let insert_repr x q s = carry_repr 1 q (Internal Leaf x Leaf) s (ms_singleton x) let merge_repr p q sp sq = join_repr 1 p q Leaf sp sq ms_empty /// Towards proof of delete correctness let rec last_key_in_keys (l:forest) : Lemma (requires Cons? l /\ Internal? (L.last l)) (ensures (let Internal _ k _ = L.last l in S.subset (S.singleton k) (keys l).ms_elems)) = match l with | [Internal _ _ _] -> () | _::tl -> last_key_in_keys tl let rec find_max_some_is_some (k:key_t) (l:forest) : Lemma (ensures Some? (find_max (Some k) l) /\ k <= Some?.v (find_max (Some k) l)) (decreases l) = match l with | [] -> () | Leaf::tl -> find_max_some_is_some k tl | (Internal _ k' _)::tl -> let k = if k < k' then k' else k in find_max_some_is_some k tl let find_max_emp_repr_l (l:priq) : Lemma (requires l `repr_l` ms_empty) (ensures find_max None l == None) = match l with | [] -> () | _ -> last_key_in_keys l let rec find_max_emp_repr_r (l:forest) : Lemma (requires find_max None l == None) (ensures permutation (keys l) ms_empty) = match l with | [] -> () | Leaf::tl -> find_max_emp_repr_r tl | (Internal _ k _)::tl -> find_max_some_is_some k tl #push-options "--warn_error -271" let delete_max_none_repr p = let delete_max_none_repr_l (l:priq) : Lemma (requires l `repr` ms_empty) (ensures delete_max l == None) [SMTPat ()] = find_max_emp_repr_l l in let delete_max_none_repr_r (l:priq) : Lemma (requires delete_max l == None) (ensures l `repr` ms_empty) [SMTPat ()] = find_max_emp_repr_r l in () #pop-options let rec keys_append (l1 l2:forest) (ms1 ms2:ms) : Lemma (requires l1 `repr_l` ms1 /\ l2 `repr_l` ms2) (ensures (L.append l1 l2) `repr_l` (ms_append ms1 ms2)) = match l1 with | [] -> () | _::tl -> keys_append tl l2 (keys tl) ms2 let rec unzip_repr (d:nat) (upper_bound:key_t) (t:tree) (lt:ms) : Lemma (requires pow2heap_pred d upper_bound t /\ permutation (keys_of_tree t) lt) (ensures permutation lt (keys (unzip d upper_bound t))) (decreases t) = match t with | Leaf -> () | Internal left k right -> let q = unzip (d - 1) upper_bound right in unzip_repr (d - 1) upper_bound right (keys_of_tree right); keys_append q [Internal left k Leaf] (keys_of_tree right) (ms_append (keys_of_tree left) (ms_append (ms_singleton k) ms_empty)) let heap_delete_max_repr (d:pos) (t:tree) (lt:ms) : Lemma (requires is_pow2heap d t /\ t `repr_t` lt) (ensures ( let Internal left k Leaf = t in permutation lt (ms_append (ms_singleton k) (keys (heap_delete_max d t))))) = let Internal left k Leaf = t in unzip_repr (d - 1) k left (keys_of_tree left) let max (k:key_t) (s:S.set key_t) = forall (x:key_t). Set.mem x s ==> x <= k let rec tree_root_is_max_aux (d:nat) (upper_bound:key_t) (t:tree) : Lemma (requires pow2heap_pred d upper_bound t) (ensures max upper_bound (keys_of_tree t).ms_elems) (decreases t) = match t with | Leaf -> () | Internal left k right -> tree_root_is_max_aux (d - 1) k left; tree_root_is_max_aux (d - 1) upper_bound right let tree_root_is_max (d:pos) (t:tree) : Lemma (requires is_pow2heap d t) (ensures (let Internal left k Leaf = t in max k (keys_of_tree left).ms_elems)) = let Internal left k Leaf = t in tree_root_is_max_aux (d - 1) k left #push-options "--z3rlimit 40" let rec delete_max_aux_repr (m:key_t) (d:pos) (q:forest) (x:key_t) (r:forest) (p:priq) (lq lr lp:ms) : Lemma (requires S.mem m (keys q).ms_elems /\ is_binomial_queue d q /\ q `repr_l` lq /\ delete_max_aux m d q == (x, r, p) /\ r `repr_l` lr /\ p `repr_l` lp) (ensures permutation lq (ms_append (ms_singleton x) (ms_append lr lp))) (decreases q) = match q with | [] -> () | Leaf::q -> delete_max_aux_repr m (d + 1) q x (L.tl r) p lq lr lp | (Internal left x Leaf)::q -> if x < m then begin tree_root_is_max d (Internal left x Leaf); assert (~ (S.mem m (keys_of_tree left).ms_elems)); let y, _, _ = delete_max_aux m (d + 1) q in delete_max_aux_repr m (d + 1) q y (L.tl r) p (keys q) (keys (L.tl r)) lp end else heap_delete_max_repr d (Internal left x Leaf) (keys_of_tree (Internal left x Leaf)) #pop-options

{ "checked_file": "/", "dependencies": [ "prims.fst.checked", "FStar.Set.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked" ], "interface_file": true, "source_file": "BinomialQueue.fst" }

[ { "abbrev": true, "full_module": "FStar.List.Tot", "short_module": "L" }, { "abbrev": true, "full_module": "FStar.Set", "short_module": "S" }, { "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 } ]

{ "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" }

false

kopt: FStar.Pervasives.Native.option BinomialQueue.key_t -> q: BinomialQueue.forest -> FStar.Pervasives.Lemma (ensures BinomialQueue.find_max kopt q == kopt \/ (let kopt = BinomialQueue.find_max kopt q in Some? kopt /\ FStar.Set.mem (Some?.v kopt) (Mkms?.ms_elems (BinomialQueue.keys q)))) (decreases q)

FStar.Pervasives.Lemma

[ "lemma", "" ]

[]

[ "FStar.Pervasives.Native.option", "BinomialQueue.key_t", "BinomialQueue.forest", "Prims.list", "BinomialQueue.tree", "BinomialQueue.find_max_mem_keys", "FStar.Pervasives.Native.Some", "Prims.op_LessThan", "Prims.bool", "Prims.unit", "Prims.l_True", "Prims.squash", "Prims.l_or", "Prims.eq2", "BinomialQueue.find_max", "Prims.l_and", "Prims.b2t", "FStar.Pervasives.Native.uu___is_Some", "FStar.Set.mem", "FStar.Pervasives.Native.__proj__Some__item__v", "BinomialQueue.__proj__Mkms__item__ms_elems", "BinomialQueue.keys", "Prims.Nil", "FStar.Pervasives.pattern" ]

[ "recursion" ]

false

true

false

let rec find_max_mem_keys (kopt: option key_t) (q: forest) : Lemma (ensures find_max kopt q == kopt \/ (let kopt = find_max kopt q in Some? kopt /\ S.mem (Some?.v kopt) (keys q).ms_elems)) (decreases q) =

false