microsoft/FStarDataSet-V2 · Datasets at Hugging Face

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51_pow51

val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime))

let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 104, "end_line": 161, "start_col": 0, "start_line": 150 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime ==

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

r: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (requires (let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ r3 r4 = _ in Lib.IntTypes.v r4 * 19 <= 190 * Hacl.Spec.Curve25519.Field51.Definition.pow51 /\ Lib.IntTypes.v r3 * 19 <= 190 * Hacl.Spec.Curve25519.Field51.Definition.pow51) <: Type0)) (ensures (let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in (Hacl.Spec.Curve25519.Field51.Definition.pow51 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) % Spec.Curve25519.prime) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "FStar.Pervasives.Native.Mktuple5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.u64", "Spec.Curve25519.prime", "Prims.unit", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "FStar.Mul.op_Star", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_3" ]

[]

false

true

false

let lemma_fmul5_pow51_pow51 r =

let r0, r1, r2, r3, r4 = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert (((pow51 * pow51) * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert (((pow51 * pow51) * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51

val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime))

let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 69, "end_line": 141, "start_col": 0, "start_line": 124 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

r: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (requires (let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ _ r4 = _ in Lib.IntTypes.v r4 * 19 <= 190 * Hacl.Spec.Curve25519.Field51.Definition.pow51) <: Type0)) (ensures (let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.pow51 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) % Spec.Curve25519.prime) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "FStar.Mul.op_Star", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Spec.Curve25519.prime", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Prims.pow2", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_prime", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Prims._assert", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Prims.op_Addition", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul5_distr_l" ]

[]

false

true

false

let lemma_fmul5_pow51 r =

let r0, r1, r2, r3, r4 = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + (v r2 * pow51) * pow51 + ((v r3 * pow51) * pow51) * pow51 + (((v r4 * pow51) * pow51) * pow51) * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) ((v r2 * pow51) * pow51) (((v r3 * pow51) * pow51) * pow51) ((((v r4 * pow51) * pow51) * pow51) * pow51); let p51r0123 = pow51 * v r0 + (pow51 * v r1) * pow51 + ((pow51 * v r2) * pow51) * pow51 + (((pow51 * v r3) * pow51) * pow51) * pow51 in let p51r4 = ((((pow51 * v r4) * pow51) * pow51) * pow51) * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_1

val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime))

let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 61, "end_line": 248, "start_col": 0, "start_line": 225 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f1: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f1 (9, 10, 9, 9, 9)} -> r: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 r (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (requires (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ _ _ = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + (Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + (((Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0)) (ensures (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + ((Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + (((Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Mul.op_Star", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.u64", "Prims.op_Addition", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Spec.Curve25519.prime", "Prims.unit", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_3", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Prims.b2t", "Prims.op_LessThanOrEqual", "Hacl.Spec.Curve25519.Field51.Definition.max51" ]

[]

false

true

false

let lemma_fmul5_1 f1 r =

let f10, f11, f12, f13, f14 = f1 in let r0, r1, r2, r3, r4 = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + (v f11 * pow51) * as_nat5 r + ((v f12 * pow51) * pow51) * as_nat5 r + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l ((v f11 * pow51) * as_nat5 r) (v f10 * as_nat5 r + ((v f12 * pow51) * pow51) * as_nat5 r + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + ((v f12 * pow51) * pow51) * as_nat5 r + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_subtract_p5_0

val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime)

let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 51, "end_line": 697, "start_col": 0, "start_line": 685 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)))

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1)} -> f': Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (requires (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let _ = f' in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in Lib.IntTypes.v f4 <> 0x7ffffffffffff || Lib.IntTypes.v f3 <> 0x7ffffffffffff || Lib.IntTypes.v f2 <> 0x7ffffffffffff || Lib.IntTypes.v f1 <> 0x7ffffffffffff || Lib.IntTypes.v f0 < 0x7ffffffffffed /\ Lib.IntTypes.v f0' = Lib.IntTypes.v f0 && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 && Lib.IntTypes.v f2' = Lib.IntTypes.v f2 && Lib.IntTypes.v f3' = Lib.IntTypes.v f3 && Lib.IntTypes.v f4' = Lib.IntTypes.v f4) <: Type0) <: Type0)) (ensures Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f' == Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f % Spec.Curve25519.prime)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.modulo_lemma", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Spec.Curve25519.prime", "Prims.unit", "Prims._assert", "Prims.eq2", "Prims.b2t", "Prims.op_LessThan", "Prims.op_Subtraction", "Prims.pow2", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "FStar.Mul.op_Star", "Prims.int", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "FStar.Pervasives.assert_norm", "Prims.op_Equality", "Prims.pos" ]

[]

false

true

false

let lemma_subtract_p5_0 f f' =

let f0, f1, f2, f3, f4 = f in let f0', f1', f2', f3', f4' = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + (v f2 * pow51) * pow51 + ((v f3 * pow51) * pow51) * pow51 + (((v f4 * pow51) * pow51) * pow51) * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + ((pow2 51 - 1) * pow2 51) * pow2 51 + (((pow2 51 - 1) * pow2 51) * pow2 51) * pow2 51 + ((((pow2 51 - 1) * pow2 51) * pow2 51) * pow2 51) * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_subtract_p

val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime)

let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f'

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 31, "end_line": 746, "start_col": 0, "start_line": 740 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff)))))

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1)} -> f': Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (requires (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let _ = f' in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in Lib.IntTypes.v f4 <> 0x7ffffffffffff || Lib.IntTypes.v f3 <> 0x7ffffffffffff || Lib.IntTypes.v f2 <> 0x7ffffffffffff || Lib.IntTypes.v f1 <> 0x7ffffffffffff || Lib.IntTypes.v f0 < 0x7ffffffffffed /\ Lib.IntTypes.v f0' = Lib.IntTypes.v f0 && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 && Lib.IntTypes.v f2' = Lib.IntTypes.v f2 && Lib.IntTypes.v f3' = Lib.IntTypes.v f3 && Lib.IntTypes.v f4' = Lib.IntTypes.v f4 \/ Lib.IntTypes.v f4 = 0x7ffffffffffff && Lib.IntTypes.v f3 = 0x7ffffffffffff && Lib.IntTypes.v f2 = 0x7ffffffffffff && Lib.IntTypes.v f1 = 0x7ffffffffffff && Lib.IntTypes.v f0 >= 0x7ffffffffffed /\ Lib.IntTypes.v f0' = Lib.IntTypes.v f0 - 0x7ffffffffffed && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 - 0x7ffffffffffff && Lib.IntTypes.v f2' = Lib.IntTypes.v f2 - 0x7ffffffffffff && Lib.IntTypes.v f3' = Lib.IntTypes.v f3 - 0x7ffffffffffff && Lib.IntTypes.v f4' = Lib.IntTypes.v f4 - 0x7ffffffffffff) <: Type0) <: Type0)) (ensures Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f' == Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f % Spec.Curve25519.prime)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "Prims.op_AmpAmp", "Prims.op_BarBar", "Prims.op_disEquality", "Prims.int", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims.op_LessThan", "Prims.op_Equality", "Lib.IntTypes.range_t", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_subtract_p5_0", "Prims.bool", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_subtract_p5_1", "Prims.unit" ]

[]

false

true

false

let lemma_subtract_p f f' =

let f0, f1, f2, f3, f4 = f in let f0', f1', f2', f3', f4' = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f'

false

InterpreterTarget.fst

InterpreterTarget.join_inv

val join_inv : d0: FStar.Pervasives.Native.option InterpreterTarget.inv -> d1: FStar.Pervasives.Native.option InterpreterTarget.inv -> FStar.Pervasives.Native.option InterpreterTarget.inv

let join_inv = join_index Inv_conj

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 34, "end_line": 63, "start_col": 0, "start_line": 63 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

d0: FStar.Pervasives.Native.option InterpreterTarget.inv -> d1: FStar.Pervasives.Native.option InterpreterTarget.inv -> FStar.Pervasives.Native.option InterpreterTarget.inv

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.join_index", "InterpreterTarget.inv", "InterpreterTarget.Inv_conj" ]

[]

false

true

false

let join_inv =

join_index Inv_conj

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_carry51_wide

val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1))

let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 66, "end_line": 486, "start_col": 0, "start_line": 477 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

l: Lib.IntTypes.uint128{Hacl.Spec.Curve25519.Field51.Definition.felem_wide_fits1 l m} -> cin: Lib.IntTypes.uint64 -> FStar.Pervasives.Lemma (ensures (let l' = l +! Lib.IntTypes.to_u128 cin in let l0 = Lib.IntTypes.to_u64 l' &. Hacl.Spec.Curve25519.Field51.Definition.mask51 in let l1 = Lib.IntTypes.to_u64 (l' >>. 51ul) in Lib.IntTypes.v l + Lib.IntTypes.v cin == Lib.IntTypes.v l1 * Prims.pow2 51 + Lib.IntTypes.v l0 /\ Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 l0 1 /\ Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 l1 (m + 1)))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.scale64", "Prims.b2t", "Prims.op_LessThan", "Lib.IntTypes.uint128", "Hacl.Spec.Curve25519.Field51.Definition.felem_wide_fits1", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.euclidean_division_definition", "Lib.IntTypes.v", "Lib.IntTypes.U128", "Lib.IntTypes.SEC", "Prims.pow2", "Prims.unit", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1", "Prims._assert", "Prims.eq2", "Lib.IntTypes.range_t", "Lib.IntTypes.U64", "Lib.IntTypes.mod_mask", "FStar.UInt32.__uint_to_t", "Hacl.Spec.Curve25519.Field51.Definition.mask51", "Lib.IntTypes.mod_mask_lemma", "Lib.IntTypes.to_u64", "Lib.IntTypes.int_t", "Lib.IntTypes.op_Greater_Greater_Dot", "Lib.IntTypes.op_Amp_Dot", "Lib.IntTypes.op_Plus_Bang", "Lib.IntTypes.to_u128" ]

[]

true

false

true

false

let lemma_carry51_wide #m l cin =

let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51)

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_2

val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime))

let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 61, "end_line": 294, "start_col": 0, "start_line": 270 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f1: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f1 (9, 10, 9, 9, 9)} -> r: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 r (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (requires (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + ((Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + (((Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0)) (ensures (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + (((Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Mul.op_Star", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.u64", "Prims.op_Addition", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Spec.Curve25519.prime", "Prims.unit", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51_pow51", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_4" ]

[]

false

true

false

let lemma_fmul5_2 f1 r =

let f10, f11, f12, f13, f14 = f1 in let r0, r1, r2, r3, r4 = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = (pow51 * pow51) * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + (((v f13 * pow51) * pow51) * pow51) * as_nat5 r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha224_finish8

val sha224_finish8 : Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

let sha224_finish8 = finish #SHA2_224 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 26, "start_col": 19, "start_line": 26 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.finish", "Spec.Hash.Definitions.SHA2_224", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha224_finish8 =

finish #SHA2_224 #M256

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5

val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)

let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 80, "end_line": 413, "start_col": 0, "start_line": 400 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f1: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f1 (9, 10, 9, 9, 9)} -> r: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 r (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (ensures (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Spec.Curve25519.fmul (Hacl.Spec.Curve25519.Field51.Definition.feval f1) (Hacl.Spec.Curve25519.Field51.Definition.feval r) == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r0, r1, r2, r3, r4) + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1) + Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r1 *! Lib.IntTypes.u64 19, r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0)) % Spec.Curve25519.prime) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Prims.op_Modulus", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Spec.Curve25519.prime", "Prims.unit", "FStar.Math.Lemmas.lemma_mod_mul_distr_l", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_4", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_3", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_2", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_1", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul5_distr_r", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.Mul.op_Star", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Addition" ]

[]

false

true

false

let lemma_fmul5 f1 r =

let f10, f11, f12, f13, f14 = f1 in let r0, r1, r2, r3, r4 = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + (v f12 * pow51) * pow51 + ((v f13 * pow51) * pow51) * pow51 + (((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) ((v f12 * pow51) * pow51) (((v f13 * pow51) * pow51) * pow51) ((((v f14 * pow51) * pow51) * pow51) * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime

false

InterpreterTarget.fst

InterpreterTarget.join_disj

val join_disj : d0: FStar.Pervasives.Native.option InterpreterTarget.disj -> d1: FStar.Pervasives.Native.option InterpreterTarget.disj -> FStar.Pervasives.Native.option InterpreterTarget.disj

let join_disj = join_index Disj_conj

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 36, "end_line": 65, "start_col": 0, "start_line": 65 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

d0: FStar.Pervasives.Native.option InterpreterTarget.disj -> d1: FStar.Pervasives.Native.option InterpreterTarget.disj -> FStar.Pervasives.Native.option InterpreterTarget.disj

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.join_index", "InterpreterTarget.disj", "InterpreterTarget.Disj_conj" ]

[]

false

true

false

let join_disj =

join_index Disj_conj

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha224_update8

val sha224_update8 : Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

let sha224_update8 = update #SHA2_224 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 23, "start_col": 19, "start_line": 23 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0"

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update", "Spec.Hash.Definitions.SHA2_224", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha224_update8 =

update #SHA2_224 #M256

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha224_init8

val sha224_init8 : Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

let sha224_init8 = init #SHA2_224 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 58, "end_line": 22, "start_col": 19, "start_line": 22 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0"

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.init", "Spec.Hash.Definitions.SHA2_224", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha224_init8 =

init #SHA2_224 #M256

false

InterpreterTarget.fst

InterpreterTarget.subst_inv

val subst_inv : s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.inv)

let subst_inv s = subst_index (subst_inv' s)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 44, "end_line": 77, "start_col": 0, "start_line": 77 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x ->

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.inv)

FStar.All.ALL

[]

[ "Target.subst", "InterpreterTarget.subst_index", "InterpreterTarget.inv", "InterpreterTarget.subst_inv'", "InterpreterTarget.index", "FStar.Pervasives.Native.option", "FStar.Pervasives.all_post_h", "FStar.Monotonic.Heap.heap", "Prims.l_Forall", "Prims.l_imp", "FStar.Pervasives.result", "Prims.guard_free", "Prims.l_and", "Prims.l_True", "Prims.l_not", "Prims.b2t", "FStar.Pervasives.Native.uu___is_None", "FStar.Pervasives.Native.uu___is_Some", "Prims.l_False", "Prims.eq2", "FStar.Pervasives.Native.None", "FStar.Pervasives.V", "FStar.Pervasives.Native.Some", "Prims.exn", "FStar.Pervasives.E", "Prims.string", "FStar.Pervasives.Err", "Prims.logical" ]

[]

false

true

false

let subst_inv s =

subst_index (subst_inv' s)

false

InterpreterTarget.fst

InterpreterTarget.eq_tags

val eq_tags : e: InterpreterTarget.eloc -> e': InterpreterTarget.eloc -> Prims.bool

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 14, "end_line": 85, "start_col": 0, "start_line": 79 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

e: InterpreterTarget.eloc -> e': InterpreterTarget.eloc -> Prims.bool

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.eloc", "FStar.Pervasives.Native.Mktuple2", "InterpreterTarget.expr", "Prims.b2t", "Target.uu___is_Identifier", "FStar.Pervasives.Native.fst", "Target.expr'", "Ast.range", "FStar.Pervasives.Native.tuple2", "Prims.bool" ]

[]

false

true

false

let eq_tags e e' =

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_carry51

val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13))

let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 36, "end_line": 465, "start_col": 0, "start_line": 457 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

l: Lib.IntTypes.uint64 -> cin: Lib.IntTypes.uint64 -> FStar.Pervasives.Lemma (requires Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 l 2 /\ Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 cin 8190) (ensures (let l0 = l +! cin &. Hacl.Spec.Curve25519.Field51.Definition.mask51 in let l1 = l +! cin >>. 51ul in Lib.IntTypes.v l + Lib.IntTypes.v cin == Lib.IntTypes.v l1 * Prims.pow2 51 + Lib.IntTypes.v l0 /\ Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 l0 1 /\ Lib.IntTypes.v l1 < Prims.pow2 13))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Lib.IntTypes.uint64", "FStar.Math.Lemmas.pow2_minus", "Prims.unit", "FStar.Math.Lemmas.euclidean_division_definition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims.pow2", "FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1", "Prims._assert", "Prims.eq2", "Lib.IntTypes.range_t", "Lib.IntTypes.mod_mask", "FStar.UInt32.__uint_to_t", "Hacl.Spec.Curve25519.Field51.Definition.mask51", "Lib.IntTypes.mod_mask_lemma", "Lib.IntTypes.to_u64", "Lib.IntTypes.int_t", "Lib.IntTypes.op_Greater_Greater_Dot", "Lib.IntTypes.op_Amp_Dot", "Lib.IntTypes.op_Plus_Bang" ]

[]

true

false

true

false

let lemma_carry51 l cin =

let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51

false

InterpreterTarget.fst

InterpreterTarget.join_eloc

val join_eloc : d0: FStar.Pervasives.Native.option InterpreterTarget.eloc -> d1: FStar.Pervasives.Native.option InterpreterTarget.eloc -> FStar.Pervasives.Native.option InterpreterTarget.eloc

let join_eloc = join_index Eloc_union

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 37, "end_line": 64, "start_col": 0, "start_line": 64 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

d0: FStar.Pervasives.Native.option InterpreterTarget.eloc -> d1: FStar.Pervasives.Native.option InterpreterTarget.eloc -> FStar.Pervasives.Native.option InterpreterTarget.eloc

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.join_index", "InterpreterTarget.eloc", "InterpreterTarget.Eloc_union" ]

[]

false

true

false

let join_eloc =

join_index Eloc_union

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha224_update_nblocks8

val sha224_update_nblocks8 : Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 93, "end_line": 24, "start_col": 19, "start_line": 24 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_nblocks", "Spec.Hash.Definitions.SHA2_224", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha224_update8" ]

[]

false

true

false

let sha224_update_nblocks8 =

update_nblocks #SHA2_224 #M256 sha224_update8

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_as_nat1

val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204)

let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 64, "end_line": 813, "start_col": 0, "start_line": 809 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f == Lib.IntTypes.v f0 + Lib.IntTypes.v f1 * Prims.pow2 51 + Lib.IntTypes.v f2 * Prims.pow2 102 + Lib.IntTypes.v f3 * Prims.pow2 153 + Lib.IntTypes.v f4 * Prims.pow2 204) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "FStar.Pervasives.assert_norm", "Prims.b2t", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star", "Prims.pow2", "Prims.unit", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51" ]

[]

true

false

true

false

let lemma_as_nat1 f =

assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm ((pow2 51 * pow2 51) * pow2 51 = pow2 153); assert_norm (((pow2 51 * pow2 51) * pow2 51) * pow2 51 = pow2 204)

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_subtract_p5_1

val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime)

let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 53, "end_line": 725, "start_col": 0, "start_line": 710 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff)))

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1)} -> f': Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (requires (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let _ = f' in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0' f1' f2' f3' f4' = _ in Lib.IntTypes.v f4 = 0x7ffffffffffff && Lib.IntTypes.v f3 = 0x7ffffffffffff && Lib.IntTypes.v f2 = 0x7ffffffffffff && Lib.IntTypes.v f1 = 0x7ffffffffffff && Lib.IntTypes.v f0 >= 0x7ffffffffffed /\ Lib.IntTypes.v f0' = Lib.IntTypes.v f0 - 0x7ffffffffffed && Lib.IntTypes.v f1' = Lib.IntTypes.v f1 - 0x7ffffffffffff && Lib.IntTypes.v f2' = Lib.IntTypes.v f2 - 0x7ffffffffffff && Lib.IntTypes.v f3' = Lib.IntTypes.v f3 - 0x7ffffffffffff && Lib.IntTypes.v f4' = Lib.IntTypes.v f4 - 0x7ffffffffffff) <: Type0) <: Type0)) (ensures Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f' == Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f % Spec.Curve25519.prime)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_sub", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Spec.Curve25519.prime", "Prims.unit", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Prims.op_Subtraction", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.Mul.op_Star", "Prims.pow2", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "FStar.Pervasives.assert_norm", "Prims.b2t", "Prims.op_Equality", "Prims.pos" ]

[]

false

true

false

let lemma_subtract_p5_1 f f' =

let f0, f1, f2, f3, f4 = f in let f0', f1', f2', f3', f4' = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + (v f2' * pow51) * pow51 + ((v f3' * pow51) * pow51) * pow51 + (((v f4' * pow51) * pow51) * pow51) * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + ((v f2 - (pow2 51 - 1)) * pow2 51) * pow2 51 + (((v f3 - (pow2 51 - 1)) * pow2 51) * pow2 51) * pow2 51 + ((((v f4 - (pow2 51 - 1)) * pow2 51) * pow2 51) * pow2 51) * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + (v f2 * pow2 51) * pow2 51 + ((v f3 * pow2 51) * pow2 51) * pow2 51 + (((v f4 * pow2 51) * pow2 51) * pow2 51) * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha224_update_last8

val sha224_update_last8 : Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 87, "end_line": 25, "start_col": 19, "start_line": 25 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_224 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_last", "Spec.Hash.Definitions.SHA2_224", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha224_update8" ]

[]

false

true

false

let sha224_update_last8 =

update_last #SHA2_224 #M256 sha224_update8

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha384_update_last4

val sha384_update_last4 : Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 87, "end_line": 120, "start_col": 19, "start_line": 120 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_last", "Spec.Hash.Definitions.SHA2_384", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha384_update4" ]

[]

false

true

false

let sha384_update_last4 =

update_last #SHA2_384 #M256 sha384_update4

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha256_init8

val sha256_init8 : Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

let sha256_init8 = init #SHA2_256 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 58, "end_line": 70, "start_col": 19, "start_line": 70 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.init", "Spec.Hash.Definitions.SHA2_256", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha256_init8 =

init #SHA2_256 #M256

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha256_finish8

val sha256_finish8 : Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

let sha256_finish8 = finish #SHA2_256 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 74, "start_col": 19, "start_line": 74 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.finish", "Spec.Hash.Definitions.SHA2_256", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha256_finish8 =

finish #SHA2_256 #M256

false

InterpreterTarget.fst

InterpreterTarget.subst_eloc

val subst_eloc : s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.eloc)

let subst_eloc s = subst_index (subst_eloc' s)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 46, "end_line": 103, "start_col": 0, "start_line": 103 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.eloc)

FStar.All.ALL

[]

[ "Target.subst", "InterpreterTarget.subst_index", "InterpreterTarget.eloc", "InterpreterTarget.subst_eloc'", "InterpreterTarget.index", "FStar.Pervasives.Native.option", "FStar.Pervasives.all_post_h", "FStar.Monotonic.Heap.heap", "Prims.l_Forall", "Prims.l_imp", "FStar.Pervasives.result", "Prims.guard_free", "Prims.l_and", "Prims.l_True", "Prims.l_not", "Prims.b2t", "FStar.Pervasives.Native.uu___is_None", "FStar.Pervasives.Native.uu___is_Some", "Prims.l_False", "Prims.eq2", "FStar.Pervasives.Native.None", "FStar.Pervasives.V", "FStar.Pervasives.Native.Some", "Prims.exn", "FStar.Pervasives.E", "Prims.string", "FStar.Pervasives.Err", "Prims.logical" ]

[]

false

true

false

let subst_eloc s =

subst_index (subst_eloc' s)

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha256_update8

val sha256_update8 : Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

let sha256_update8 = update #SHA2_256 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 71, "start_col": 19, "start_line": 71 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update", "Spec.Hash.Definitions.SHA2_256", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha256_update8 =

update #SHA2_256 #M256

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha384_init4

val sha384_init4 : Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

let sha384_init4 = init #SHA2_384 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 58, "end_line": 117, "start_col": 19, "start_line": 117 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.init", "Spec.Hash.Definitions.SHA2_384", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha384_init4 =

init #SHA2_384 #M256

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.mul64_wide_add3_lemma

val mul64_wide_add3_lemma: #m0:scale64 -> #m1:scale64 -> #m2:scale64 -> #m3:scale64 -> #m4:scale64 -> #m5:scale64 -> a0:uint64{felem_fits1 a0 m0} -> a1:uint64{felem_fits1 a1 m1} -> b0:uint64{felem_fits1 b0 m2} -> b1:uint64{felem_fits1 b1 m3} -> c0:uint64{felem_fits1 c0 m4} -> c1:uint64{felem_fits1 c1 m5} -> Lemma (requires m0 * m1 + m2 * m3 + m4 * m5 < pow2 13) (ensures v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < pow2 128 /\ (v a0 * v a1 + v b0 * v b1 + v c0 * v c1) <= (m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51)

let mul64_wide_add3_lemma #m0 #m1 #m2 #m3 #m4 #m5 a0 a1 b0 b1 c0 c1 = assert (pow51 = pow2 51); lemma_mul_le (v a0) (m0 * max51) (v a1) (m1 * max51); lemma_mul_le (v b0) (m2 * max51) (v b1) (m3 * max51); lemma_mul_le (v c0) (m4 * max51) (v c1) (m5 * max51); lemma_add_le (v a0 * v a1) (m0 * max51 * m1 * max51) (v b0 * v b1) (m2 * max51 * m3 * max51); lemma_add_le (v a0 * v a1 + v b0 * v b1) (m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51) (v c0 * v c1) (m4 * max51 * m5 * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 <= m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51 + m4 * max51 * m5 * max51); assert_by_tactic (m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51 + m4 * max51 * m5 * max51 == (m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51) canon; assert_norm (pow2 13 > 0); lemma_mul_le (m0 * m1 + m2 * m3 + m4 * m5) (pow2 13 - 1) (max51 * max51) (max51 * max51); assert ((m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51 < pow2 13 * max51 * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < pow2 13 * max51 * max51); assert_norm (pow2 13 * pow2 51 * pow2 51 = pow2 115); assert_norm (pow2 115 < pow2 128)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 35, "end_line": 942, "start_col": 0, "start_line": 924 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204) val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in as_nat5 f == o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem0 f = assert_norm (pow51 = pow2 51); let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64 * pow2 64 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 64 * pow2 64 * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f val lemma_store_felem: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = f0 |. (f1 <<. 51ul) in let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in as_nat5 f == v o0 + v o1 * pow2 64 + v o2 * pow2 64 * pow2 64 + v o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow51 = pow2 51); let o0 = f0 |. (f1 <<. 51ul) in FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f1) 64 51; logor_disjoint f0 (f1 <<. 51ul) 51; let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in FStar.Math.Lemmas.lemma_div_lt (v f1) 51 13; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 38; FStar.Math.Lemmas.multiple_modulo_lemma (v f2 % pow2 26) (pow2 38); logor_disjoint (f1 >>. 13ul) (f2 <<. 38ul) 38; let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in FStar.Math.Lemmas.lemma_div_lt (v f2) 51 26; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f3) 64 25; FStar.Math.Lemmas.multiple_modulo_lemma (v f3 % pow2 39) (pow2 25); logor_disjoint (f2 >>. 26ul) (f3 <<. 25ul) 25; let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in FStar.Math.Lemmas.lemma_div_lt (v f3) 51 39; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 12; FStar.Math.Lemmas.multiple_modulo_lemma (v f4 % pow2 52) (pow2 12); logor_disjoint (f3 >>. 39ul) (f4 <<. 12ul) 12; lemma_store_felem0 f val lemma_cswap2_step: bit:uint64{v bit <= 1} -> p1:uint64 -> p2:uint64 -> Lemma ( let mask = u64 0 -. bit in let dummy = mask &. (p1 ^. p2) in let p1' = p1 ^. dummy in let p2' = p2 ^. dummy in if v bit = 1 then p1' == p2 /\ p2' == p1 else p1' == p1 /\ p2' == p2) let lemma_cswap2_step bit p1 p2 = let mask = u64 0 -. bit in assert (v bit == 0 ==> v mask == 0); assert (v bit == 1 ==> v mask == pow2 64 - 1); let dummy = mask &. (p1 ^. p2) in logand_lemma mask (p1 ^. p2); assert (v bit == 1 ==> v dummy == v (p1 ^. p2)); assert (v bit == 0 ==> v dummy == 0); let p1' = p1 ^. dummy in assert (v dummy == v (if v bit = 1 then (p1 ^. p2) else u64 0)); logxor_lemma p1 p2; let p2' = p2 ^. dummy in logxor_lemma p2 p1 #push-options "--max_fuel 0 --max_ifuel 0" val mul64_wide_add3_lemma: #m0:scale64 -> #m1:scale64 -> #m2:scale64 -> #m3:scale64 -> #m4:scale64 -> #m5:scale64 -> a0:uint64{felem_fits1 a0 m0} -> a1:uint64{felem_fits1 a1 m1} -> b0:uint64{felem_fits1 b0 m2} -> b1:uint64{felem_fits1 b1 m3} -> c0:uint64{felem_fits1 c0 m4} -> c1:uint64{felem_fits1 c1 m5} -> Lemma (requires m0 * m1 + m2 * m3 + m4 * m5 < pow2 13) (ensures v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < pow2 128 /\ (v a0 * v a1 + v b0 * v b1 + v c0 * v c1) <=

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 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: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 a0 m0} -> a1: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 a1 m1} -> b0: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 b0 m2} -> b1: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 b1 m3} -> c0: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 c0 m4} -> c1: Lib.IntTypes.uint64{Hacl.Spec.Curve25519.Field51.Definition.felem_fits1 c1 m5} -> FStar.Pervasives.Lemma (requires m0 * m1 + m2 * m3 + m4 * m5 < Prims.pow2 13) (ensures Lib.IntTypes.v a0 * Lib.IntTypes.v a1 + Lib.IntTypes.v b0 * Lib.IntTypes.v b1 + Lib.IntTypes.v c0 * Lib.IntTypes.v c1 < Prims.pow2 128 /\ Lib.IntTypes.v a0 * Lib.IntTypes.v a1 + Lib.IntTypes.v b0 * Lib.IntTypes.v b1 + Lib.IntTypes.v c0 * Lib.IntTypes.v c1 <= ((m0 * m1 + m2 * m3 + m4 * m5) * Hacl.Spec.Curve25519.Field51.Definition.max51) * Hacl.Spec.Curve25519.Field51.Definition.max51)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.scale64", "Lib.IntTypes.uint64", "Prims.b2t", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits1", "FStar.Pervasives.assert_norm", "Prims.op_LessThan", "Prims.pow2", "Prims.unit", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star", "Prims._assert", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.max51", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_le", "Prims.op_Subtraction", "Prims.op_GreaterThan", "FStar.Tactics.Effect.assert_by_tactic", "Prims.eq2", "FStar.Tactics.Canon.canon", "Prims.op_LessThanOrEqual", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_add_le", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51" ]

[]

true

false

true

false

let mul64_wide_add3_lemma #m0 #m1 #m2 #m3 #m4 #m5 a0 a1 b0 b1 c0 c1 =

assert (pow51 = pow2 51); lemma_mul_le (v a0) (m0 * max51) (v a1) (m1 * max51); lemma_mul_le (v b0) (m2 * max51) (v b1) (m3 * max51); lemma_mul_le (v c0) (m4 * max51) (v c1) (m5 * max51); lemma_add_le (v a0 * v a1) (((m0 * max51) * m1) * max51) (v b0 * v b1) (((m2 * max51) * m3) * max51); lemma_add_le (v a0 * v a1 + v b0 * v b1) (((m0 * max51) * m1) * max51 + ((m2 * max51) * m3) * max51) (v c0 * v c1) (((m4 * max51) * m5) * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 <= ((m0 * max51) * m1) * max51 + ((m2 * max51) * m3) * max51 + ((m4 * max51) * m5) * max51); assert_by_tactic (((m0 * max51) * m1) * max51 + ((m2 * max51) * m3) * max51 + ((m4 * max51) * m5) * max51 == ((m0 * m1 + m2 * m3 + m4 * m5) * max51) * max51) canon; assert_norm (pow2 13 > 0); lemma_mul_le (m0 * m1 + m2 * m3 + m4 * m5) (pow2 13 - 1) (max51 * max51) (max51 * max51); assert (((m0 * m1 + m2 * m3 + m4 * m5) * max51) * max51 < (pow2 13 * max51) * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < (pow2 13 * max51) * max51); assert_norm ((pow2 13 * pow2 51) * pow2 51 = pow2 115); assert_norm (pow2 115 < pow2 128)

false

InterpreterTarget.fst

InterpreterTarget.typ_indexes

val typ_indexes : Type0

let typ_indexes = index inv & index eloc & index disj & on_success

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 66, "end_line": 122, "start_col": 0, "start_line": 122 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

Type0

Prims.Tot

[ "total" ]

[]

[ "FStar.Pervasives.Native.tuple4", "InterpreterTarget.index", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success" ]

[]

false

true

let typ_indexes =

index inv & index eloc & index disj & on_success

false

InterpreterTarget.fst

InterpreterTarget.typ_indexes_nil

val typ_indexes_nil:typ_indexes

let typ_indexes_nil : typ_indexes = None, None, None, On_success false

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 70, "end_line": 123, "start_col": 0, "start_line": 123 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

InterpreterTarget.typ_indexes

Prims.Tot

[ "total" ]

[]

[ "FStar.Pervasives.Native.Mktuple4", "InterpreterTarget.index", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success", "FStar.Pervasives.Native.None", "InterpreterTarget.On_success" ]

[]

false

true

false

let typ_indexes_nil:typ_indexes =

None, None, None, On_success false

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_cswap2_step

val lemma_cswap2_step: bit:uint64{v bit <= 1} -> p1:uint64 -> p2:uint64 -> Lemma ( let mask = u64 0 -. bit in let dummy = mask &. (p1 ^. p2) in let p1' = p1 ^. dummy in let p2' = p2 ^. dummy in if v bit = 1 then p1' == p2 /\ p2' == p1 else p1' == p1 /\ p2' == p2)

let lemma_cswap2_step bit p1 p2 = let mask = u64 0 -. bit in assert (v bit == 0 ==> v mask == 0); assert (v bit == 1 ==> v mask == pow2 64 - 1); let dummy = mask &. (p1 ^. p2) in logand_lemma mask (p1 ^. p2); assert (v bit == 1 ==> v dummy == v (p1 ^. p2)); assert (v bit == 0 ==> v dummy == 0); let p1' = p1 ^. dummy in assert (v dummy == v (if v bit = 1 then (p1 ^. p2) else u64 0)); logxor_lemma p1 p2; let p2' = p2 ^. dummy in logxor_lemma p2 p1

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 20, "end_line": 906, "start_col": 0, "start_line": 894 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204) val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in as_nat5 f == o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem0 f = assert_norm (pow51 = pow2 51); let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64 * pow2 64 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 64 * pow2 64 * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f val lemma_store_felem: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = f0 |. (f1 <<. 51ul) in let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in as_nat5 f == v o0 + v o1 * pow2 64 + v o2 * pow2 64 * pow2 64 + v o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow51 = pow2 51); let o0 = f0 |. (f1 <<. 51ul) in FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f1) 64 51; logor_disjoint f0 (f1 <<. 51ul) 51; let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in FStar.Math.Lemmas.lemma_div_lt (v f1) 51 13; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 38; FStar.Math.Lemmas.multiple_modulo_lemma (v f2 % pow2 26) (pow2 38); logor_disjoint (f1 >>. 13ul) (f2 <<. 38ul) 38; let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in FStar.Math.Lemmas.lemma_div_lt (v f2) 51 26; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f3) 64 25; FStar.Math.Lemmas.multiple_modulo_lemma (v f3 % pow2 39) (pow2 25); logor_disjoint (f2 >>. 26ul) (f3 <<. 25ul) 25; let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in FStar.Math.Lemmas.lemma_div_lt (v f3) 51 39; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 12; FStar.Math.Lemmas.multiple_modulo_lemma (v f4 % pow2 52) (pow2 12); logor_disjoint (f3 >>. 39ul) (f4 <<. 12ul) 12; lemma_store_felem0 f val lemma_cswap2_step: bit:uint64{v bit <= 1} -> p1:uint64 -> p2:uint64 -> Lemma ( let mask = u64 0 -. bit in let dummy = mask &. (p1 ^. p2) in let p1' = p1 ^. dummy in let p2' = p2 ^. dummy in

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

bit: Lib.IntTypes.uint64{Lib.IntTypes.v bit <= 1} -> p1: Lib.IntTypes.uint64 -> p2: Lib.IntTypes.uint64 -> FStar.Pervasives.Lemma (ensures (let mask = Lib.IntTypes.u64 0 -. bit in let dummy = mask &. p1 ^. p2 in let p1' = p1 ^. dummy in let p2' = p2 ^. dummy in (match Lib.IntTypes.v bit = 1 with | true -> p1' == p2 /\ p2' == p1 | _ -> p1' == p1 /\ p2' == p2) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Lib.IntTypes.uint64", "Prims.b2t", "Prims.op_LessThanOrEqual", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.logxor_lemma", "Lib.IntTypes.int_t", "Lib.IntTypes.op_Hat_Dot", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.IntTypes.range_t", "Prims.op_Equality", "Prims.int", "Prims.bool", "Lib.IntTypes.u64", "Prims.l_imp", "Lib.IntTypes.logand_lemma", "Lib.IntTypes.op_Amp_Dot", "Prims.op_Subtraction", "Prims.pow2", "Lib.IntTypes.op_Subtraction_Dot" ]

[]

false

true

false

let lemma_cswap2_step bit p1 p2 =

let mask = u64 0 -. bit in assert (v bit == 0 ==> v mask == 0); assert (v bit == 1 ==> v mask == pow2 64 - 1); let dummy = mask &. (p1 ^. p2) in logand_lemma mask (p1 ^. p2); assert (v bit == 1 ==> v dummy == v (p1 ^. p2)); assert (v bit == 0 ==> v dummy == 0); let p1' = p1 ^. dummy in assert (v dummy == v (if v bit = 1 then (p1 ^. p2) else u64 0)); logxor_lemma p1 p2; let p2' = p2 ^. dummy in logxor_lemma p2 p1

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_carry5_simplify

val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime)

let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 20, "end_line": 525, "start_col": 0, "start_line": 499 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

c0: Lib.IntTypes.uint64 -> c1: Lib.IntTypes.uint64 -> c2: Lib.IntTypes.uint64 -> c3: Lib.IntTypes.uint64 -> c4: Lib.IntTypes.uint64 -> t0: Lib.IntTypes.uint64 -> t1: Lib.IntTypes.uint64 -> t2: Lib.IntTypes.uint64 -> t3: Lib.IntTypes.uint64 -> t4: Lib.IntTypes.uint64 -> FStar.Pervasives.Lemma (ensures (Lib.IntTypes.v c0 * Prims.pow2 51 + Lib.IntTypes.v t0 + (Lib.IntTypes.v c1 * Prims.pow2 51 + Lib.IntTypes.v t1 - Lib.IntTypes.v c0) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + ((Lib.IntTypes.v c2 * Prims.pow2 51 + Lib.IntTypes.v t2 - Lib.IntTypes.v c1) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + (((Lib.IntTypes.v c3 * Prims.pow2 51 + Lib.IntTypes.v t3 - Lib.IntTypes.v c2) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + ((((Lib.IntTypes.v c4 * Prims.pow2 51 + Lib.IntTypes.v t4 - Lib.IntTypes.v c3) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) % Spec.Curve25519.prime == (Lib.IntTypes.v t0 + Lib.IntTypes.v c4 * 19 + Lib.IntTypes.v t1 * Hacl.Spec.Curve25519.Field51.Definition.pow51 + (Lib.IntTypes.v t2 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + ((Lib.IntTypes.v t3 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + (((Lib.IntTypes.v t4 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) % Spec.Curve25519.prime)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_r", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.Mul.op_Star", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Spec.Curve25519.prime", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Prims.pow2", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_prime", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Prims.b2t", "Prims.op_Equality", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_6", "Prims._assert", "Prims.op_Subtraction", "Prims.pos" ]

[]

true

false

true

false

let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 =

assert_norm (pow51 = pow2 51); assert (v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + ((v c2 * pow2 51 + v t2 - v c1) * pow51) * pow51 + (((v c3 * pow2 51 + v t3 - v c2) * pow51) * pow51) * pow51 + ((((v c4 * pow2 51 + v t4 - v c3) * pow51) * pow51) * pow51) * pow51 == v t0 + v t1 * pow51 + (v t2 * pow51) * pow51 + ((v t3 * pow51) * pow51) * pow51 + (((v t4 * pow51) * pow51) * pow51) * pow51 + ((((v c4 * pow2 51) * pow51) * pow51) * pow51) * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + (v t2 * pow51) * pow51 + ((v t3 * pow51) * pow51) * pow51 + (((v t4 * pow51) * pow51) * pow51) * pow51) (((((v c4 * pow2 51) * pow51) * pow51) * pow51) * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm ((((pow2 51 * pow51) * pow51) * pow51) * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + (v t2 * pow51) * pow51 + ((v t3 * pow51) * pow51) * pow51 + (((v t4 * pow51) * pow51) * pow51) * pow51) (v c4 * 19) prime

false

InterpreterTarget.fst

InterpreterTarget.subst_disj

val subst_disj : s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.disj)

let subst_disj s = subst_index (subst_disj' s)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 46, "end_line": 114, "start_col": 0, "start_line": 114 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

s: Target.subst -> i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ALL (FStar.Pervasives.Native.option InterpreterTarget.disj)

FStar.All.ALL

[]

[ "Target.subst", "InterpreterTarget.subst_index", "InterpreterTarget.disj", "InterpreterTarget.subst_disj'", "InterpreterTarget.index", "FStar.Pervasives.Native.option", "FStar.Pervasives.all_post_h", "FStar.Monotonic.Heap.heap", "Prims.l_Forall", "Prims.l_imp", "FStar.Pervasives.result", "Prims.guard_free", "Prims.l_and", "Prims.l_True", "Prims.l_not", "Prims.b2t", "FStar.Pervasives.Native.uu___is_None", "FStar.Pervasives.Native.uu___is_Some", "Prims.l_False", "Prims.eq2", "FStar.Pervasives.Native.None", "FStar.Pervasives.V", "FStar.Pervasives.Native.Some", "Prims.exn", "FStar.Pervasives.E", "Prims.string", "FStar.Pervasives.Err", "Prims.logical" ]

[]

false

true

false

let subst_disj s =

subst_index (subst_disj' s)

false

InterpreterTarget.fst

InterpreterTarget.typ_indexes_union

val typ_indexes_union : _: (((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success) -> _: (((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success) -> ((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success

let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b'

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 23, "end_line": 128, "start_col": 0, "start_line": 124 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

_: (((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success) -> _: (((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success) -> ((FStar.Pervasives.Native.option InterpreterTarget.inv * FStar.Pervasives.Native.option InterpreterTarget.eloc) * FStar.Pervasives.Native.option InterpreterTarget.disj) * InterpreterTarget.on_success

Prims.Tot

[ "total" ]

[]

[ "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.option", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success", "FStar.Pervasives.Native.Mktuple2", "FStar.Pervasives.Native.Mktuple4", "InterpreterTarget.join_inv", "InterpreterTarget.join_eloc", "InterpreterTarget.join_disj", "InterpreterTarget.On_success_union" ]

[]

false

true

false

let typ_indexes_union (i, e, d, b) (i', e', d', b') =

join_inv i i', join_eloc e e', join_disj d d', On_success_union b b'

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha384_update4

val sha384_update4 : Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

let sha384_update4 = update #SHA2_384 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 118, "start_col": 19, "start_line": 118 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update", "Spec.Hash.Definitions.SHA2_384", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha384_update4 =

update #SHA2_384 #M256

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem2

val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204)

let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 66, "end_line": 765, "start_col": 0, "start_line": 756 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 ==

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in Lib.IntTypes.v f0 + (Lib.IntTypes.v f1 % Prims.pow2 13) * Prims.pow2 51 + (Lib.IntTypes.v f1 / Prims.pow2 13) * Prims.pow2 64 + (Lib.IntTypes.v f2 % Prims.pow2 26) * Prims.pow2 102 + (Lib.IntTypes.v f2 / Prims.pow2 26) * Prims.pow2 128 + (Lib.IntTypes.v f3 % Prims.pow2 39) * Prims.pow2 153 + (Lib.IntTypes.v f3 / Prims.pow2 39) * Prims.pow2 192 + Lib.IntTypes.v f4 * Prims.pow2 204 == Lib.IntTypes.v f0 + Lib.IntTypes.v f1 * Prims.pow2 51 + Lib.IntTypes.v f2 * Prims.pow2 102 + Lib.IntTypes.v f3 * Prims.pow2 153 + Lib.IntTypes.v f4 * Prims.pow2 204) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.euclidean_division_definition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims.pow2", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.b2t", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star" ]

[]

false

true

false

let lemma_store_felem2 f =

let f0, f1, f2, f3, f4 = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39)

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha256_update_nblocks8

val sha256_update_nblocks8 : Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 93, "end_line": 72, "start_col": 19, "start_line": 72 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_nblocks", "Spec.Hash.Definitions.SHA2_256", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha256_update8" ]

[]

false

true

false

let sha256_update_nblocks8 =

update_nblocks #SHA2_256 #M256 sha256_update8

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha256_update_last8

val sha256_update_last8 : Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 87, "end_line": 73, "start_col": 19, "start_line": 73 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_256 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_last", "Spec.Hash.Definitions.SHA2_256", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha256_update8" ]

[]

false

true

false

let sha256_update_last8 =

update_last #SHA2_256 #M256 sha256_update8

false

InterpreterTarget.fst

InterpreterTarget.subst_index

val subst_index : s: (_: 'a -> FStar.All.ML 'a) -> i: InterpreterTarget.index 'a -> FStar.All.ALL (FStar.Pervasives.Native.option 'a)

let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 24, "end_line": 55, "start_col": 0, "start_line": 52 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

s: (_: 'a -> FStar.All.ML 'a) -> i: InterpreterTarget.index 'a -> FStar.All.ALL (FStar.Pervasives.Native.option 'a)

FStar.All.ALL

[]

[ "InterpreterTarget.index", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.Some" ]

[]

false

true

false

let subst_index (s: ('a -> ML 'a)) (i: index 'a) =

match i with | None -> None | Some i -> Some (s i)

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_3

val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime))

let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 61, "end_line": 340, "start_col": 0, "start_line": 316 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f1: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f1 (9, 10, 9, 9, 9)} -> r: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 r (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (requires (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + (((Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0)) (ensures (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1) + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Mul.op_Star", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.u64", "Prims.op_Addition", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Spec.Curve25519.prime", "Prims.unit", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51_pow51_pow51", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_5" ]

[]

false

true

false

let lemma_fmul5_3 f1 r =

let f10, f11, f12, f13, f14 = f1 in let r0, r1, r2, r3, r4 = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = ((pow51 * pow51) * pow51) * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + ((((v f14 * pow51) * pow51) * pow51) * pow51) * as_nat5 r) prime

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha384_finish4

val sha384_finish4 : Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

let sha384_finish4 = finish #SHA2_384 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 121, "start_col": 19, "start_line": 121 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.finish", "Spec.Hash.Definitions.SHA2_384", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha384_finish4 =

finish #SHA2_384 #M256

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha512_init4

val sha512_init4 : Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

let sha512_init4 = init #SHA2_512 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 58, "end_line": 153, "start_col": 19, "start_line": 153 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_finish4 = finish #SHA2_384 #M256 val sha384_4 (dst0 dst1 dst2 dst3: lbuffer uint8 48ul) (input_len:size_t) (input0 input1 input2 input3: lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_384 /\ live4 h0 input0 input1 input2 input3 /\ live4 h0 dst0 dst1 dst2 dst3 /\ internally_disjoint4 dst0 dst1 dst2 dst3) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| loc dst1 |+| loc dst2 |+| loc dst3) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_384 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_384 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_384 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_384 (as_seq h0 input3)) let sha384_4 dst0 dst1 dst2 dst3 input_len input0 input1 input2 input3 = let ib = ntup4 (input0,(input1,(input2,input3))) in let rb = ntup4 (dst0,(dst1,(dst2,dst3))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi4 rb; hash #SHA2_384 #M256 sha384_init4 sha384_update_nblocks4 sha384_update_last4 sha384_finish4 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_384 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.init_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.init", "Spec.Hash.Definitions.SHA2_512", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha512_init4 =

init #SHA2_512 #M256

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha384_update_nblocks4

val sha384_update_nblocks4 : Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 93, "end_line": 119, "start_col": 19, "start_line": 119 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_384 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_nblocks", "Spec.Hash.Definitions.SHA2_384", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha384_update4" ]

[]

false

true

false

let sha384_update_nblocks4 =

update_nblocks #SHA2_384 #M256 sha384_update4

false

InterpreterTarget.fst

InterpreterTarget.filter_args_for_inv

val filter_args_for_inv (args: list expr) (td: type_decl) : ML (list expr)

let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 21, "end_line": 190, "start_col": 0, "start_line": 177 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

args: Prims.list InterpreterTarget.expr -> td: InterpreterTarget.type_decl -> FStar.All.ML (Prims.list InterpreterTarget.expr)

FStar.All.ML

[ "ml" ]

[]

[ "Prims.list", "InterpreterTarget.expr", "InterpreterTarget.type_decl", "FStar.List.Tot.Base.flatten", "FStar.List.map2", "FStar.Pervasives.Native.tuple2", "Ast.with_meta_t", "Ast.ident'", "Target.typ", "Prims.Cons", "Prims.Nil", "Prims.bool", "FStar.Pervasives.Native.uu___is_Some", "FStar.Pervasives.Native.option", "FStar.List.tryFind", "Prims.op_Equality", "Prims.string", "Ast.ident_name", "Target.__proj__Mktypedef_name__item__td_params", "InterpreterTarget.__proj__Mktype_decl__item__name", "Ast.ident", "InterpreterTarget.free_vars_of_typ_indexes", "InterpreterTarget.__proj__Mktype_decl__item__typ_indexes" ]

[]

false

true

false

let filter_args_for_inv (args: list expr) (td: type_decl) : ML (list expr) =

let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args

false

InterpreterTarget.fst

InterpreterTarget.id_as_expr

val id_as_expr : i: Ast.ident -> Target.expr' * (Ast.pos * Ast.pos)

let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 55, "end_line": 260, "start_col": 0, "start_line": 260 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: Ast.ident -> Target.expr' * (Ast.pos * Ast.pos)

Prims.Tot

[ "total" ]

[]

[ "Ast.ident", "Target.mk_expr", "Target.Identifier", "FStar.Pervasives.Native.tuple2", "Target.expr'", "Ast.pos" ]

[]

false

true

false

let id_as_expr (i: A.ident) =

T.mk_expr (T.Identifier i)

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_disj

val free_vars_of_disj : i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ML (Prims.list Ast.ident)

let free_vars_of_disj = map_index [] free_vars_of_disj'

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 55, "end_line": 169, "start_col": 0, "start_line": 169 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.map_index", "InterpreterTarget.disj", "Prims.list", "Ast.ident", "Prims.Nil", "InterpreterTarget.free_vars_of_disj'" ]

[]

false

true

false

let free_vars_of_disj =

map_index [] free_vars_of_disj'

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_eloc

val free_vars_of_eloc : i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ML (Prims.list Ast.ident)

let free_vars_of_eloc = map_index [] free_vars_of_eloc'

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 55, "end_line": 162, "start_col": 0, "start_line": 162 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.map_index", "InterpreterTarget.eloc", "Prims.list", "Ast.ident", "Prims.Nil", "InterpreterTarget.free_vars_of_eloc'" ]

[]

false

true

false

let free_vars_of_eloc =

map_index [] free_vars_of_eloc'

false

InterpreterTarget.fst

InterpreterTarget.itype_of_ident

val itype_of_ident (hd: A.ident) : option itype

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 15, "end_line": 206, "start_col": 0, "start_line": 192 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

hd: Ast.ident -> FStar.Pervasives.Native.option InterpreterTarget.itype

Prims.Tot

[ "total" ]

[]

[ "Ast.ident", "Ast.__proj__Mkident'__item__name", "Ast.__proj__Mkwith_meta_t__item__v", "Ast.ident'", "FStar.Pervasives.Native.Some", "InterpreterTarget.itype", "InterpreterTarget.UInt8", "InterpreterTarget.UInt16", "InterpreterTarget.UInt32", "InterpreterTarget.UInt64", "InterpreterTarget.UInt8BE", "InterpreterTarget.UInt16BE", "InterpreterTarget.UInt32BE", "InterpreterTarget.UInt64BE", "InterpreterTarget.Unit", "InterpreterTarget.AllBytes", "InterpreterTarget.AllZeros", "Prims.string", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.option" ]

[]

false

true

false

let itype_of_ident (hd: A.ident) : option itype =

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_inv

val free_vars_of_inv : i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ML (Prims.list Ast.ident)

let free_vars_of_inv = map_index [] free_vars_of_inv'

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 53, "end_line": 153, "start_col": 0, "start_line": 153 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.map_index", "InterpreterTarget.inv", "Prims.list", "Ast.ident", "Prims.Nil", "InterpreterTarget.free_vars_of_inv'" ]

[]

false

true

false

let free_vars_of_inv =

map_index [] free_vars_of_inv'

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_typ_indexes

val free_vars_of_typ_indexes : i: InterpreterTarget.typ_indexes -> FStar.All.ALL (Prims.list Ast.ident)

let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 21, "end_line": 175, "start_col": 0, "start_line": 171 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj'

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.typ_indexes -> FStar.All.ALL (Prims.list Ast.ident)

FStar.All.ALL

[]

[ "InterpreterTarget.typ_indexes", "InterpreterTarget.index", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success", "FStar.List.Tot.Base.op_At", "Ast.ident", "Prims.list", "InterpreterTarget.free_vars_of_disj", "InterpreterTarget.free_vars_of_eloc", "InterpreterTarget.free_vars_of_inv" ]

[]

false

true

false

let free_vars_of_typ_indexes (i: typ_indexes) =

let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d

false

InterpreterTarget.fst

InterpreterTarget.join_index

val join_index : j: (_: _ -> _: _ -> _) -> d0: FStar.Pervasives.Native.option _ -> d1: FStar.Pervasives.Native.option _ -> FStar.Pervasives.Native.option _

let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 38, "end_line": 61, "start_col": 0, "start_line": 57 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

j: (_: _ -> _: _ -> _) -> d0: FStar.Pervasives.Native.option _ -> d1: FStar.Pervasives.Native.option _ -> FStar.Pervasives.Native.option _

Prims.Tot

[ "total" ]

[]

[ "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.Mktuple2", "FStar.Pervasives.Native.Some" ]

[]

false

true

false

let join_index j d0 d1 =

match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1)

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha512_finish4

val sha512_finish4 : Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

let sha512_finish4 = finish #SHA2_512 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 157, "start_col": 19, "start_line": 157 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_finish4 = finish #SHA2_384 #M256 val sha384_4 (dst0 dst1 dst2 dst3: lbuffer uint8 48ul) (input_len:size_t) (input0 input1 input2 input3: lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_384 /\ live4 h0 input0 input1 input2 input3 /\ live4 h0 dst0 dst1 dst2 dst3 /\ internally_disjoint4 dst0 dst1 dst2 dst3) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| loc dst1 |+| loc dst2 |+| loc dst3) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_384 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_384 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_384 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_384 (as_seq h0 input3)) let sha384_4 dst0 dst1 dst2 dst3 input_len input0 input1 input2 input3 = let ib = ntup4 (input0,(input1,(input2,input3))) in let rb = ntup4 (dst0,(dst1,(dst2,dst3))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi4 rb; hash #SHA2_384 #M256 sha384_init4 sha384_update_nblocks4 sha384_update_last4 sha384_finish4 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_384 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3) [@CInline] private let sha512_init4 = init #SHA2_512 #M256 [@CInline] private let sha512_update4 = update #SHA2_512 #M256 [@CInline] private let sha512_update_nblocks4 = update_nblocks #SHA2_512 #M256 sha512_update4

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.finish_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.finish", "Spec.Hash.Definitions.SHA2_512", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha512_finish4 =

finish #SHA2_512 #M256

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem0

val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in as_nat5 f == o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64)

let lemma_store_felem0 f = assert_norm (pow51 = pow2 51); let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64 * pow2 64 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 64 * pow2 64 * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 17, "end_line": 848, "start_col": 0, "start_line": 823 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204) val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 { Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1) /\ Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f < Spec.Curve25519.prime } -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let o0 = Lib.IntTypes.v f0 + (Lib.IntTypes.v f1 % Prims.pow2 13) * Prims.pow2 51 in let o1 = Lib.IntTypes.v f1 / Prims.pow2 13 + (Lib.IntTypes.v f2 % Prims.pow2 26) * Prims.pow2 38 in let o2 = Lib.IntTypes.v f2 / Prims.pow2 26 + (Lib.IntTypes.v f3 % Prims.pow2 39) * Prims.pow2 25 in let o3 = Lib.IntTypes.v f3 / Prims.pow2 39 + (Lib.IntTypes.v f4 % Prims.pow2 52) * Prims.pow2 12 in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f == o0 + o1 * Prims.pow2 64 + (o2 * Prims.pow2 64) * Prims.pow2 64 + ((o3 * Prims.pow2 64) * Prims.pow2 64) * Prims.pow2 64) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Prims.l_and", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Spec.Curve25519.prime", "Lib.IntTypes.uint64", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_as_nat1", "Prims.unit", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem1", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Addition", "FStar.Mul.op_Star", "Prims.pow2", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims.op_Modulus", "Prims.op_Division", "FStar.Pervasives.assert_norm", "Prims.op_Equality", "FStar.Math.Lemmas.modulo_lemma", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51" ]

[]

false

true

false

let lemma_store_felem0 f =

assert_norm (pow51 = pow2 51); let f0, f1, f2, f3, f4 = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert (o0 + o1 * pow2 64 + (o2 * pow2 64) * pow2 64 + ((o3 * pow2 64) * pow2 64) * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + ((v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64) * pow2 64 + (((v f3 / pow2 39 + v f4 * pow2 12) * pow2 64) * pow2 64) * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm ((pow2 64 * pow2 64) * pow2 64 = pow2 192); assert (o0 + o1 * pow2 64 + (o2 * pow2 64) * pow2 64 + ((o3 * pow2 64) * pow2 64) * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f

false

InterpreterTarget.fst

InterpreterTarget.print_derived_name

val print_derived_name : mname: Prims.string -> tag: Prims.string -> i: Ast.ident -> Prims.string

let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 21, "end_line": 635, "start_col": 0, "start_line": 631 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> tag: Prims.string -> i: Ast.ident -> Prims.string

Prims.Tot

[ "total" ]

[]

[ "Prims.string", "Ast.ident", "FStar.Printf.sprintf", "Target.maybe_mname_prefix", "Target.print_ident" ]

[]

false

true

false

let print_derived_name (mname tag: string) (i: A.ident) =

Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i)

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_4

val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime))

let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 78, "end_line": 386, "start_col": 0, "start_line": 362 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f1: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f1 (9, 10, 9, 9, 9)} -> r: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 r (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (requires (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1) + ((((Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r) % Spec.Curve25519.prime) <: Type0) <: Type0)) (ensures (let _ = f1 in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in let _ = r in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f1 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r % Spec.Curve25519.prime == (Lib.IntTypes.v f10 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 r + Lib.IntTypes.v f11 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r4 *! Lib.IntTypes.u64 19, r0, r1, r2, r3) + Lib.IntTypes.v f12 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1, r2) + Lib.IntTypes.v f13 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0, r1) + Lib.IntTypes.v f14 * Hacl.Spec.Curve25519.Field51.Definition.as_nat5 (r1 *! Lib.IntTypes.u64 19, r2 *! Lib.IntTypes.u64 19, r3 *! Lib.IntTypes.u64 19, r4 *! Lib.IntTypes.u64 19, r0)) % Spec.Curve25519.prime) <: Type0) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "FStar.Math.Lemmas.lemma_mod_plus_distr_l", "FStar.Mul.op_Star", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.u64", "Prims.op_Addition", "Spec.Curve25519.prime", "Prims.unit", "FStar.Math.Lemmas.lemma_mod_mul_distr_r", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5_pow51_pow51_pow51_pow51", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Modulus", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_6" ]

[]

false

true

false

let lemma_fmul5_4 f1 r =

let f10, f11, f12, f13, f14 = f1 in let r0, r1, r2, r3, r4 = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = (((pow51 * pow51) * pow51) * pow51) * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_load_felem_fits5

val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1))

let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 25, "end_line": 604, "start_col": 0, "start_line": 576 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12))

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> u64s: Lib.Sequence.lseq Lib.IntTypes.uint64 4 -> FStar.Pervasives.Lemma (requires (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let _ = u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ] in (let FStar.Pervasives.Native.Mktuple4 #_ #_ #_ #_ s0 s1 s2 s3 = _ in Lib.IntTypes.v s3 < Prims.pow2 63 /\ Lib.IntTypes.v f0 == Lib.IntTypes.v s0 % Prims.pow2 51 /\ Lib.IntTypes.v f1 == Lib.IntTypes.v s0 / Prims.pow2 51 + (Lib.IntTypes.v s1 % Prims.pow2 38) * Prims.pow2 13 /\ Lib.IntTypes.v f2 == Lib.IntTypes.v s1 / Prims.pow2 38 + (Lib.IntTypes.v s2 % Prims.pow2 25) * Prims.pow2 26 /\ Lib.IntTypes.v f3 == Lib.IntTypes.v s2 / Prims.pow2 25 + (Lib.IntTypes.v s3 % Prims.pow2 12) * Prims.pow2 39 /\ Lib.IntTypes.v f4 == Lib.IntTypes.v s3 / Prims.pow2 12) <: Type0) <: Type0)) (ensures Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.Sequence.lseq", "Lib.IntTypes.uint64", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims._assert", "Prims.b2t", "Prims.op_LessThan", "Lib.IntTypes.v", "Prims.pow2", "Prims.unit", "FStar.Pervasives.assert_norm", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star", "Prims.op_LessThanOrEqual", "Prims.op_Subtraction", "Prims.op_Addition", "Prims.op_Modulus", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_le", "FStar.Math.Lemmas.lemma_div_lt", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.Mktuple4", "Lib.Sequence.op_String_Access" ]

[]

false

true

false

let lemma_load_felem_fits5 f u64s =

let open Lib.Sequence in let f0, f1, f2, f3, f4 = f in let s0, s1, s2, s3 = (u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51)

false

InterpreterTarget.fst

InterpreterTarget.print_ident

val print_ident : mname: Prims.string -> i: Ast.ident -> FStar.All.ML Prims.string

let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 39, "end_line": 629, "start_col": 0, "start_line": 628 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros"

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> i: Ast.ident -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "Ast.ident", "Target.print_maybe_qualified_ident" ]

[]

false

true

false

let print_ident (mname: string) (i: A.ident) =

T.print_maybe_qualified_ident mname i

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha512_update4

val sha512_update4 : Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

let sha512_update4 = update #SHA2_512 #M256

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 62, "end_line": 154, "start_col": 19, "start_line": 154 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_finish4 = finish #SHA2_384 #M256 val sha384_4 (dst0 dst1 dst2 dst3: lbuffer uint8 48ul) (input_len:size_t) (input0 input1 input2 input3: lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_384 /\ live4 h0 input0 input1 input2 input3 /\ live4 h0 dst0 dst1 dst2 dst3 /\ internally_disjoint4 dst0 dst1 dst2 dst3) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| loc dst1 |+| loc dst2 |+| loc dst3) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_384 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_384 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_384 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_384 (as_seq h0 input3)) let sha384_4 dst0 dst1 dst2 dst3 input_len input0 input1 input2 input3 = let ib = ntup4 (input0,(input1,(input2,input3))) in let rb = ntup4 (dst0,(dst1,(dst2,dst3))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi4 rb; hash #SHA2_384 #M256 sha384_init4 sha384_update_nblocks4 sha384_update_last4 sha384_finish4 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_384 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3)

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_vec_t Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update", "Spec.Hash.Definitions.SHA2_512", "Hacl.Spec.SHA2.Vec.M256" ]

[]

false

true

false

let sha512_update4 =

update #SHA2_512 #M256

false

InterpreterTarget.fst

InterpreterTarget.print_lam

val print_lam : mname: Prims.string -> p: (_: 'a -> FStar.All.ML Prims.string) -> x: InterpreterTarget.lam 'a -> FStar.All.ALL Prims.string

let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x))

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 15, "end_line": 650, "start_col": 0, "start_line": 647 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ")

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> p: (_: 'a -> FStar.All.ML Prims.string) -> x: InterpreterTarget.lam 'a -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "InterpreterTarget.lam", "FStar.Printf.sprintf", "InterpreterTarget.print_ident", "FStar.Pervasives.Native.fst", "Ast.ident", "FStar.Pervasives.Native.snd" ]

[]

false

true

false

let print_lam (mname: string) (p: ('a -> ML string)) (x: lam 'a) =

Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x))

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha512_update_nblocks4

val sha512_update_nblocks4 : Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

let sha512_update_nblocks4 = update_nblocks #SHA2_512 #M256 sha512_update4

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 93, "end_line": 155, "start_col": 19, "start_line": 155 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_finish4 = finish #SHA2_384 #M256 val sha384_4 (dst0 dst1 dst2 dst3: lbuffer uint8 48ul) (input_len:size_t) (input0 input1 input2 input3: lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_384 /\ live4 h0 input0 input1 input2 input3 /\ live4 h0 dst0 dst1 dst2 dst3 /\ internally_disjoint4 dst0 dst1 dst2 dst3) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| loc dst1 |+| loc dst2 |+| loc dst3) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_384 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_384 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_384 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_384 (as_seq h0 input3)) let sha384_4 dst0 dst1 dst2 dst3 input_len input0 input1 input2 input3 = let ib = ntup4 (input0,(input1,(input2,input3))) in let rb = ntup4 (dst0,(dst1,(dst2,dst3))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi4 rb; hash #SHA2_384 #M256 sha384_init4 sha384_update_nblocks4 sha384_update_last4 sha384_finish4 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_384 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3) [@CInline] private let sha512_init4 = init #SHA2_512 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_nblocks_vec_t' Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_nblocks", "Spec.Hash.Definitions.SHA2_512", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha512_update4" ]

[]

false

true

false

let sha512_update_nblocks4 =

update_nblocks #SHA2_512 #M256 sha512_update4

false

Steel.Effect.Atomic.fst

Steel.Effect.Atomic.mk_selector_vprop_elim

val mk_selector_vprop_elim (#opened: _) (#t: Type0) (p: t -> vprop) (p_inj: interp_hp_of_injective p) : SteelGhost (Ghost.erased t) opened (mk_selector_vprop p p_inj) (fun x -> p x) (fun _ -> True) (fun h x _ -> h (mk_selector_vprop p p_inj) == Ghost.reveal x)

let mk_selector_vprop_elim #_ #t p p_inj = let x0 = gget (mk_selector_vprop p p_inj) in let refinement (x: t) : Tot prop = x == Ghost.reveal x0 in intro_vrefine (mk_selector_vprop p p_inj) refinement; rewrite_slprop (mk_selector_vprop p p_inj `vrefine` refinement) (p x0) (fun m -> interp_vrefine_hp (mk_selector_vprop p p_inj) refinement m // injectivity is not needed, because the return value of the // selector is exactly the witness of exists_ ); x0

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

{ "end_col": 4, "end_line": 940, "start_col": 0, "start_line": 926 }

(* 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.Effect.Atomic open Steel.Effect friend Steel.Effect #set-options "--warn_error -330" //turn off the experimental feature warning let _ : squash (forall (pre:pre_t) (m0:mem{interp (hp_of pre) m0}) (m1:mem{disjoint m0 m1}). mk_rmem pre m0 == mk_rmem pre (join m0 m1)) = Classical.forall_intro rmem_depends_only_on let req_to_act_req (#pre:vprop) (req:req_t pre) : mprop (hp_of pre) = fun m -> rmem_depends_only_on pre; interp (hp_of pre) m /\ req (mk_rmem pre m) unfold let to_post (#a:Type) (post:post_t a) = fun x -> (hp_of (post x)) let ens_to_act_ens (#pre:pre_t) (#a:Type) (#post:post_t a) (ens:ens_t pre a post) : mprop2 (hp_of pre) (to_post post) = fun m0 x m1 -> interp (hp_of pre) m0 /\ interp (hp_of (post x)) m1 /\ ens (mk_rmem pre m0) x (mk_rmem (post x) m1) let repr a framed opened f pre post req ens = action_except_full a opened (hp_of pre) (to_post post) (req_to_act_req req) (ens_to_act_ens ens) let return_ a x opened #p = fun _ -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem (p x) (core_mem m0) in lemma_frame_equalities_refl (p x) h0; x #push-options "--fuel 0 --ifuel 0" #push-options "--z3rlimit 20 --fuel 1 --ifuel 1" val frame00 (#a:Type) (#framed:bool) (#opened:inames) (#obs:observability) (#pre:pre_t) (#post:post_t a) (#req:req_t pre) (#ens:ens_t pre a post) ($f:repr a framed opened obs pre post req ens) (frame:vprop) : repr a true opened obs (pre `star` frame) (fun x -> post x `star` frame) (fun h -> req (focus_rmem h pre)) (fun h0 r h1 -> req (focus_rmem h0 pre) /\ ens (focus_rmem h0 pre) r (focus_rmem h1 (post r)) /\ frame_opaque frame (focus_rmem h0 frame) (focus_rmem h1 frame)) module Sem = Steel.Semantics.Hoare.MST module Mem = Steel.Memory let equiv_middle_left_assoc (a b c d:slprop) : Lemma (((a `Mem.star` b) `Mem.star` c `Mem.star` d) `Mem.equiv` (a `Mem.star` (b `Mem.star` c) `Mem.star` d)) = let open Steel.Memory in star_associative a b c; star_congruence ((a `star` b) `star` c) d (a `star` (b `star` c)) d let frame00 #a #framed #opened #obs #pre #post #req #ens f frame = fun frame' -> let m0:full_mem = NMSTTotal.get () in let snap:rmem frame = mk_rmem frame (core_mem m0) in // Need to define it with type annotation, although unused, for it to trigger // the pattern on the framed ensures in the def of MstTot let aux:mprop (hp_of frame `Mem.star` frame') = req_frame frame snap in focus_is_restrict_mk_rmem (pre `star` frame) pre (core_mem m0); assert (interp (hp_of (pre `star` frame) `Mem.star` frame' `Mem.star` locks_invariant opened m0) m0); equiv_middle_left_assoc (hp_of pre) (hp_of frame) frame' (locks_invariant opened m0); assert (interp (hp_of pre `Mem.star` (hp_of frame `Mem.star` frame') `Mem.star` locks_invariant opened m0) m0); let x = f (hp_of frame `Mem.star` frame') in let m1:full_mem = NMSTTotal.get () in assert (interp (hp_of (post x) `Mem.star` (hp_of frame `Mem.star` frame') `Mem.star` locks_invariant opened m1) m1); equiv_middle_left_assoc (hp_of (post x)) (hp_of frame) frame' (locks_invariant opened m1); assert (interp ((hp_of (post x) `Mem.star` hp_of frame) `Mem.star` frame' `Mem.star` locks_invariant opened m1) m1); focus_is_restrict_mk_rmem (pre `star` frame) frame (core_mem m0); focus_is_restrict_mk_rmem (post x `star` frame) frame (core_mem m1); let h0:rmem (pre `star` frame) = mk_rmem (pre `star` frame) (core_mem m0) in let h1:rmem (post x `star` frame) = mk_rmem (post x `star` frame) (core_mem m1) in assert (focus_rmem h0 frame == focus_rmem h1 frame); focus_is_restrict_mk_rmem (post x `star` frame) (post x) (core_mem m1); lemma_frame_opaque_refl frame (focus_rmem h0 frame); x unfold let bind_req_opaque (#a:Type) (#pre_f:pre_t) (#post_f:post_t a) (req_f:req_t pre_f) (ens_f:ens_t pre_f a post_f) (#pre_g:a -> pre_t) (#pr:a -> prop) (req_g:(x:a -> req_t (pre_g x))) (frame_f:vprop) (frame_g:a -> vprop) (_:squash (can_be_split_forall_dep pr (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g x))) : req_t (pre_f `star` frame_f) = fun m0 -> req_f (focus_rmem m0 pre_f) /\ (forall (x:a) (h1:hmem (post_f x `star` frame_f)). (ens_f (focus_rmem m0 pre_f) x (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) (post_f x)) /\ frame_opaque frame_f (focus_rmem m0 frame_f) (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) frame_f)) ==> pr x /\ (can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x); (req_g x) (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) (pre_g x)))) unfold let bind_ens_opaque (#a:Type) (#b:Type) (#pre_f:pre_t) (#post_f:post_t a) (req_f:req_t pre_f) (ens_f:ens_t pre_f a post_f) (#pre_g:a -> pre_t) (#post_g:a -> post_t b) (#pr:a -> prop) (ens_g:(x:a -> ens_t (pre_g x) b (post_g x))) (frame_f:vprop) (frame_g:a -> vprop) (post:post_t b) (_:squash (can_be_split_forall_dep pr (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g x))) (_:squash (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post)) : ens_t (pre_f `star` frame_f) b post = fun m0 y m2 -> req_f (focus_rmem m0 pre_f) /\ (exists (x:a) (h1:hmem (post_f x `star` frame_f)). pr x /\ ( can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x); can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (frame_g x); can_be_split_trans (post y) (post_g x y `star` frame_g x) (post_g x y); can_be_split_trans (post y) (post_g x y `star` frame_g x) (frame_g x); frame_opaque frame_f (focus_rmem m0 frame_f) (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) frame_f) /\ frame_opaque (frame_g x) (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) (frame_g x)) (focus_rmem m2 (frame_g x)) /\ ens_f (focus_rmem m0 pre_f) x (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) (post_f x)) /\ (ens_g x) (focus_rmem (mk_rmem (post_f x `star` frame_f) h1) (pre_g x)) y (focus_rmem m2 (post_g x y)))) val bind_opaque (a:Type) (b:Type) (opened_invariants:inames) (o1:eqtype_as_type observability) (o2:eqtype_as_type observability) (#framed_f:eqtype_as_type bool) (#framed_g:eqtype_as_type bool) (#pre_f:pre_t) (#post_f:post_t a) (#req_f:req_t pre_f) (#ens_f:ens_t pre_f a post_f) (#pre_g:a -> pre_t) (#post_g:a -> post_t b) (#req_g:(x:a -> req_t (pre_g x))) (#ens_g:(x:a -> ens_t (pre_g x) b (post_g x))) (#frame_f:vprop) (#frame_g:a -> vprop) (#post:post_t b) (# _ : squash (maybe_emp framed_f frame_f)) (# _ : squash (maybe_emp_dep framed_g frame_g)) (#pr:a -> prop) (#p1:squash (can_be_split_forall_dep pr (fun x -> post_f x `star` frame_f) (fun x -> pre_g x `star` frame_g x))) (#p2:squash (can_be_split_post (fun x y -> post_g x y `star` frame_g x) post)) (f:repr a framed_f opened_invariants o1 pre_f post_f req_f ens_f) (g:(x:a -> repr b framed_g opened_invariants o2 (pre_g x) (post_g x) (req_g x) (ens_g x))) : Pure (repr b true opened_invariants (join_obs o1 o2) (pre_f `star` frame_f) post (bind_req_opaque req_f ens_f req_g frame_f frame_g p1) (bind_ens_opaque req_f ens_f ens_g frame_f frame_g post p1 p2) ) (requires obs_at_most_one o1 o2) (ensures fun _ -> True) #push-options "--z3rlimit 20" let bind_opaque a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g = fun frame -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem (pre_f `star` frame_f) (core_mem m0) in let x = frame00 f frame_f frame in let m1:full_mem = NMSTTotal.get () in let h1 = mk_rmem (post_f x `star` frame_f) (core_mem m1) in let h1' = mk_rmem (pre_g x `star` frame_g x) (core_mem m1) in can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x); focus_is_restrict_mk_rmem (post_f x `star` frame_f) (pre_g x `star` frame_g x) (core_mem m1); focus_focus_is_focus (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x) (core_mem m1); assert (focus_rmem h1' (pre_g x) == focus_rmem h1 (pre_g x)); can_be_split_3_interp (hp_of (post_f x `star` frame_f)) (hp_of (pre_g x `star` frame_g x)) frame (locks_invariant opened m1) m1; let y = frame00 (g x) (frame_g x) frame in let m2:full_mem = NMSTTotal.get () in can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (pre_g x); can_be_split_trans (post_f x `star` frame_f) (pre_g x `star` frame_g x) (frame_g x); can_be_split_trans (post y) (post_g x y `star` frame_g x) (post_g x y); can_be_split_trans (post y) (post_g x y `star` frame_g x) (frame_g x); let h2' = mk_rmem (post_g x y `star` frame_g x) (core_mem m2) in let h2 = mk_rmem (post y) (core_mem m2) in // assert (focus_rmem h1' (pre_g x) == focus_rmem h1 (pre_g x)); focus_focus_is_focus (post_f x `star` frame_f) (pre_g x `star` frame_g x) (frame_g x) (core_mem m1); focus_is_restrict_mk_rmem (post_g x y `star` frame_g x) (post y) (core_mem m2); focus_focus_is_focus (post_g x y `star` frame_g x) (post y) (frame_g x) (core_mem m2); focus_focus_is_focus (post_g x y `star` frame_g x) (post y) (post_g x y) (core_mem m2); can_be_split_3_interp (hp_of (post_g x y `star` frame_g x)) (hp_of (post y)) frame (locks_invariant opened m2) m2; y let norm_repr (#a:Type) (#framed:bool) (#opened:inames) (#obs:observability) (#pre:pre_t) (#post:post_t a) (#req:req_t pre) (#ens:ens_t pre a post) (f:repr a framed opened obs pre post req ens) : repr a framed opened obs pre post (fun h -> norm_opaque (req h)) (fun h0 x h1 -> norm_opaque (ens h0 x h1)) = f let bind a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g = norm_repr (bind_opaque a b opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #frame_f #frame_g #post #_ #_ #p #p2 f g) val subcomp_opaque (a:Type) (opened:inames) (o1:eqtype_as_type observability) (o2:eqtype_as_type observability) (#framed_f:eqtype_as_type bool) (#framed_g:eqtype_as_type bool) (#[@@@ framing_implicit] pre_f:pre_t) (#[@@@ framing_implicit] post_f:post_t a) (#[@@@ framing_implicit] req_f:req_t pre_f) (#[@@@ framing_implicit] ens_f:ens_t pre_f a post_f) (#[@@@ framing_implicit] pre_g:pre_t) (#[@@@ framing_implicit] post_g:post_t a) (#[@@@ framing_implicit] req_g:req_t pre_g) (#[@@@ framing_implicit] ens_g:ens_t pre_g a post_g) (#[@@@ framing_implicit] frame:vprop) (#[@@@ framing_implicit] pr : prop) (#[@@@ framing_implicit] _ : squash (maybe_emp framed_f frame)) (#[@@@ framing_implicit] p1:squash (can_be_split_dep pr pre_g (pre_f `star` frame))) (#[@@@ framing_implicit] p2:squash (equiv_forall post_g (fun x -> post_f x `star` frame))) (f:repr a framed_f opened o1 pre_f post_f req_f ens_f) : Pure (repr a framed_g opened o2 pre_g post_g req_g ens_g) (requires (o1 = Unobservable || o2 = Observable) /\ subcomp_pre_opaque req_f ens_f req_g ens_g p1 p2) (ensures fun _ -> True) let subcomp_opaque a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #pr #_ #p1 #p2 f = fun frame -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem pre_g (core_mem m0) in can_be_split_trans pre_g (pre_f `star` fr) pre_f; can_be_split_trans pre_g (pre_f `star` fr) fr; can_be_split_3_interp (hp_of pre_g) (hp_of (pre_f `star` fr)) frame (locks_invariant opened m0) m0; focus_replace pre_g (pre_f `star` fr) pre_f (core_mem m0); let x = frame00 f fr frame in let m1:full_mem = NMSTTotal.get () in let h1 = mk_rmem (post_g x) (core_mem m1) in let h0' = mk_rmem (pre_f `star` fr) (core_mem m0) in let h1' = mk_rmem (post_f x `star` fr) (core_mem m1) in // From frame00 assert (frame_opaque fr (focus_rmem h0' fr) (focus_rmem h1' fr)); // Replace h0'/h1' by h0/h1 focus_replace pre_g (pre_f `star` fr) fr (core_mem m0); focus_replace (post_g x) (post_f x `star` fr) fr (core_mem m1); assert (frame_opaque fr (focus_rmem h0 fr) (focus_rmem h1 fr)); can_be_split_trans (post_g x) (post_f x `star` fr) (post_f x); can_be_split_trans (post_g x) (post_f x `star` fr) fr; can_be_split_3_interp (hp_of (post_f x `star` fr)) (hp_of (post_g x)) frame (locks_invariant opened m1) m1; focus_replace (post_g x) (post_f x `star` fr) (post_f x) (core_mem m1); x let subcomp a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #_ #pr #p1 #p2 f = lemma_subcomp_pre_opaque req_f ens_f req_g ens_g p1 p2; subcomp_opaque a opened o1 o2 #framed_f #framed_g #pre_f #post_f #req_f #ens_f #pre_g #post_g #req_g #ens_g #fr #pr #_ #p1 #p2 f #pop-options let bind_pure_steela_ a b opened o #wp f g = FStar.Monotonic.Pure.elim_pure_wp_monotonicity wp; fun frame -> let x = f () in g x frame let lift_ghost_atomic a o f = f let lift_atomic_steel a o f = f let as_atomic_action f = SteelAtomic?.reflect f let as_atomic_action_ghost f = SteelGhost?.reflect f let as_atomic_unobservable_action f = SteelAtomicU?.reflect f (* Some helpers *) let get0 (#opened:inames) (#p:vprop) (_:unit) : repr (erased (rmem p)) true opened Unobservable p (fun _ -> p) (requires fun _ -> True) (ensures fun h0 r h1 -> frame_equalities p h0 h1 /\ frame_equalities p r h1) = fun frame -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem p (core_mem m0) in lemma_frame_equalities_refl p h0; h0 let get () = SteelGhost?.reflect (get0 ()) let intro_star (p q:vprop) (r:slprop) (vp:erased (t_of p)) (vq:erased (t_of q)) (m:mem) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m /\ sel_of p m == reveal vp) (ensures interp (hp_of q) m) ) : Lemma (requires interp ((hp_of p) `Mem.star` r) m /\ sel_of p m == reveal vp) (ensures interp ((hp_of q) `Mem.star` r) m) = let p = hp_of p in let q = hp_of q in let intro (ml mr:mem) : Lemma (requires interp q ml /\ interp r mr /\ disjoint ml mr) (ensures disjoint ml mr /\ interp (q `Mem.star` r) (Mem.join ml mr)) = Mem.intro_star q r ml mr in elim_star p r m; Classical.forall_intro (Classical.move_requires proof); Classical.forall_intro_2 (Classical.move_requires_2 intro) #push-options "--z3rlimit 20 --fuel 1 --ifuel 0" let rewrite_slprop0 (#opened:inames) (p q:vprop) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m) (ensures interp (hp_of q) m) ) : repr unit false opened Unobservable p (fun _ -> q) (fun _ -> True) (fun _ _ _ -> True) = fun frame -> let m:full_mem = NMSTTotal.get () in proof (core_mem m); Classical.forall_intro (Classical.move_requires proof); Mem.star_associative (hp_of p) frame (locks_invariant opened m); intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p m) (sel_of q m) m proof; Mem.star_associative (hp_of q) frame (locks_invariant opened m) #pop-options let rewrite_slprop p q l = SteelGhost?.reflect (rewrite_slprop0 p q l) #push-options "--z3rlimit 20 --fuel 1 --ifuel 0" let change_slprop0 (#opened:inames) (p q:vprop) (vp:erased (t_of p)) (vq:erased (t_of q)) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m /\ sel_of p m == reveal vp) (ensures interp (hp_of q) m /\ sel_of q m == reveal vq) ) : repr unit false opened Unobservable p (fun _ -> q) (fun h -> h p == reveal vp) (fun _ _ h1 -> h1 q == reveal vq) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; proof (core_mem m); Classical.forall_intro (Classical.move_requires proof); Mem.star_associative (hp_of p) frame (locks_invariant opened m); intro_star p q (frame `Mem.star` locks_invariant opened m) vp vq m proof; Mem.star_associative (hp_of q) frame (locks_invariant opened m) #pop-options let change_slprop p q vp vq l = SteelGhost?.reflect (change_slprop0 p q vp vq l) let change_equal_slprop p q = let m = get () in let x : Ghost.erased (t_of p) = hide ((reveal m) p) in let y : Ghost.erased (t_of q) = Ghost.hide (Ghost.reveal x) in change_slprop p q x y (fun _ -> ()) #push-options "--z3rlimit 20 --fuel 1 --ifuel 0" let change_slprop_20 (#opened:inames) (p q:vprop) (vq:erased (t_of q)) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m) (ensures interp (hp_of q) m /\ sel_of q m == reveal vq) ) : repr unit false opened Unobservable p (fun _ -> q) (fun _ -> True) (fun _ _ h1 -> h1 q == reveal vq) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; proof (core_mem m); Classical.forall_intro (Classical.move_requires proof); Mem.star_associative (hp_of p) frame (locks_invariant opened m); intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p m) vq m proof; Mem.star_associative (hp_of q) frame (locks_invariant opened m) #pop-options let change_slprop_2 p q vq l = SteelGhost?.reflect (change_slprop_20 p q vq l) let change_slprop_rel0 (#opened:inames) (p q:vprop) (rel : normal (t_of p) -> normal (t_of q) -> prop) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m) (ensures interp (hp_of p) m /\ interp (hp_of q) m /\ rel (sel_of p m) (sel_of q m)) ) : repr unit false opened Unobservable p (fun _ -> q) (fun _ -> True) (fun h0 _ h1 -> rel (h0 p) (h1 q)) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; proof (core_mem m); let h0 = mk_rmem p (core_mem m) in let h1 = mk_rmem q (core_mem m) in reveal_mk_rmem p (core_mem m) p; reveal_mk_rmem q (core_mem m) q; Mem.star_associative (hp_of p) frame (locks_invariant opened m); intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p (core_mem m)) (sel_of q (core_mem m)) m proof; Mem.star_associative (hp_of q) frame (locks_invariant opened m) let change_slprop_rel p q rel proof = SteelGhost?.reflect (change_slprop_rel0 p q rel proof) let change_slprop_rel_with_cond0 (#opened:inames) (p q:vprop) (cond: t_of p -> prop) (rel : (t_of p) -> (t_of q) -> prop) (proof:(m:mem) -> Lemma (requires interp (hp_of p) m /\ cond (sel_of p m)) (ensures interp (hp_of p) m /\ interp (hp_of q) m /\ rel (sel_of p m) (sel_of q m)) ) : repr unit false opened Unobservable p (fun _ -> q) (fun m -> cond (m p)) (fun h0 _ h1 -> rel (h0 p) (h1 q)) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; proof (core_mem m); let h0 = mk_rmem p (core_mem m) in let h1 = mk_rmem q (core_mem m) in reveal_mk_rmem p (core_mem m) p; reveal_mk_rmem q (core_mem m) q; Mem.star_associative (hp_of p) frame (locks_invariant opened m); intro_star p q (frame `Mem.star` locks_invariant opened m) (sel_of p (core_mem m)) (sel_of q (core_mem m)) m proof; Mem.star_associative (hp_of q) frame (locks_invariant opened m) let change_slprop_rel_with_cond p q cond rel proof = SteelGhost?.reflect (change_slprop_rel_with_cond0 p q cond rel proof) let extract_info0 (#opened:inames) (p:vprop) (vp:erased (normal (t_of p))) (fact:prop) (l:(m:mem) -> Lemma (requires interp (hp_of p) m /\ sel_of p m == reveal vp) (ensures fact) ) : repr unit false opened Unobservable p (fun _ -> p) (fun h -> h p == reveal vp) (fun h0 _ h1 -> frame_equalities p h0 h1 /\ fact) = fun frame -> let m0:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; let h0 = mk_rmem p (core_mem m0) in lemma_frame_equalities_refl p h0; l (core_mem m0) let extract_info p vp fact l = SteelGhost?.reflect (extract_info0 p vp fact l) let extract_info_raw0 (#opened:inames) (p:vprop) (fact:prop) (l:(m:mem) -> Lemma (requires interp (hp_of p) m) (ensures fact) ) : repr unit false opened Unobservable p (fun _ -> p) (fun h -> True) (fun h0 _ h1 -> frame_equalities p h0 h1 /\ fact) = fun frame -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem p (core_mem m0) in lemma_frame_equalities_refl p h0; l (core_mem m0) let extract_info_raw p fact l = SteelGhost?.reflect (extract_info_raw0 p fact l) let noop _ = change_slprop_rel emp emp (fun _ _ -> True) (fun _ -> ()) let sladmit _ = SteelGhostF?.reflect (fun _ -> NMSTTotal.nmst_tot_admit ()) let slassert0 (#opened:inames) (p:vprop) : repr unit false opened Unobservable p (fun _ -> p) (requires fun _ -> True) (ensures fun h0 r h1 -> frame_equalities p h0 h1) = fun frame -> let m0:full_mem = NMSTTotal.get () in let h0 = mk_rmem p (core_mem m0) in lemma_frame_equalities_refl p h0 let slassert p = SteelGhost?.reflect (slassert0 p) let drop p = rewrite_slprop p emp (fun m -> emp_unit (hp_of p); affine_star (hp_of p) Mem.emp m; reveal_emp()) let reveal_star0 (#opened:inames) (p1 p2:vprop) : repr unit false opened Unobservable (p1 `star` p2) (fun _ -> p1 `star` p2) (fun _ -> True) (fun h0 _ h1 -> h0 p1 == h1 p1 /\ h0 p2 == h1 p2 /\ h0 (p1 `star` p2) == (h0 p1, h0 p2) /\ h1 (p1 `star` p2) == (h1 p1, h1 p2) ) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem let reveal_star p1 p2 = SteelGhost?.reflect (reveal_star0 p1 p2) let reveal_star_30 (#opened:inames) (p1 p2 p3:vprop) : repr unit false opened Unobservable (p1 `star` p2 `star` p3) (fun _ -> p1 `star` p2 `star` p3) (requires fun _ -> True) (ensures fun h0 _ h1 -> can_be_split (p1 `star` p2 `star` p3) p1 /\ can_be_split (p1 `star` p2 `star` p3) p2 /\ h0 p1 == h1 p1 /\ h0 p2 == h1 p2 /\ h0 p3 == h1 p3 /\ h0 (p1 `star` p2 `star` p3) == ((h0 p1, h0 p2), h0 p3) /\ h1 (p1 `star` p2 `star` p3) == ((h1 p1, h1 p2), h1 p3) ) = fun frame -> let m:full_mem = NMSTTotal.get () in Classical.forall_intro_3 reveal_mk_rmem; let h0 = mk_rmem (p1 `star` p2 `star` p3) (core_mem m) in can_be_split_trans (p1 `star` p2 `star` p3) (p1 `star` p2) p1; can_be_split_trans (p1 `star` p2 `star` p3) (p1 `star` p2) p2; reveal_mk_rmem (p1 `star` p2 `star` p3) m (p1 `star` p2 `star` p3); reveal_mk_rmem (p1 `star` p2 `star` p3) m (p1 `star` p2); reveal_mk_rmem (p1 `star` p2 `star` p3) m p3 let reveal_star_3 p1 p2 p3 = SteelGhost?.reflect (reveal_star_30 p1 p2 p3) let intro_pure p = rewrite_slprop emp (pure p) (fun m -> pure_interp p m) let elim_pure_aux #uses (p:prop) : SteelGhostT (_:unit{p}) uses (pure p) (fun _ -> to_vprop Mem.emp) = as_atomic_action_ghost (Steel.Memory.elim_pure #uses p) let elim_pure #uses p = let _ = elim_pure_aux p in rewrite_slprop (to_vprop Mem.emp) emp (fun _ -> reveal_emp ()) let return #a #opened #p x = SteelAtomicBase?.reflect (return_ a x opened #p) let intro_exists #a #opened x p = rewrite_slprop (p x) (h_exists p) (fun m -> Steel.Memory.intro_h_exists x (h_exists_sl' p) m) let intro_exists_erased #a #opened x p = rewrite_slprop (p x) (h_exists p) (fun m -> Steel.Memory.intro_h_exists (Ghost.reveal x) (h_exists_sl' p) m) let witness_exists #a #u #p _ = SteelGhost?.reflect (Steel.Memory.witness_h_exists #u (fun x -> hp_of (p x))) let lift_exists #a #u p = as_atomic_action_ghost (Steel.Memory.lift_h_exists #u (fun x -> hp_of (p x))) let exists_equiv p q = Classical.forall_intro_2 reveal_equiv; h_exists_cong (h_exists_sl' p) (h_exists_sl' q) let exists_cong p q = rewrite_slprop (h_exists p) (h_exists q) (fun m -> reveal_equiv (h_exists p) (h_exists q); exists_equiv p q) let fresh_invariant #uses p ctxt = rewrite_slprop p (to_vprop (hp_of p)) (fun _ -> ()); let i = as_atomic_unobservable_action (fresh_invariant uses (hp_of p) ctxt) in rewrite_slprop (to_vprop Mem.emp) emp (fun _ -> reveal_emp ()); return i let new_invariant #uses p = let i = fresh_invariant #uses p [] in return i (* * AR: SteelAtomic and SteelGhost are not marked reifiable since we intend to run Steel programs natively * However to implement the with_inv combinators we need to reify their thunks to reprs * We could implement it better by having support for reification only in the .fst file * But for now assuming a function *) assume val reify_steel_atomic_comp (#a:Type) (#framed:bool) (#opened_invariants:inames) (#g:observability) (#pre:pre_t) (#post:post_t a) (#req:req_t pre) (#ens:ens_t pre a post) ($f:unit -> SteelAtomicBase a framed opened_invariants g pre post req ens) : repr a framed opened_invariants g pre post req ens [@@warn_on_use "as_unobservable_atomic_action is a trusted primitive"] let as_atomic_o_action (#a:Type u#a) (#opened_invariants:inames) (#fp:slprop) (#fp': a -> slprop) (o:observability) (f:action_except a opened_invariants fp fp') : SteelAtomicBaseT a opened_invariants o (to_vprop fp) (fun x -> to_vprop (fp' x)) = SteelAtomicBaseT?.reflect f let with_invariant #a #fp #fp' #obs #opened #p i f = rewrite_slprop fp (to_vprop (hp_of fp)) (fun _ -> ()); let x = as_atomic_o_action obs (Steel.Memory.with_invariant #a #(hp_of fp) #(fun x -> hp_of (fp' x)) #opened #(hp_of p) i (reify_steel_atomic_comp f)) in rewrite_slprop (to_vprop (hp_of (fp' x))) (fp' x) (fun _ -> ()); return x assume val reify_steel_ghost_comp (#a:Type) (#framed:bool) (#opened_invariants:inames) (#pre:pre_t) (#post:post_t a) (#req:req_t pre) (#ens:ens_t pre a post) ($f:unit -> SteelGhostBase a framed opened_invariants Unobservable pre post req ens) : repr a framed opened_invariants Unobservable pre post req ens let with_invariant_g #a #fp #fp' #opened #p i f = rewrite_slprop fp (to_vprop (hp_of fp)) (fun _ -> ()); let x = as_atomic_unobservable_action (Steel.Memory.with_invariant #a #(hp_of fp) #(fun x -> hp_of (fp' x)) #opened #(hp_of p) i (reify_steel_ghost_comp f)) in rewrite_slprop (to_vprop (hp_of (fp' x))) (fp' x) (fun _ -> ()); return (hide x) let intro_vrefine v p = let m = get () in let x : Ghost.erased (t_of v) = gget v in let x' : Ghost.erased (vrefine_t v p) = Ghost.hide (Ghost.reveal x) in change_slprop v (vrefine v p) x x' (fun m -> interp_vrefine_hp v p m; vrefine_sel_eq v p m ) let elim_vrefine v p = let h = get() in let x : Ghost.erased (vrefine_t v p) = gget (vrefine v p) in let x' : Ghost.erased (t_of v) = Ghost.hide (Ghost.reveal x) in change_slprop (vrefine v p) v x x' (fun m -> interp_vrefine_hp v p m; vrefine_sel_eq v p m ) let vdep_cond (v: vprop) (q: vprop) (p: (t_of v -> Tot vprop)) (x1: t_of (v `star` q)) : Tot prop = q == p (fst x1) let vdep_rel (v: vprop) (q: vprop) (p: (t_of v -> Tot vprop)) (x1: t_of (v `star` q)) (x2: (t_of (vdep v p))) : Tot prop = q == p (fst x1) /\ dfst (x2 <: (dtuple2 (t_of v) (vdep_payload v p))) == fst x1 /\ dsnd (x2 <: (dtuple2 (t_of v) (vdep_payload v p))) == snd x1 let intro_vdep_lemma (v: vprop) (q: vprop) (p: (t_of v -> Tot vprop)) (m: mem) : Lemma (requires ( interp (hp_of (v `star` q)) m /\ q == p (fst (sel_of (v `star` q) m)) )) (ensures ( interp (hp_of (v `star` q)) m /\ interp (hp_of (vdep v p)) m /\ vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m) )) = Mem.interp_star (hp_of v) (hp_of q) m; interp_vdep_hp v p m; vdep_sel_eq v p m let intro_vdep v q p = reveal_star v q; change_slprop_rel_with_cond (v `star` q) (vdep v p) (vdep_cond v q p) (vdep_rel v q p) (fun m -> intro_vdep_lemma v q p m) let vdep_cond_recip (v: vprop) (p: (t_of v -> Tot vprop)) (q: vprop) (x2: t_of (vdep v p)) : Tot prop = q == p (dfst (x2 <: dtuple2 (t_of v) (vdep_payload v p))) let vdep_rel_recip (v: vprop) (q: vprop) (p: (t_of v -> Tot vprop)) (x2: (t_of (vdep v p))) (x1: t_of (v `star` q)) : Tot prop = vdep_rel v q p x1 x2 let elim_vdep_lemma (v: vprop) (q: vprop) (p: (t_of v -> Tot vprop)) (m: mem) : Lemma (requires ( interp (hp_of (vdep v p)) m /\ q == p (dfst (sel_of (vdep v p) m <: dtuple2 (t_of v) (vdep_payload v p))) )) (ensures ( interp (hp_of (v `star` q)) m /\ interp (hp_of (vdep v p)) m /\ vdep_rel v q p (sel_of (v `star` q) m) (sel_of (vdep v p) m) )) = Mem.interp_star (hp_of v) (hp_of q) m; interp_vdep_hp v p m; vdep_sel_eq v p m let elim_vdep0 (#opened:inames) (v: vprop) (p: (t_of v -> Tot vprop)) (q: vprop) : SteelGhost unit opened (vdep v p) (fun _ -> v `star` q) (requires (fun h -> q == p (dfst (h (vdep v p))))) (ensures (fun h _ h' -> let fs = h' v in let sn = h' q in let x2 = h (vdep v p) in q == p fs /\ dfst x2 == fs /\ dsnd x2 == sn )) = change_slprop_rel_with_cond (vdep v p) (v `star` q) (vdep_cond_recip v p q) (vdep_rel_recip v q p) (fun m -> elim_vdep_lemma v q p m); reveal_star v q let elim_vdep v p = let r = gget (vdep v p) in let res = Ghost.hide (dfst #(t_of v) #(vdep_payload v p) (Ghost.reveal r)) in elim_vdep0 v p (p (Ghost.reveal res)); res let intro_vrewrite v #t f = let x : Ghost.erased (t_of v) = gget v in let x' : Ghost.erased t = Ghost.hide (f (Ghost.reveal x)) in change_slprop v (vrewrite v f) x x' (fun m -> vrewrite_sel_eq v f m ) let elim_vrewrite v #t f = change_slprop_rel (vrewrite v f) v (fun y x -> y == f x) (fun m -> vrewrite_sel_eq v f m) /// Deriving a selector-style vprop from an injective pts-to-style vprop let hp_of_pointwise (#t: Type) (p: t -> vprop) (x: t) : Tot slprop = hp_of (p x) let mk_selector_vprop_hp p = Steel.Memory.h_exists (hp_of_pointwise p) let mk_selector_vprop_sel' (#t: Type) (p: t -> vprop) (p_inj: interp_hp_of_injective p) // unused in the definition, but necessary for the local SMTPats below : Tot (selector' t (mk_selector_vprop_hp p)) = fun m -> id_elim_exists (hp_of_pointwise p) m let mk_selector_vprop_sel #t p p_inj = let varrayp_sel_depends_only_on (#t: Type) (p: t -> vprop) (p_inj: interp_hp_of_injective p) (m0: Steel.Memory.hmem (mk_selector_vprop_hp p)) (m1: mem { disjoint m0 m1 }) : Lemma ( mk_selector_vprop_sel' p p_inj m0 == mk_selector_vprop_sel' p p_inj (Steel.Memory.join m0 m1) ) [SMTPat (mk_selector_vprop_sel' p p_inj (Steel.Memory.join m0 m1))] = p_inj (mk_selector_vprop_sel' p p_inj m0) (mk_selector_vprop_sel' p p_inj (Steel.Memory.join m0 m1)) (Steel.Memory.join m0 m1) in let varrayp_sel_depends_only_on_core (#t: Type) (p: t -> vprop) (p_inj: interp_hp_of_injective p) (m0: Steel.Memory.hmem (mk_selector_vprop_hp p)) : Lemma ( mk_selector_vprop_sel' p p_inj m0 == mk_selector_vprop_sel' p p_inj (core_mem m0) ) [SMTPat (mk_selector_vprop_sel' p p_inj (core_mem m0))] = p_inj (mk_selector_vprop_sel' p p_inj m0) (mk_selector_vprop_sel' p p_inj (core_mem m0)) m0 in mk_selector_vprop_sel' p p_inj let mk_selector_vprop_intro #_ #_ #x p p_inj = change_slprop_rel (p _) (mk_selector_vprop p p_inj) (fun _ x' -> x == x') (fun m -> intro_h_exists x (hp_of_pointwise p) m; let x' = mk_selector_vprop_sel' p p_inj m in p_inj x x' m )

{ "checked_file": "/", "dependencies": [ "Steel.Semantics.Hoare.MST.fst.checked", "Steel.Memory.fsti.checked", "Steel.Effect.fst.checked", "Steel.Effect.fst.checked", "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.NMSTTotal.fst.checked", "FStar.Monotonic.Pure.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": true, "source_file": "Steel.Effect.Atomic.fst" }

[ { "abbrev": true, "full_module": "FStar.Universe", "short_module": "U" }, { "abbrev": false, "full_module": "FStar.Ghost", "short_module": null }, { "abbrev": true, "full_module": "Steel.Memory", "short_module": "Mem" }, { "abbrev": true, "full_module": "Steel.Semantics.Hoare.MST", "short_module": "Sem" }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect.Common", "short_module": null }, { "abbrev": true, "full_module": "FStar.Tactics", "short_module": "T" }, { "abbrev": false, "full_module": "Steel.Memory", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "short_module": null }, { "abbrev": false, "full_module": "Steel.Effect", "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": 1, "initial_ifuel": 1, "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": 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": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

p: (_: t -> Steel.Effect.Common.vprop) -> p_inj: Steel.Effect.Atomic.interp_hp_of_injective p -> Steel.Effect.Atomic.SteelGhost (FStar.Ghost.erased t)

Steel.Effect.Atomic.SteelGhost

[]

[ "Steel.Memory.inames", "Steel.Effect.Common.vprop", "Steel.Effect.Atomic.interp_hp_of_injective", "FStar.Ghost.erased", "Prims.unit", "Steel.Effect.Atomic.rewrite_slprop", "Steel.Effect.Common.vrefine", "Steel.Effect.Atomic.mk_selector_vprop", "FStar.Ghost.reveal", "Steel.Effect.Common.t_of", "Steel.Memory.mem", "Steel.Effect.Common.interp_vrefine_hp", "Steel.Effect.Atomic.intro_vrefine", "Prims.prop", "Prims.eq2", "Steel.Effect.Atomic.gget" ]

[]

false

true

false

let mk_selector_vprop_elim #_ #t p p_inj =

let x0 = gget (mk_selector_vprop p p_inj) in let refinement (x: t) : Tot prop = x == Ghost.reveal x0 in intro_vrefine (mk_selector_vprop p p_inj) refinement; rewrite_slprop ((mk_selector_vprop p p_inj) `vrefine` refinement) (p x0) (fun m -> interp_vrefine_hp (mk_selector_vprop p p_inj) refinement m); x0

false

Hacl.SHA2.Vec256.fst

Hacl.SHA2.Vec256.sha512_update_last4

val sha512_update_last4 : Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

let sha512_update_last4 = update_last #SHA2_512 #M256 sha512_update4

{ "file_name": "code/sha2-mb/Hacl.SHA2.Vec256.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 87, "end_line": 156, "start_col": 19, "start_line": 156 }

module Hacl.SHA2.Vec256 open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.IntTypes open Lib.NTuple open Lib.Buffer open Lib.MultiBuffer open Spec.Hash.Definitions open Hacl.Spec.SHA2.Vec open Hacl.Impl.SHA2.Generic module ST = FStar.HyperStack.ST module Spec = Spec.Agile.Hash module SpecVec = Hacl.Spec.SHA2.Vec #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] private let sha224_init8 = init #SHA2_224 #M256 [@CInline] private let sha224_update8 = update #SHA2_224 #M256 [@CInline] private let sha224_update_nblocks8 = update_nblocks #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_update_last8 = update_last #SHA2_224 #M256 sha224_update8 [@CInline] private let sha224_finish8 = finish #SHA2_224 #M256 val sha224_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 28ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_224 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_224 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_224 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_224 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_224 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_224 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_224 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_224 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_224 (as_seq h0 input7)) let sha224_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_224 #M256 sha224_init8 sha224_update_nblocks8 sha224_update_last8 sha224_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_224 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha256_init8 = init #SHA2_256 #M256 [@CInline] private let sha256_update8 = update #SHA2_256 #M256 [@CInline] private let sha256_update_nblocks8 = update_nblocks #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_update_last8 = update_last #SHA2_256 #M256 sha256_update8 [@CInline] private let sha256_finish8 = finish #SHA2_256 #M256 val sha256_8 (dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 : lbuffer uint8 32ul) (input_len:size_t) (input0 input1 input2 input3 input4 input5 input6 input7 : lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_256 /\ live8 h0 input0 input1 input2 input3 input4 input5 input6 input7 /\ live8 h0 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 /\ internally_disjoint8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| (loc dst1 |+| (loc dst2 |+| (loc dst3 |+| (loc dst4 |+| (loc dst5 |+| (loc dst6 |+| loc dst7))))))) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_256 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_256 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_256 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_256 (as_seq h0 input3) /\ as_seq h1 dst4 == Spec.hash SHA2_256 (as_seq h0 input4) /\ as_seq h1 dst5 == Spec.hash SHA2_256 (as_seq h0 input5) /\ as_seq h1 dst6 == Spec.hash SHA2_256 (as_seq h0 input6) /\ as_seq h1 dst7 == Spec.hash SHA2_256 (as_seq h0 input7)) let sha256_8 dst0 dst1 dst2 dst3 dst4 dst5 dst6 dst7 input_len input0 input1 input2 input3 input4 input5 input6 input7 = let ib = ntup8 (input0,(input1,(input2,(input3,(input4,(input5,(input6,input7))))))) in let rb = ntup8 (dst0,(dst1,(dst2,(dst3,(dst4,(dst5,(dst6,dst7))))))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi8 rb; hash #SHA2_256 #M256 sha256_init8 sha256_update_nblocks8 sha256_update_last8 sha256_finish8 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_256 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3); assert ((as_seq_multi h1 rb).(|4|) == as_seq h1 dst4); assert ((as_seq_multi h1 rb).(|5|) == as_seq h1 dst5); assert ((as_seq_multi h1 rb).(|6|) == as_seq h1 dst6); assert ((as_seq_multi h1 rb).(|7|) == as_seq h1 dst7) [@CInline] private let sha384_init4 = init #SHA2_384 #M256 [@CInline] private let sha384_update4 = update #SHA2_384 #M256 [@CInline] private let sha384_update_nblocks4 = update_nblocks #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_update_last4 = update_last #SHA2_384 #M256 sha384_update4 [@CInline] private let sha384_finish4 = finish #SHA2_384 #M256 val sha384_4 (dst0 dst1 dst2 dst3: lbuffer uint8 48ul) (input_len:size_t) (input0 input1 input2 input3: lbuffer uint8 input_len) : Stack unit (requires fun h0 -> v input_len `less_than_max_input_length` SHA2_384 /\ live4 h0 input0 input1 input2 input3 /\ live4 h0 dst0 dst1 dst2 dst3 /\ internally_disjoint4 dst0 dst1 dst2 dst3) (ensures fun h0 _ h1 -> modifies (loc dst0 |+| loc dst1 |+| loc dst2 |+| loc dst3) h0 h1 /\ as_seq h1 dst0 == Spec.hash SHA2_384 (as_seq h0 input0) /\ as_seq h1 dst1 == Spec.hash SHA2_384 (as_seq h0 input1) /\ as_seq h1 dst2 == Spec.hash SHA2_384 (as_seq h0 input2) /\ as_seq h1 dst3 == Spec.hash SHA2_384 (as_seq h0 input3)) let sha384_4 dst0 dst1 dst2 dst3 input_len input0 input1 input2 input3 = let ib = ntup4 (input0,(input1,(input2,input3))) in let rb = ntup4 (dst0,(dst1,(dst2,dst3))) in let h0 = ST.get() in assert (live_multi h0 ib); assert (live_multi h0 rb); assert (internally_disjoint rb); loc_multi4 rb; hash #SHA2_384 #M256 sha384_init4 sha384_update_nblocks4 sha384_update_last4 sha384_finish4 rb input_len ib; let h1 = ST.get() in Hacl.Spec.SHA2.Equiv.hash_agile_lemma #SHA2_384 #M256 (v input_len) (as_seq_multi h0 ib); assert ((as_seq_multi h1 rb).(|0|) == as_seq h1 dst0); assert ((as_seq_multi h1 rb).(|1|) == as_seq h1 dst1); assert ((as_seq_multi h1 rb).(|2|) == as_seq h1 dst2); assert ((as_seq_multi h1 rb).(|3|) == as_seq h1 dst3) [@CInline] private let sha512_init4 = init #SHA2_512 #M256 [@CInline] private let sha512_update4 = update #SHA2_512 #M256

{ "checked_file": "/", "dependencies": [ "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.NTuple.fsti.checked", "Lib.MultiBuffer.fst.checked", "Lib.IntTypes.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.SHA2.Vec.fst.checked", "Hacl.Spec.SHA2.Equiv.fst.checked", "Hacl.Impl.SHA2.Generic.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.SHA2.Vec256.fst" }

[ { "abbrev": true, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": "SpecVec" }, { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Spec" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Impl.SHA2.Generic", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.SHA2.Vec", "short_module": null }, { "abbrev": false, "full_module": "Spec.Hash.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.MultiBuffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.NTuple", "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": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "short_module": null }, { "abbrev": false, "full_module": "Hacl.SHA2", "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

Hacl.Impl.SHA2.Generic.update_last_vec_t' Spec.Hash.Definitions.SHA2_512 Hacl.Spec.SHA2.Vec.M256

Prims.Tot

[ "total" ]

[]

[ "Hacl.Impl.SHA2.Generic.update_last", "Spec.Hash.Definitions.SHA2_512", "Hacl.Spec.SHA2.Vec.M256", "Hacl.SHA2.Vec256.sha512_update4" ]

[]

false

true

false

let sha512_update_last4 =

update_last #SHA2_512 #M256 sha512_update4

false

InterpreterTarget.fst

InterpreterTarget.print_typedef_name

val print_typedef_name : mname: Prims.string -> n: Target.typedef_name -> FStar.All.ALL Prims.string

let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ")

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 67, "end_line": 842, "start_col": 0, "start_line": 839 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p))

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> n: Target.typedef_name -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "Target.typedef_name", "FStar.Printf.sprintf", "InterpreterTarget.print_ident", "Target.__proj__Mktypedef_name__item__td_name", "FStar.String.concat", "Prims.list", "FStar.List.map", "Target.param", "InterpreterTarget.print_param", "Target.__proj__Mktypedef_name__item__td_params" ]

[]

false

true

false

let print_typedef_name mname (n: T.typedef_name) =

Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ")

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr5

val lemma_fmul_fsqr5: f:felem5{felem_fits5 f (9, 10, 9, 9, 9)} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let s0 = v f0 * v f0 + 38 * v f4 * v f1 + 38 * v f2 * v f3 in let s1 = 2 * v f0 * v f1 + 38 * v f4 * v f2 + 19 * v f3 * v f3 in let s2 = 2 * v f0 * v f2 + v f1 * v f1 + 38 * v f4 * v f3 in let s3 = 2 * v f0 * v f3 + 2 * v f1 * v f2 + 19 * v f4 * v f4 in let s4 = 2 * v f0 * v f4 + 2 * v f1 * v f3 + v f2 * v f2 in fmul (feval f) (feval f) == (s0 + s1 * pow51 + s2 * pow51 * pow51 + s3 * pow51 * pow51 * pow51 + s4 * pow51 * pow51 * pow51 * pow51) % prime)

let lemma_fmul_fsqr5 f = let (f0, f1, f2, f3, f4) = f in lemma_fmul5 f f; lemma_smul_felem5 f0 (f0, f1, f2, f3, f4); lemma_smul_felem5 f1 (f4 *! u64 19, f0, f1, f2, f3); lemma_mul_assos_3 (v f1) (v f4) 19; lemma_smul_felem5 f2 (f3 *! u64 19, f4 *! u64 19, f0, f1, f2); lemma_mul_assos_3 (v f2) (v f3) 19; lemma_mul_assos_3 (v f2) (v f4) 19; lemma_smul_felem5 f3 (f2 *! u64 19, f3 *! u64 19, f4 *! u64 19, f0, f1); lemma_mul_assos_3 (v f3) (v f2) 19; lemma_mul_assos_3 (v f3) (v f3) 19; lemma_mul_assos_3 (v f3) (v f4) 19; lemma_smul_felem5 f4 (f1 *! u64 19, f2 *! u64 19, f3 *! u64 19, f4 *! u64 19, f0); lemma_mul_assos_3 (v f4) (v f1) 19; lemma_mul_assos_3 (v f4) (v f2) 19; lemma_mul_assos_3 (v f4) (v f3) 19; lemma_mul_assos_3 (v f4) (v f4) 19; lemma_fmul_fsqr50 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr51 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr52 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr53 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr54 (v f0) (v f1) (v f2) (v f3) (v f4)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 54, "end_line": 1014, "start_col": 0, "start_line": 991 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204) val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in as_nat5 f == o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem0 f = assert_norm (pow51 = pow2 51); let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64 * pow2 64 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 64 * pow2 64 * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f val lemma_store_felem: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = f0 |. (f1 <<. 51ul) in let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in as_nat5 f == v o0 + v o1 * pow2 64 + v o2 * pow2 64 * pow2 64 + v o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow51 = pow2 51); let o0 = f0 |. (f1 <<. 51ul) in FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f1) 64 51; logor_disjoint f0 (f1 <<. 51ul) 51; let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in FStar.Math.Lemmas.lemma_div_lt (v f1) 51 13; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 38; FStar.Math.Lemmas.multiple_modulo_lemma (v f2 % pow2 26) (pow2 38); logor_disjoint (f1 >>. 13ul) (f2 <<. 38ul) 38; let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in FStar.Math.Lemmas.lemma_div_lt (v f2) 51 26; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f3) 64 25; FStar.Math.Lemmas.multiple_modulo_lemma (v f3 % pow2 39) (pow2 25); logor_disjoint (f2 >>. 26ul) (f3 <<. 25ul) 25; let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in FStar.Math.Lemmas.lemma_div_lt (v f3) 51 39; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 12; FStar.Math.Lemmas.multiple_modulo_lemma (v f4 % pow2 52) (pow2 12); logor_disjoint (f3 >>. 39ul) (f4 <<. 12ul) 12; lemma_store_felem0 f val lemma_cswap2_step: bit:uint64{v bit <= 1} -> p1:uint64 -> p2:uint64 -> Lemma ( let mask = u64 0 -. bit in let dummy = mask &. (p1 ^. p2) in let p1' = p1 ^. dummy in let p2' = p2 ^. dummy in if v bit = 1 then p1' == p2 /\ p2' == p1 else p1' == p1 /\ p2' == p2) let lemma_cswap2_step bit p1 p2 = let mask = u64 0 -. bit in assert (v bit == 0 ==> v mask == 0); assert (v bit == 1 ==> v mask == pow2 64 - 1); let dummy = mask &. (p1 ^. p2) in logand_lemma mask (p1 ^. p2); assert (v bit == 1 ==> v dummy == v (p1 ^. p2)); assert (v bit == 0 ==> v dummy == 0); let p1' = p1 ^. dummy in assert (v dummy == v (if v bit = 1 then (p1 ^. p2) else u64 0)); logxor_lemma p1 p2; let p2' = p2 ^. dummy in logxor_lemma p2 p1 #push-options "--max_fuel 0 --max_ifuel 0" val mul64_wide_add3_lemma: #m0:scale64 -> #m1:scale64 -> #m2:scale64 -> #m3:scale64 -> #m4:scale64 -> #m5:scale64 -> a0:uint64{felem_fits1 a0 m0} -> a1:uint64{felem_fits1 a1 m1} -> b0:uint64{felem_fits1 b0 m2} -> b1:uint64{felem_fits1 b1 m3} -> c0:uint64{felem_fits1 c0 m4} -> c1:uint64{felem_fits1 c1 m5} -> Lemma (requires m0 * m1 + m2 * m3 + m4 * m5 < pow2 13) (ensures v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < pow2 128 /\ (v a0 * v a1 + v b0 * v b1 + v c0 * v c1) <= (m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51) let mul64_wide_add3_lemma #m0 #m1 #m2 #m3 #m4 #m5 a0 a1 b0 b1 c0 c1 = assert (pow51 = pow2 51); lemma_mul_le (v a0) (m0 * max51) (v a1) (m1 * max51); lemma_mul_le (v b0) (m2 * max51) (v b1) (m3 * max51); lemma_mul_le (v c0) (m4 * max51) (v c1) (m5 * max51); lemma_add_le (v a0 * v a1) (m0 * max51 * m1 * max51) (v b0 * v b1) (m2 * max51 * m3 * max51); lemma_add_le (v a0 * v a1 + v b0 * v b1) (m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51) (v c0 * v c1) (m4 * max51 * m5 * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 <= m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51 + m4 * max51 * m5 * max51); assert_by_tactic (m0 * max51 * m1 * max51 + m2 * max51 * m3 * max51 + m4 * max51 * m5 * max51 == (m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51) canon; assert_norm (pow2 13 > 0); lemma_mul_le (m0 * m1 + m2 * m3 + m4 * m5) (pow2 13 - 1) (max51 * max51) (max51 * max51); assert ((m0 * m1 + m2 * m3 + m4 * m5) * max51 * max51 < pow2 13 * max51 * max51); assert (v a0 * v a1 + v b0 * v b1 + v c0 * v c1 < pow2 13 * max51 * max51); assert_norm (pow2 13 * pow2 51 * pow2 51 = pow2 115); assert_norm (pow2 115 < pow2 128) #pop-options val lemma_fmul_fsqr50: f0:nat -> f1:nat -> f2:nat -> f3:nat -> f4:nat -> Lemma (f0 * f0 + f1 * f4 * 19 + f2 * f3 * 19 + f3 * f2 * 19 + f4 * f1 * 19 == f0 * f0 + 38 * f4 * f1 + 38 * f2 * f3) let lemma_fmul_fsqr50 f0 f1 f2 f3 f4 = () val lemma_fmul_fsqr51: f0:nat -> f1:nat -> f2:nat -> f3:nat -> f4:nat -> Lemma (f0 * f1 * pow51 + f1 * f0 * pow51 + f2 * f4 * 19 * pow51 + f3 * f3 * 19 * pow51 + f4 * f2 * 19 * pow51 == (2 * f0 * f1 + 38 * f4 * f2 + 19 * f3 * f3) * pow51) let lemma_fmul_fsqr51 f0 f1 f2 f3 f4 = () val lemma_fmul_fsqr52: f0:nat -> f1:nat -> f2:nat -> f3:nat -> f4:nat -> Lemma (f0 * f2 * pow51 * pow51 + f1 * f1 * pow51 * pow51 + f2 * f0 * pow51 * pow51 + f3 * f4 * 19 * pow51 * pow51 + f4 * f3 * 19 * pow51 * pow51 == (2 * f0 * f2 + f1 * f1 + 38 * f4 * f3) * pow51 * pow51) let lemma_fmul_fsqr52 f0 f1 f2 f3 f4 = () val lemma_fmul_fsqr53: f0:nat -> f1:nat -> f2:nat -> f3:nat -> f4:nat -> Lemma (f0 * f3 * pow51 * pow51 * pow51 + f1 * f2 * pow51 * pow51 * pow51 + f2 * f1 * pow51 * pow51 * pow51 + f3 * f0 * pow51 * pow51 * pow51 + f4 * f4 * 19 * pow51 * pow51 * pow51 == (2 * f0 * f3 + 2 * f1 * f2 + 19 * f4 * f4) * pow51 * pow51 * pow51) let lemma_fmul_fsqr53 f0 f1 f2 f3 f4 = () val lemma_fmul_fsqr54: f0:nat -> f1:nat -> f2:nat -> f3:nat -> f4:nat -> Lemma (f0 * f4 * pow51 * pow51 * pow51 * pow51 + f1 * f3 * pow51 * pow51 * pow51 * pow51 + f2 * f2 * pow51 * pow51 * pow51 * pow51 + f3 * f1 * pow51 * pow51 * pow51 * pow51 + f4 * f0 * pow51 * pow51 * pow51 * pow51 == (2 * f0 * f4 + 2 * f1 * f3 + f2 * f2) * pow51 * pow51 * pow51 * pow51) let lemma_fmul_fsqr54 f0 f1 f2 f3 f4 = () val lemma_fmul_fsqr5: f:felem5{felem_fits5 f (9, 10, 9, 9, 9)} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let s0 = v f0 * v f0 + 38 * v f4 * v f1 + 38 * v f2 * v f3 in let s1 = 2 * v f0 * v f1 + 38 * v f4 * v f2 + 19 * v f3 * v f3 in let s2 = 2 * v f0 * v f2 + v f1 * v f1 + 38 * v f4 * v f3 in let s3 = 2 * v f0 * v f3 + 2 * v f1 * v f2 + 19 * v f4 * v f4 in let s4 = 2 * v f0 * v f4 + 2 * v f1 * v f3 + v f2 * v f2 in fmul (feval f) (feval f) == (s0 + s1 * pow51 + s2 * pow51 * pow51 +

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 {Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (9, 10, 9, 9, 9)} -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let s0 = Lib.IntTypes.v f0 * Lib.IntTypes.v f0 + (38 * Lib.IntTypes.v f4) * Lib.IntTypes.v f1 + (38 * Lib.IntTypes.v f2) * Lib.IntTypes.v f3 in let s1 = (2 * Lib.IntTypes.v f0) * Lib.IntTypes.v f1 + (38 * Lib.IntTypes.v f4) * Lib.IntTypes.v f2 + (19 * Lib.IntTypes.v f3) * Lib.IntTypes.v f3 in let s2 = (2 * Lib.IntTypes.v f0) * Lib.IntTypes.v f2 + Lib.IntTypes.v f1 * Lib.IntTypes.v f1 + (38 * Lib.IntTypes.v f4) * Lib.IntTypes.v f3 in let s3 = (2 * Lib.IntTypes.v f0) * Lib.IntTypes.v f3 + (2 * Lib.IntTypes.v f1) * Lib.IntTypes.v f2 + (19 * Lib.IntTypes.v f4) * Lib.IntTypes.v f4 in let s4 = (2 * Lib.IntTypes.v f0) * Lib.IntTypes.v f4 + (2 * Lib.IntTypes.v f1) * Lib.IntTypes.v f3 + Lib.IntTypes.v f2 * Lib.IntTypes.v f2 in Spec.Curve25519.fmul (Hacl.Spec.Curve25519.Field51.Definition.feval f) (Hacl.Spec.Curve25519.Field51.Definition.feval f) == (s0 + s1 * Hacl.Spec.Curve25519.Field51.Definition.pow51 + (s2 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + ((s3 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51 + (((s4 * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) * Hacl.Spec.Curve25519.Field51.Definition.pow51) % Spec.Curve25519.prime) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Lib.IntTypes.uint64", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr54", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Prims.unit", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr53", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr52", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr51", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul_fsqr50", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_3", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_smul_felem5", "Lib.IntTypes.op_Star_Bang", "Lib.IntTypes.u64", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_fmul5" ]

[]

false

true

false

let lemma_fmul_fsqr5 f =

let f0, f1, f2, f3, f4 = f in lemma_fmul5 f f; lemma_smul_felem5 f0 (f0, f1, f2, f3, f4); lemma_smul_felem5 f1 (f4 *! u64 19, f0, f1, f2, f3); lemma_mul_assos_3 (v f1) (v f4) 19; lemma_smul_felem5 f2 (f3 *! u64 19, f4 *! u64 19, f0, f1, f2); lemma_mul_assos_3 (v f2) (v f3) 19; lemma_mul_assos_3 (v f2) (v f4) 19; lemma_smul_felem5 f3 (f2 *! u64 19, f3 *! u64 19, f4 *! u64 19, f0, f1); lemma_mul_assos_3 (v f3) (v f2) 19; lemma_mul_assos_3 (v f3) (v f3) 19; lemma_mul_assos_3 (v f3) (v f4) 19; lemma_smul_felem5 f4 (f1 *! u64 19, f2 *! u64 19, f3 *! u64 19, f4 *! u64 19, f0); lemma_mul_assos_3 (v f4) (v f1) 19; lemma_mul_assos_3 (v f4) (v f2) 19; lemma_mul_assos_3 (v f4) (v f3) 19; lemma_mul_assos_3 (v f4) (v f4) 19; lemma_fmul_fsqr50 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr51 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr52 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr53 (v f0) (v f1) (v f2) (v f3) (v f4); lemma_fmul_fsqr54 (v f0) (v f1) (v f2) (v f3) (v f4)

false

InterpreterTarget.fst

InterpreterTarget.print_param

val print_param : mname: Prims.string -> p: Target.param -> FStar.All.ALL Prims.string

let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p))

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 31, "end_line": 837, "start_col": 0, "start_line": 834 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> p: Target.param -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "Target.param", "FStar.Printf.sprintf", "InterpreterTarget.print_ident", "FStar.Pervasives.Native.fst", "Ast.ident", "Target.typ", "Target.print_typ", "FStar.Pervasives.Native.snd" ]

[]

false

true

false

let print_param mname (p: T.param) =

Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p))

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem1

val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204)

let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 804, "start_col": 0, "start_line": 775 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 ==

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in Lib.IntTypes.v f0 + (Lib.IntTypes.v f1 % Prims.pow2 13) * Prims.pow2 51 + (Lib.IntTypes.v f1 / Prims.pow2 13 + (Lib.IntTypes.v f2 % Prims.pow2 26) * Prims.pow2 38) * Prims.pow2 64 + (Lib.IntTypes.v f2 / Prims.pow2 26 + (Lib.IntTypes.v f3 % Prims.pow2 39) * Prims.pow2 25) * Prims.pow2 128 + (Lib.IntTypes.v f3 / Prims.pow2 39 + Lib.IntTypes.v f4 * Prims.pow2 12) * Prims.pow2 192 == Lib.IntTypes.v f0 + Lib.IntTypes.v f1 * Prims.pow2 51 + Lib.IntTypes.v f2 * Prims.pow2 102 + Lib.IntTypes.v f3 * Prims.pow2 153 + Lib.IntTypes.v f4 * Prims.pow2 204) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.IntTypes.uint64", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem2", "Prims.unit", "Prims._assert", "Prims.eq2", "Prims.int", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.Mul.op_Star", "Prims.op_Modulus", "Prims.pow2", "Prims.op_Division", "FStar.Pervasives.assert_norm", "Prims.b2t", "Prims.op_Equality", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_mul_assos_3" ]

[]

false

true

false

let lemma_store_felem1 f =

let f0, f1, f2, f3, f4 = f in assert (v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13) * pow2 64 + ((v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26) * pow2 128 + ((v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39) * pow2 192 + (v f4 * pow2 12) * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert (((v f2 % pow2 26) * pow2 38) * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert (((v f3 % pow2 39) * pow2 25) * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert ((v f4 * pow2 12) * pow2 192 == v f4 * pow2 204); assert (v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13) * pow2 64 + ((v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26) * pow2 128 + ((v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39) * pow2 192 + (v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13) * pow2 64 + (v f2 % pow2 26) * pow2 102 + (v f2 / pow2 26) * pow2 128 + (v f3 % pow2 39) * pow2 153 + (v f3 / pow2 39) * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f

false

InterpreterTarget.fst

InterpreterTarget.print_inv

val print_inv : mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ML Prims.string

let print_inv mname = print_index (print_inv' mname)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 52, "end_line": 865, "start_col": 0, "start_line": 865 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.inv -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "InterpreterTarget.print_index", "InterpreterTarget.inv", "InterpreterTarget.print_inv'", "InterpreterTarget.index" ]

[]

false

true

false

let print_inv mname =

print_index (print_inv' mname)

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_load_felem5

val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s)

let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192)

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 54, "end_line": 559, "start_col": 0, "start_line": 541 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12))

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 -> u64s: Lib.Sequence.lseq Lib.IntTypes.uint64 4 -> FStar.Pervasives.Lemma (requires (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let _ = u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ] in (let FStar.Pervasives.Native.Mktuple4 #_ #_ #_ #_ s0 s1 s2 s3 = _ in Lib.IntTypes.v f0 == Lib.IntTypes.v s0 % Prims.pow2 51 /\ Lib.IntTypes.v f1 == Lib.IntTypes.v s0 / Prims.pow2 51 + (Lib.IntTypes.v s1 % Prims.pow2 38) * Prims.pow2 13 /\ Lib.IntTypes.v f2 == Lib.IntTypes.v s1 / Prims.pow2 38 + (Lib.IntTypes.v s2 % Prims.pow2 25) * Prims.pow2 26 /\ Lib.IntTypes.v f3 == Lib.IntTypes.v s2 / Prims.pow2 25 + (Lib.IntTypes.v s3 % Prims.pow2 12) * Prims.pow2 39 /\ Lib.IntTypes.v f4 == Lib.IntTypes.v s3 / Prims.pow2 12) <: Type0) <: Type0)) (ensures Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f == Lib.ByteSequence.nat_from_intseq_le u64s)

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Lib.Sequence.lseq", "Lib.IntTypes.uint64", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.Pervasives.assert_norm", "Prims.b2t", "Prims.op_Equality", "Prims.int", "FStar.Mul.op_Star", "Prims.pow2", "Prims.unit", "Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4", "Prims._assert", "Prims.eq2", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Prims.op_Addition", "Lib.IntTypes.v", "FStar.Math.Lemmas.euclidean_division_definition", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51", "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.Mktuple4", "Lib.Sequence.op_String_Access" ]

[]

false

true

false

let lemma_load_felem5 f u64s =

let open Lib.Sequence in let f0, f1, f2, f3, f4 = f in let s0, s1, s2, s3 = (u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm ((pow2 26 * pow2 51) * pow2 51 = pow2 128); assert_norm ((pow2 51 * pow2 51) * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (((pow2 39 * pow2 51) * pow2 51) * pow2 51 = pow2 192); assert_norm (((pow2 51 * pow2 51) * pow2 51) * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm ((pow2 64 * pow2 64) * pow2 64 = pow2 192)

false

InterpreterTarget.fst

InterpreterTarget.env

val env : Type0

let env = H.t A.ident' type_decl

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 32, "end_line": 130, "start_col": 0, "start_line": 130 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b'

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

Type0

Prims.Tot

[ "total" ]

[]

[ "Hashtable.t", "Ast.ident'", "InterpreterTarget.type_decl" ]

[]

false

true

let env =

H.t A.ident' type_decl

false

InterpreterTarget.fst

InterpreterTarget.print_args

val print_args : mname: Prims.string -> es: Prims.list InterpreterTarget.expr -> FStar.All.ALL Prims.string

let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " "

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 57, "end_line": 853, "start_col": 0, "start_line": 852 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> es: Prims.list InterpreterTarget.expr -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "Prims.list", "InterpreterTarget.expr", "FStar.String.concat", "FStar.List.map", "Target.print_expr" ]

[]

false

true

false

let print_args mname (es: list expr) =

List.map (T.print_expr mname) es |> String.concat " "

false

InterpreterTarget.fst

InterpreterTarget.print_type_decl

val print_type_decl : mname: Prims.string -> td: InterpreterTarget.type_decl -> FStar.All.ALL Prims.string

let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 30, "end_line": 850, "start_col": 0, "start_line": 844 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ")

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> td: InterpreterTarget.type_decl -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "InterpreterTarget.type_decl", "FStar.Printf.sprintf", "InterpreterTarget.print_typedef_name", "InterpreterTarget.__proj__Mktype_decl__item__name", "InterpreterTarget.print_typ", "InterpreterTarget.__proj__Mktype_decl__item__typ" ]

[]

false

true

false

let print_type_decl mname (td: type_decl) =

FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\nnoextract\nlet def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ)

false

InterpreterTarget.fst

InterpreterTarget.print_index

val print_index (f: ('a -> ML string)) (i: index 'a) : ML string

let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 75, "end_line": 857, "start_col": 0, "start_line": 855 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " "

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

f: (_: 'a -> FStar.All.ML Prims.string) -> i: InterpreterTarget.index 'a -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "InterpreterTarget.index", "InterpreterTarget.map_index", "FStar.Printf.sprintf" ]

[]

false

true

false

let print_index (f: ('a -> ML string)) (i: index 'a) : ML string =

map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem

val lemma_store_felem: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = f0 |. (f1 <<. 51ul) in let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in as_nat5 f == v o0 + v o1 * pow2 64 + v o2 * pow2 64 * pow2 64 + v o3 * pow2 64 * pow2 64 * pow2 64)

let lemma_store_felem f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow51 = pow2 51); let o0 = f0 |. (f1 <<. 51ul) in FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f1) 64 51; logor_disjoint f0 (f1 <<. 51ul) 51; let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in FStar.Math.Lemmas.lemma_div_lt (v f1) 51 13; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 38; FStar.Math.Lemmas.multiple_modulo_lemma (v f2 % pow2 26) (pow2 38); logor_disjoint (f1 >>. 13ul) (f2 <<. 38ul) 38; let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in FStar.Math.Lemmas.lemma_div_lt (v f2) 51 26; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f3) 64 25; FStar.Math.Lemmas.multiple_modulo_lemma (v f3 % pow2 39) (pow2 25); logor_disjoint (f2 >>. 26ul) (f3 <<. 25ul) 25; let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in FStar.Math.Lemmas.lemma_div_lt (v f3) 51 39; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 12; FStar.Math.Lemmas.multiple_modulo_lemma (v f4 % pow2 52) (pow2 12); logor_disjoint (f3 >>. 39ul) (f4 <<. 12ul) 12; lemma_store_felem0 f

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 22, "end_line": 882, "start_col": 0, "start_line": 858 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s val lemma_subtract_p5_0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_0 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f == v f0 + v f1 * pow51 + v f2 * pow51 * pow51 + v f3 * pow51 * pow51 * pow51 + v f4 * pow51 * pow51 * pow51 * pow51); assert (as_nat5 f <= pow2 51 - 20 + (pow2 51 - 1) * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 + (pow2 51 - 1) * pow2 51 * pow2 51 * pow2 51 * pow2 51); assert (as_nat5 f < pow2 255 - 19); assert (as_nat5 f == as_nat5 f'); FStar.Math.Lemmas.modulo_lemma (as_nat5 f') prime val lemma_subtract_p5_1: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p5_1 f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in assert_norm (0x7ffffffffffff = pow2 51 - 1); assert_norm (0x7ffffffffffed = pow2 51 - 19); assert_norm (pow51 = pow2 51); assert (as_nat5 f' % prime == (v f0' + v f1' * pow51 + v f2' * pow51 * pow51 + v f3' * pow51 * pow51 * pow51 + v f4' * pow51 * pow51 * pow51 * pow51) % prime); assert (as_nat5 f' % prime == (v f0 - (pow2 51 - 19) + (v f1 - (pow2 51 - 1)) * pow2 51 + (v f2 - (pow2 51 - 1)) * pow2 51 * pow2 51 + (v f3 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 + (v f4 - (pow2 51 - 1)) * pow2 51 * pow2 51 * pow2 51 * pow2 51) % prime); assert (as_nat5 f' % prime == (v f0 + v f1 * pow2 51 + v f2 * pow2 51 * pow2 51 + v f3 * pow2 51 * pow2 51 * pow2 51 + v f4 * pow2 51 * pow2 51 * pow2 51 * pow2 51 - prime) % prime); FStar.Math.Lemmas.lemma_mod_sub (as_nat5 f) 1 prime val lemma_subtract_p: f:felem5{felem_fits5 f (1, 1, 1, 1, 1)} -> f':felem5 -> Lemma (requires ( let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in (((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) /\ (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) \/ ((v f4 = 0x7ffffffffffff && v f3 = 0x7ffffffffffff && v f2 = 0x7ffffffffffff && v f1 = 0x7ffffffffffff && v f0 >= 0x7ffffffffffed) /\ (v f0' = v f0 - 0x7ffffffffffed && v f1' = v f1 - 0x7ffffffffffff && v f2' = v f2 - 0x7ffffffffffff && v f3' = v f3 - 0x7ffffffffffff && v f4' = v f4 - 0x7ffffffffffff))))) (ensures as_nat5 f' == as_nat5 f % prime) let lemma_subtract_p f f' = let (f0, f1, f2, f3, f4) = f in let (f0', f1', f2', f3', f4') = f' in if ((v f4 <> 0x7ffffffffffff || v f3 <> 0x7ffffffffffff || v f2 <> 0x7ffffffffffff || v f1 <> 0x7ffffffffffff || v f0 < 0x7ffffffffffed) && (v f0' = v f0 && v f1' = v f1 && v f2' = v f2 && v f3' = v f3 && v f4' = v f4)) then lemma_subtract_p5_0 f f' else lemma_subtract_p5_1 f f' val lemma_store_felem2: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem2 f = let (f0, f1, f2, f3, f4) = f in assert_norm (pow2 64 = pow2 13 * pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v f1) (pow2 13); assert_norm (pow2 128 = pow2 26 * pow2 102); FStar.Math.Lemmas.euclidean_division_definition (v f2) (pow2 26); assert_norm (pow2 192 = pow2 39 * pow2 153); FStar.Math.Lemmas.euclidean_division_definition (v f3) (pow2 39) val lemma_store_felem1: f:felem5 -> Lemma ( let (f0, f1, f2, f3, f4) = f in v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_store_felem1 f = let (f0, f1, f2, f3, f4) = f in assert ( v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192); lemma_mul_assos_3 (v f2 % pow2 26) (pow2 38) (pow2 64); assert_norm (pow2 38 * pow2 64 = pow2 102); assert ((v f2 % pow2 26) * pow2 38 * pow2 64 == (v f2 % pow2 26) * pow2 102); lemma_mul_assos_3 (v f3 % pow2 39) (pow2 25) (pow2 128); assert_norm (pow2 25 * pow2 128 = pow2 153); assert ((v f3 % pow2 39) * pow2 25 * pow2 128 == (v f3 % pow2 39) * pow2 153); lemma_mul_assos_3 (v f4) (pow2 12) (pow2 192); assert_norm (pow2 12 * pow2 192 = pow2 204); assert (v f4 * pow2 12 * pow2 192 == v f4 * pow2 204); assert ( v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 38 * pow2 64 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 25 * pow2 128 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 12 * pow2 192 == v f0 + (v f1 % pow2 13) * pow2 51 + v f1 / pow2 13 * pow2 64 + (v f2 % pow2 26) * pow2 102 + v f2 / pow2 26 * pow2 128 + (v f3 % pow2 39) * pow2 153 + v f3 / pow2 39 * pow2 192 + v f4 * pow2 204); lemma_store_felem2 f val lemma_as_nat1: f:felem5 -> Lemma (let (f0, f1, f2, f3, f4) = f in as_nat5 f == v f0 + v f1 * pow2 51 + v f2 * pow2 102 + v f3 * pow2 153 + v f4 * pow2 204) let lemma_as_nat1 f = assert_norm (pow51 = pow2 51); assert_norm (pow2 51 * pow2 51 = pow2 102); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 153); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 204) val lemma_store_felem0: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in as_nat5 f == o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64) let lemma_store_felem0 f = assert_norm (pow51 = pow2 51); let (f0, f1, f2, f3, f4) = f in let o0 = v f0 + (v f1 % pow2 13) * pow2 51 in let o1 = v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38 in let o2 = v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25 in let o3 = v f3 / pow2 39 + (v f4 % pow2 52) * pow2 12 in assert_norm (pow2 51 < pow2 52); FStar.Math.Lemmas.modulo_lemma (v f4) (pow2 52); assert (v f4 % pow2 52 = v f4); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 64 * pow2 64 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 64 * pow2 64 * pow2 64); assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192); assert ( o0 + o1 * pow2 64 + o2 * pow2 64 * pow2 64 + o3 * pow2 64 * pow2 64 * pow2 64 == v f0 + (v f1 % pow2 13) * pow2 51 + (v f1 / pow2 13 + (v f2 % pow2 26) * pow2 38) * pow2 64 + (v f2 / pow2 26 + (v f3 % pow2 39) * pow2 25) * pow2 128 + (v f3 / pow2 39 + v f4 * pow2 12) * pow2 192); lemma_store_felem1 f; lemma_as_nat1 f val lemma_store_felem: f:felem5{felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f < prime} -> Lemma ( let (f0, f1, f2, f3, f4) = f in let o0 = f0 |. (f1 <<. 51ul) in let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

f: Hacl.Spec.Curve25519.Field51.Definition.felem5 { Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1) /\ Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f < Spec.Curve25519.prime } -> FStar.Pervasives.Lemma (ensures (let _ = f in (let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f0 f1 f2 f3 f4 = _ in let o0 = f0 |. f1 <<. 51ul in let o1 = f1 >>. 13ul |. f2 <<. 38ul in let o2 = f2 >>. 26ul |. f3 <<. 25ul in let o3 = f3 >>. 39ul |. f4 <<. 12ul in Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f == Lib.IntTypes.v o0 + Lib.IntTypes.v o1 * Prims.pow2 64 + (Lib.IntTypes.v o2 * Prims.pow2 64) * Prims.pow2 64 + ((Lib.IntTypes.v o3 * Prims.pow2 64) * Prims.pow2 64) * Prims.pow2 64) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Hacl.Spec.Curve25519.Field51.Definition.felem5", "Prims.l_and", "Hacl.Spec.Curve25519.Field51.Definition.felem_fits5", "FStar.Pervasives.Native.Mktuple5", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "Hacl.Spec.Curve25519.Field51.Definition.as_nat5", "Spec.Curve25519.prime", "Lib.IntTypes.uint64", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_store_felem0", "Prims.unit", "Lib.IntTypes.logor_disjoint", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Greater_Greater_Dot", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.op_Less_Less_Dot", "FStar.Math.Lemmas.multiple_modulo_lemma", "Prims.op_Modulus", "Lib.IntTypes.v", "Prims.pow2", "FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2", "FStar.Math.Lemmas.lemma_div_lt", "Lib.IntTypes.int_t", "Lib.IntTypes.op_Bar_Dot", "FStar.Pervasives.assert_norm", "Prims.op_Equality", "Prims.pos", "Hacl.Spec.Curve25519.Field51.Definition.pow51" ]

[]

false

true

false

let lemma_store_felem f =

let f0, f1, f2, f3, f4 = f in assert_norm (pow51 = pow2 51); let o0 = f0 |. (f1 <<. 51ul) in FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f1) 64 51; logor_disjoint f0 (f1 <<. 51ul) 51; let o1 = (f1 >>. 13ul) |. (f2 <<. 38ul) in FStar.Math.Lemmas.lemma_div_lt (v f1) 51 13; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f2) 64 38; FStar.Math.Lemmas.multiple_modulo_lemma (v f2 % pow2 26) (pow2 38); logor_disjoint (f1 >>. 13ul) (f2 <<. 38ul) 38; let o2 = (f2 >>. 26ul) |. (f3 <<. 25ul) in FStar.Math.Lemmas.lemma_div_lt (v f2) 51 26; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f3) 64 25; FStar.Math.Lemmas.multiple_modulo_lemma (v f3 % pow2 39) (pow2 25); logor_disjoint (f2 >>. 26ul) (f3 <<. 25ul) 25; let o3 = (f3 >>. 39ul) |. (f4 <<. 12ul) in FStar.Math.Lemmas.lemma_div_lt (v f3) 51 39; FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 (v f4) 64 12; FStar.Math.Lemmas.multiple_modulo_lemma (v f4 % pow2 52) (pow2 12); logor_disjoint (f3 >>. 39ul) (f4 <<. 12ul) 12; lemma_store_felem0 f

false

InterpreterTarget.fst

InterpreterTarget.print_eloc

val print_eloc : mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ML Prims.string

let print_eloc mname = print_index (print_eloc' mname)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 54, "end_line": 874, "start_col": 0, "start_line": 874 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.eloc -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "InterpreterTarget.print_index", "InterpreterTarget.eloc", "InterpreterTarget.print_eloc'", "InterpreterTarget.index" ]

[]

false

true

false

let print_eloc mname =

print_index (print_eloc' mname)

false

InterpreterTarget.fst

InterpreterTarget.print_disj

val print_disj : mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ML Prims.string

let print_disj mname = print_index (print_disj' mname)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 54, "end_line": 881, "start_col": 0, "start_line": 881 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x) | Eloc_copy_buf x -> Printf.sprintf "(A.copy_buffer_loc %s)" (T.print_expr mname x) let print_eloc mname = print_index (print_eloc' mname) let rec print_disj' mname (d:disj) : ML string = match d with | Disj_pair i j -> Printf.sprintf "(A.disjoint %s %s)" (print_eloc' mname i) (print_eloc' mname j)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> i: InterpreterTarget.index InterpreterTarget.disj -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "InterpreterTarget.print_index", "InterpreterTarget.disj", "InterpreterTarget.print_disj'", "InterpreterTarget.index" ]

[]

false

true

false

let print_disj mname =

print_index (print_disj' mname)

false

InterpreterTarget.fst

InterpreterTarget.create_env

val create_env (_:unit) : ML env

let create_env (_:unit) : ML env = H.create 100

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 47, "end_line": 131, "start_col": 0, "start_line": 131 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b'

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

_: Prims.unit -> FStar.All.ML InterpreterTarget.env

FStar.All.ML

[ "ml" ]

[]

[ "Prims.unit", "Hashtable.create", "Ast.ident'", "InterpreterTarget.type_decl", "Hashtable.t", "InterpreterTarget.env" ]

[]

false

true

false

let create_env (_: unit) : ML env =

H.create 100

false

InterpreterTarget.fst

InterpreterTarget.map_index

val map_index (def: 'b) (f: ('a -> ML 'b)) (i: index 'a) : ML 'b

let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 17, "end_line": 145, "start_col": 0, "start_line": 142 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

def: 'b -> f: (_: 'a -> FStar.All.ML 'b) -> i: InterpreterTarget.index 'a -> FStar.All.ML 'b

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.index" ]

[]

false

true

false

let map_index (def: 'b) (f: ('a -> ML 'b)) (i: index 'a) : ML 'b =

match i with | None -> def | Some i -> f i

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_eloc'

val free_vars_of_eloc' (e: eloc) : ML (list A.ident)

let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 44, "end_line": 161, "start_col": 0, "start_line": 155 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv'

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

e: InterpreterTarget.eloc -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.eloc", "Prims.Nil", "Ast.ident", "Prims.list", "FStar.List.Tot.Base.op_At", "InterpreterTarget.free_vars_of_eloc'", "InterpreterTarget.expr", "InterpreterTarget.free_vars_of_expr", "Prims.b2t", "Target.uu___is_Identifier", "FStar.Pervasives.Native.fst", "Target.expr'", "Ast.range" ]

[ "recursion" ]

false

true

false

let rec free_vars_of_eloc' (e: eloc) : ML (list A.ident) =

match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_expr

val free_vars_of_expr (e: T.expr) : ML (list A.ident)

let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 76, "end_line": 140, "start_col": 0, "start_line": 133 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

e: Target.expr -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "Target.expr", "FStar.Pervasives.Native.fst", "Target.expr'", "Ast.range", "Ast.constant", "Prims.Nil", "Ast.ident", "Prims.list", "Prims.Cons", "Target.op", "FStar.Pervasives.Native.tuple2", "FStar.List.collect", "InterpreterTarget.free_vars_of_expr" ]

[ "recursion" ]

false

true

false

let rec free_vars_of_expr (e: T.expr) : ML (list A.ident) =

let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args

false

InterpreterTarget.fst

InterpreterTarget.print_binders

val print_binders : mname: Prims.string -> binders: Prims.list Target.param -> FStar.All.ALL Prims.string

let print_binders mname binders = List.map (print_param mname) binders |> String.concat " "

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 21, "end_line": 923, "start_col": 0, "start_line": 921 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x) | Eloc_copy_buf x -> Printf.sprintf "(A.copy_buffer_loc %s)" (T.print_expr mname x) let print_eloc mname = print_index (print_eloc' mname) let rec print_disj' mname (d:disj) : ML string = match d with | Disj_pair i j -> Printf.sprintf "(A.disjoint %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Disj_conj i j -> Printf.sprintf "(join_disj %s %s)" (print_disj' mname i) (print_disj' mname j) let print_disj mname = print_index (print_disj' mname) let print_td_iface is_entrypoint mname root_name binders args inv eloc disj ar pk_wk pk_nz = let kind_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ inline_for_extraction\n\ noextract\n\ val kind_%s : P.parser_kind %b P.%s" root_name pk_nz pk_wk in let def'_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ noextract\n\ val def'_%s %s: typ kind_%s %s %s %s %b" root_name binders root_name inv disj eloc ar in let validator_t = Printf.sprintf "val validate_%s %s : validator_of %s (def'_%s %s)" root_name binders (if is_entrypoint then "#false" else "") root_name args in let dtyp_t = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ val dtyp_%s %s : dtyp_of (def'_%s %s)" root_name binders root_name args in String.concat "\n\n" [kind_t; def'_t; validator_t; dtyp_t]

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> binders: Prims.list Target.param -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "Prims.list", "Target.param", "FStar.String.concat", "FStar.List.map", "InterpreterTarget.print_param" ]

[]

false

true

false

let print_binders mname binders =

List.map (print_param mname) binders |> String.concat " "

false

Hacl.Spec.Curve25519.Field51.Lemmas.fst

Hacl.Spec.Curve25519.Field51.Lemmas.lemma_load_felem

val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\ as_nat5 f == BSeq.nat_from_intseq_le u64s)

let lemma_load_felem u64s = assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s

{ "file_name": "code/curve25519/Hacl.Spec.Curve25519.Field51.Lemmas.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 26, "end_line": 673, "start_col": 0, "start_line": 618 }

module Hacl.Spec.Curve25519.Field51.Lemmas open FStar.Mul open Lib.Sequence open Lib.IntTypes open FStar.Tactics open FStar.Tactics.Canon open Spec.Curve25519 open Hacl.Spec.Curve25519.Field51.Definition module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence #reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq -FStar.Tactics'" val lemma_mod_sub_distr: a:int -> b:int -> n:pos -> Lemma ((a - b % n) % n = (a - b) % n) let lemma_mod_sub_distr a b n = FStar.Math.Lemmas.lemma_div_mod b n; FStar.Math.Lemmas.distributivity_sub_left 0 (b / n) n; // (a - b) % n == (a - (b % n) - (b / n) * n) % n FStar.Math.Lemmas.lemma_mod_plus (a - (b % n)) (-(b / n)) n val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma ((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f) let lemma_mul5_distr_r a b c d e f = () val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f) let lemma_mul5_distr_l a b c d e f = () val lemma_mul_assos_3: a:nat -> b:nat -> c:nat -> Lemma (a * b * c == a * (b * c)) let lemma_mul_assos_3 a b c = () val lemma_mul_assos_4: a:nat -> b:nat -> c:nat -> d:nat -> Lemma (a * b * c * d == a * (b * c * d)) let lemma_mul_assos_4 a b c d = () val lemma_mul_assos_5: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> Lemma (a * b * c * d * e == a * (b * c * d * e)) let lemma_mul_assos_5 a b c d e = () val lemma_mul_assos_6: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma (a * b * c * d * e * f == a * (b * c * d * e * f)) let lemma_mul_assos_6 a b c d e f = () val lemma_add_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a + c <= b + d) let lemma_add_le a b c d = () val lemma_mul_le:a:nat -> b:nat -> c:nat -> d:nat -> Lemma (requires a <= b /\ c <= d) (ensures a * c <= b * d) let lemma_mul_le a b c d = () val lemma_prime: unit -> Lemma (pow2 255 % prime = 19) let lemma_prime () = assert_norm (pow2 255 % prime = 19 % prime); assert_norm (19 < prime); FStar.Math.Lemmas.modulo_lemma 19 prime val lemma_add_zero: f1:felem5{felem_fits5 f1 (1, 2, 1, 1, 1)} -> Lemma ( let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in feval out == feval f1) let lemma_add_zero f1 = let (f10, f11, f12, f13, f14) = f1 in let o0 = f10 +! u64 0x3fffffffffff68 in let o1 = f11 +! u64 0x3ffffffffffff8 in let o2 = f12 +! u64 0x3ffffffffffff8 in let o3 = f13 +! u64 0x3ffffffffffff8 in let o4 = f14 +! u64 0x3ffffffffffff8 in let out = (o0, o1, o2, o3, o4) in assert (feval out == (v f10 + 0x3fffffffffff68 + (v f11 + 0x3ffffffffffff8) * pow51 + (v f12 + 0x3ffffffffffff8) * pow51 * pow51 + (v f13 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 + (v f14 + 0x3ffffffffffff8) * pow51 * pow51 * pow51 * pow51) % prime); FStar.Math.Lemmas.distributivity_add_left (v f11) 0x3ffffffffffff8 pow51; FStar.Math.Lemmas.distributivity_add_left (v f12) 0x3ffffffffffff8 (pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f13) 0x3ffffffffffff8 (pow51 * pow51 * pow51); FStar.Math.Lemmas.distributivity_add_left (v f14) 0x3ffffffffffff8 (pow51 * pow51 * pow51 * pow51); assert_norm ( 0x3fffffffffff68 + 0x3ffffffffffff8 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 + 0x3ffffffffffff8 * pow51 * pow51 * pow51 * pow51 = 8 * prime); assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51 + 8 * prime) % prime); FStar.Math.Lemmas.lemma_mod_plus (as_nat5 f1) 8 prime; assert (feval out == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) % prime) val lemma_fmul5_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * as_nat5 r) % prime == as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) let lemma_fmul5_pow51 r = let (r0, r1, r2, r3, r4) = r in assert (pow51 * as_nat5 r == pow51 * (v r0 + v r1 * pow51 + v r2 * pow51 * pow51 + v r3 * pow51 * pow51 * pow51 + v r4 * pow51 * pow51 * pow51 * pow51)); lemma_mul5_distr_l pow51 (v r0) (v r1 * pow51) (v r2 * pow51 * pow51) (v r3 * pow51 * pow51 * pow51) (v r4 * pow51 * pow51 * pow51 * pow51); let p51r0123 = pow51 * v r0 + pow51 * v r1 * pow51 + pow51 * v r2 * pow51 * pow51 + pow51 * v r3 * pow51 * pow51 * pow51 in let p51r4 = pow51 * v r4 * pow51 * pow51 * pow51 * pow51 in assert ((pow51 * as_nat5 r) % prime == (p51r0123 + p51r4) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 p51r4 prime; assert_norm (p51r4 % prime == (v r4 * pow2 255) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 255) prime; lemma_prime (); assert_norm ((v r4 * pow2 255) % prime == (v r4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r p51r0123 (v r4 * 19) prime val lemma_fmul5_pow51_pow51:r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) let lemma_fmul5_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_3 pow51 pow51 (as_nat5 r); let p51r = pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51r prime; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51r % prime)) % prime); lemma_fmul5_pow51 r; assert ((pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r4 *! u64 19, r0, r1, r2, r3) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; lemma_fmul5_pow51 (r4 *! u64 19, r0, r1, r2, r3); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime val lemma_fmul5_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) let lemma_fmul5_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 pow51 pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51r prime; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; lemma_fmul5_pow51 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5_pow51_pow51_pow51_pow51: r:felem5 -> Lemma (requires (let (r0, r1, r2, r3, r4) = r in v r4 * 19 <= 190 * pow51 /\ v r3 * 19 <= 190 * pow51 /\ v r2 * 19 <= 190 * pow51 /\ v r1 * 19 <= 190 * pow51)) (ensures (let (r0, r1, r2, r3, r4) = r in (pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0) % prime)) let lemma_fmul5_pow51_pow51_pow51_pow51 r = let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 p51p51p51r prime; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (p51p51p51r % prime)) % prime); lemma_fmul5_pow51_pow51_pow51 r; assert ((pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime == (pow51 * (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) % prime)) % prime); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; lemma_fmul5_pow51 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1); FStar.Math.Lemmas.lemma_mod_mul_distr_r pow51 (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime val lemma_fmul5_1: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_1 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert (v r4 * 19 <= 190 * max51); assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * pow51 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * pow51 * as_nat5 r) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; lemma_mul_assos_3 (v f11) pow51 (as_nat5 r); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow51 * as_nat5 r) prime; lemma_fmul5_pow51 (r0, r1, r2, r3, r4); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3)) (v f10 * as_nat5 r + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_2: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * pow51 * pow51 * as_nat5 r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_2 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_4 (v f12) pow51 pow51 (as_nat5 r); let p51p51r = pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * p51p51r + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) p51p51r prime; lemma_fmul5_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_3: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * pow51 * pow51 * pow51 * as_nat5 r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) let lemma_fmul5_3 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_5 (v f13) pow51 pow51 pow51 (as_nat5 r); let p51p51p51r = pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * p51p51p51r + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) prime val lemma_fmul5_4: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (requires (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * pow51 * pow51 * pow51 * pow51 * as_nat5 r) % prime)) (ensures (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in (as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime)) let lemma_fmul5_4 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in lemma_mul_assos_6 (v f14) pow51 pow51 pow51 pow51 (as_nat5 r); let p51p51p51p51r = pow51 * pow51 * pow51 * pow51 * as_nat5 r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * p51p51p51p51r) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * p51p51p51p51r) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) p51p51p51p51r prime; lemma_fmul5_pow51_pow51_pow51_pow51 r; FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) prime; FStar.Math.Lemmas.lemma_mod_plus_distr_l (v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) (v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1)) prime val lemma_fmul5: f1:felem5{felem_fits5 f1 (9, 10, 9, 9, 9)} -> r:felem5{felem_fits5 r (9, 10, 9, 9, 9)} -> Lemma (let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in fmul (feval f1) (feval r) == (v f10 * as_nat5 (r0, r1, r2, r3, r4) + v f11 * as_nat5 (r4 *! u64 19, r0, r1, r2, r3) + v f12 * as_nat5 (r3 *! u64 19, r4 *! u64 19, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0, r1) + v f14 * as_nat5 (r1 *! u64 19, r2 *! u64 19, r3 *! u64 19, r4 *! u64 19, r0)) % prime) let lemma_fmul5 f1 r = let (f10, f11, f12, f13, f14) = f1 in let (r0, r1, r2, r3, r4) = r in assert ((as_nat5 f1 * as_nat5 r) % prime == (v f10 + v f11 * pow51 + v f12 * pow51 * pow51 + v f13 * pow51 * pow51 * pow51 + v f14 * pow51 * pow51 * pow51 * pow51) * as_nat5 r % prime); lemma_mul5_distr_r (v f10) (v f11 * pow51) (v f12 * pow51 * pow51) (v f13 * pow51 * pow51 * pow51) (v f14 * pow51 * pow51 * pow51 * pow51) (as_nat5 r); lemma_fmul5_1 f1 r; lemma_fmul5_2 f1 r; lemma_fmul5_3 f1 r; lemma_fmul5_4 f1 r; FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime; FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime val lemma_smul_felem5: u1:uint64 -> f2:felem5 -> Lemma ( let (f20, f21, f22, f23, f24) = f2 in v u1 * as_nat5 f2 == v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_felem5 u1 f2 = () // let (f20, f21, f22, f23, f24) = f2 in // assert (as_nat5 f2 == v f20 + v f21 * pow51 + v f22 * pow51 * pow51 + // v f23 * pow51 * pow51 * pow51 + v f24 * pow51 * pow51 * pow51 * pow51); // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_smul_add_felem5: u1:uint64 -> f2:felem5 -> acc1:felem_wide5 -> Lemma (let (f20, f21, f22, f23, f24) = f2 in let (o0, o1, o2, o3, o4) = acc1 in wide_as_nat5 acc1 + uint_v u1 * as_nat5 f2 == v o0 + v o1 * pow51 + v o2 * pow51 * pow51 + v o3 * pow51 * pow51 * pow51 + v o4 * pow51 * pow51 * pow51 * pow51 + v u1 * v f20 + v u1 * v f21 * pow51 + v u1 * v f22 * pow51 * pow51 + v u1 * v f23 * pow51 * pow51 * pow51 + v u1 * v f24 * pow51 * pow51 * pow51 * pow51) let lemma_smul_add_felem5 u1 f2 acc1 = () // let (f20, f21, f22, f23, f24) = f2 in // let (o0, o1, o2, o3, o4) = acc1 in // lemma_mul5_distr_l (v u1) (v f20) (v f21 * pow51) (v f22 * pow51 * pow51) // (v f23 * pow51 * pow51 * pow51) (v f24 * pow51 * pow51 * pow51 * pow51) val lemma_carry51: l:uint64 -> cin:uint64 -> Lemma (requires felem_fits1 l 2 /\ felem_fits1 cin 8190) (ensures (let l0 = (l +! cin) &. mask51 in let l1 = (l +! cin) >>. 51ul in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ v l1 < pow2 13)) let lemma_carry51 l cin = let l' = l +! cin in let l0 = l' &. mask51 in let l1 = l' >>. 51ul in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51); FStar.Math.Lemmas.pow2_minus 64 51 val lemma_carry51_wide: #m:scale64{m < 8192} -> l:uint128{felem_wide_fits1 l m} -> cin:uint64 -> Lemma ( let l' = l +! to_u128 cin in let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in v l + v cin == v l1 * pow2 51 + v l0 /\ felem_fits1 l0 1 /\ felem_fits1 l1 (m + 1)) let lemma_carry51_wide #m l cin = let l' = l +! to_u128 cin in //assert_norm (8192 * pow51 * pow51 == pow2 115); //assert (v l' < pow2 115); let l0 = (to_u64 l') &. mask51 in let l1 = to_u64 (l' >>. 51ul) in mod_mask_lemma (to_u64 l') 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 (v l') 51 64; FStar.Math.Lemmas.euclidean_division_definition (v l') (pow2 51) val lemma_carry5_simplify: c0:uint64 -> c1:uint64 -> c2:uint64 -> c3:uint64 -> c4:uint64 -> t0:uint64 -> t1:uint64 -> t2:uint64 -> t3:uint64 -> t4:uint64 -> Lemma ((v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51) % prime == (v t0 + v c4 * 19 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) % prime) let lemma_carry5_simplify c0 c1 c2 c3 c4 t0 t1 t2 t3 t4 = assert_norm (pow51 = pow2 51); assert ( v c0 * pow2 51 + v t0 + (v c1 * pow2 51 + v t1 - v c0) * pow51 + (v c2 * pow2 51 + v t2 - v c1) * pow51 * pow51 + (v c3 * pow2 51 + v t3 - v c2) * pow51 * pow51 * pow51 + (v c4 * pow2 51 + v t4 - v c3) * pow51 * pow51 * pow51 * pow51 == v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51 + v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * pow2 51 * pow51 * pow51 * pow51 * pow51) prime; lemma_mul_assos_6 (v c4) (pow2 51) pow51 pow51 pow51 pow51; assert_norm (pow2 51 * pow51 * pow51 * pow51 * pow51 = pow2 255); FStar.Math.Lemmas.lemma_mod_mul_distr_r (v c4) (pow2 255) prime; lemma_prime (); assert_norm ((v c4 * pow2 255) % prime == (v c4 * 19) % prime); FStar.Math.Lemmas.lemma_mod_plus_distr_r (v t0 + v t1 * pow51 + v t2 * pow51 * pow51 + v t3 * pow51 * pow51 * pow51 + v t4 * pow51 * pow51 * pow51 * pow51) (v c4 * 19) prime val lemma_load_felem5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures as_nat5 f == BSeq.nat_from_intseq_le u64s) let lemma_load_felem5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); FStar.Math.Lemmas.euclidean_division_definition (v s0) (pow2 51); assert_norm (pow2 13 * pow2 51 = pow2 64); assert_norm (pow2 51 * pow2 51 = pow2 38 * pow2 64); FStar.Math.Lemmas.euclidean_division_definition (v s1) (pow2 38); assert_norm (pow2 26 * pow2 51 * pow2 51 = pow2 128); assert_norm (pow2 51 * pow2 51 * pow2 51 = pow2 25 * pow2 128); FStar.Math.Lemmas.euclidean_division_definition (v s2) (pow2 25); assert_norm (pow2 39 * pow2 51 * pow2 51 * pow2 51 = pow2 192); assert_norm (pow2 51 * pow2 51 * pow2 51 * pow2 51 = pow2 12 * pow2 192); FStar.Math.Lemmas.euclidean_division_definition (v s3) (pow2 12); assert (as_nat5 f == v s0 + v s1 * pow2 64 + v s2 * pow2 128 + v s3 * pow2 192); Hacl.Impl.Curve25519.Lemmas.lemma_nat_from_uints64_le_4 u64s; assert_norm (pow2 64 * pow2 64 = pow2 128); assert_norm (pow2 64 * pow2 64 * pow2 64 = pow2 192) val lemma_load_felem_fits5: f:felem5 -> u64s:LSeq.lseq uint64 4 -> Lemma (requires ( let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in v s3 < pow2 63 /\ v f0 == v s0 % pow2 51 /\ v f1 == v s0 / pow2 51 + (v s1 % pow2 38) * pow2 13 /\ v f2 == v s1 / pow2 38 + (v s2 % pow2 25) * pow2 26 /\ v f3 == v s2 / pow2 25 + (v s3 % pow2 12) * pow2 39 /\ v f4 == v s3 / pow2 12)) (ensures felem_fits5 f (1, 1, 1, 1, 1)) let lemma_load_felem_fits5 f u64s = let open Lib.Sequence in let (f0, f1, f2, f3, f4) = f in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in assert_norm (pow51 = pow2 51); assert (v f0 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s3) 63 12; assert (v f4 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; lemma_mul_le (v s1 % pow2 38) (pow2 38 - 1) (pow2 13) (pow2 13); assert ((v s1 % pow2 38) * pow2 13 <= (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 13 - 1 + (pow2 38 - 1) * pow2 13); assert (v f1 <= pow2 38 * pow2 13 - 1); assert_norm (pow2 38 * pow2 13 = pow2 51); assert (v f1 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; lemma_mul_le (v s2 % pow2 25) (pow2 25 - 1) (pow2 26) (pow2 26); assert ((v s2 % pow2 25) * pow2 26 <= (pow2 25 - 1) * pow2 26); assert (v f2 <= (pow2 26 - 1) + (pow2 25 - 1) * pow2 26); assert (v f2 <= pow2 25 * pow2 26 - 1); assert_norm (pow2 25 * pow2 26 = pow2 51); assert (v f2 < pow2 51); FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; lemma_mul_le (v s3 % pow2 12) (pow2 12 - 1) (pow2 39) (pow2 39); assert ((v s3 % pow2 12) * pow2 39 <= (pow2 12 - 1) * pow2 39); assert (v f3 <= (pow2 39 - 1) + (pow2 12 - 1) * pow2 39); assert (v f3 <= pow2 12 * pow2 39 - 1); assert_norm (pow2 12 * pow2 39 = pow2 51); assert (v f3 < pow2 51) val lemma_load_felem: u64s:LSeq.lseq uint64 4{v (u64s.[3]) < pow2 63} -> Lemma ( let open Lib.Sequence in let (s0, s1, s2, s3) = (u64s.[0], u64s.[1], u64s.[2], u64s.[3]) in let f0 = s0 &. mask51 in let f1 = (s0 >>. 51ul) |. ((s1 &. u64 0x3fffffffff) <<. 13ul) in let f2 = (s1 >>. 38ul) |. ((s2 &. u64 0x1ffffff) <<. 26ul) in let f3 = (s2 >>. 25ul) |. ((s3 &. u64 0xfff) <<. 39ul) in let f4 = s3 >>. 12ul in let f = (f0, f1, f2, f3, f4) in felem_fits5 f (1, 1, 1, 1, 1) /\

{ "checked_file": "/", "dependencies": [ "Spec.Curve25519.fst.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Hacl.Spec.Curve25519.Field51.Definition.fst.checked", "Hacl.Impl.Curve25519.Lemmas.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Tactics.Canon.fst.checked", "FStar.Tactics.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": false, "source_file": "Hacl.Spec.Curve25519.Field51.Lemmas.fst" }

[ { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51.Definition", "short_module": null }, { "abbrev": false, "full_module": "Spec.Curve25519", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics.Canon", "short_module": null }, { "abbrev": false, "full_module": "FStar.Tactics", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Spec.Curve25519.Field51", "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": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }

false

u64s: Lib.Sequence.lseq Lib.IntTypes.uint64 4 {Lib.IntTypes.v u64s.[ 3 ] < Prims.pow2 63} -> FStar.Pervasives.Lemma (ensures (let _ = u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ] in (let FStar.Pervasives.Native.Mktuple4 #_ #_ #_ #_ s0 s1 s2 s3 = _ in let f0 = s0 &. Hacl.Spec.Curve25519.Field51.Definition.mask51 in let f1 = s0 >>. 51ul |. (s1 &. Lib.IntTypes.u64 0x3fffffffff) <<. 13ul in let f2 = s1 >>. 38ul |. (s2 &. Lib.IntTypes.u64 0x1ffffff) <<. 26ul in let f3 = s2 >>. 25ul |. (s3 &. Lib.IntTypes.u64 0xfff) <<. 39ul in let f4 = s3 >>. 12ul in let f = f0, f1, f2, f3, f4 in Hacl.Spec.Curve25519.Field51.Definition.felem_fits5 f (1, 1, 1, 1, 1) /\ Hacl.Spec.Curve25519.Field51.Definition.as_nat5 f == Lib.ByteSequence.nat_from_intseq_le u64s) <: Type0))

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Lib.Sequence.lseq", "Lib.IntTypes.uint64", "Prims.b2t", "Prims.op_LessThan", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.Sequence.op_String_Access", "Prims.pow2", "Lib.IntTypes.int_t", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_load_felem5", "Prims.unit", "Hacl.Spec.Curve25519.Field51.Lemmas.lemma_load_felem_fits5", "FStar.Pervasives.Native.tuple5", "FStar.Pervasives.Native.Mktuple5", "Lib.IntTypes.logor_disjoint", "Lib.IntTypes.op_Bar_Dot", "Lib.IntTypes.op_Greater_Greater_Dot", "FStar.UInt32.__uint_to_t", "FStar.Math.Lemmas.modulo_lemma", "FStar.Mul.op_Star", "Prims.op_Modulus", "FStar.Pervasives.assert_norm", "Prims.op_Equality", "Prims.int", "Prims._assert", "Prims.eq2", "Lib.IntTypes.range_t", "Lib.IntTypes.mod_mask", "Lib.IntTypes.u64", "Lib.IntTypes.mod_mask_lemma", "FStar.Math.Lemmas.pow2_lt_compat", "Lib.IntTypes.op_Less_Less_Dot", "Lib.IntTypes.op_Amp_Dot", "FStar.Math.Lemmas.lemma_div_lt", "Hacl.Spec.Curve25519.Field51.Definition.mask51", "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.Mktuple4", "Prims.op_Subtraction" ]

[]

false

true

false

let lemma_load_felem u64s =

assert_norm (0x3fffffffff = pow2 38 - 1); assert_norm (0x1ffffff = pow2 25 - 1); assert_norm (0xfff = pow2 12 - 1); let open Lib.Sequence in let s0, s1, s2, s3 = (u64s.[ 0 ], u64s.[ 1 ], u64s.[ 2 ], u64s.[ 3 ]) in let f0l = s0 &. mask51 in FStar.Math.Lemmas.pow2_lt_compat 64 51; mod_mask_lemma s0 51ul; assert (v (mod_mask #U64 #SEC 51ul) == v mask51); let f0h = s0 >>. 51ul in FStar.Math.Lemmas.lemma_div_lt (v s0) 64 51; let f1l = (s1 &. u64 0x3fffffffff) <<. 13ul in FStar.Math.Lemmas.pow2_lt_compat 64 38; mod_mask_lemma s1 38ul; assert (v (mod_mask #U64 #SEC 38ul) == v (u64 0x3fffffffff)); assert_norm (pow2 38 * pow2 13 = pow2 51); assert_norm (pow2 51 < pow2 64); FStar.Math.Lemmas.modulo_lemma ((v s1 % pow2 38) * pow2 13) (pow2 64); let f1h = s1 >>. 38ul in FStar.Math.Lemmas.lemma_div_lt (v s1) 64 38; let f2l = (s2 &. u64 0x1ffffff) <<. 26ul in FStar.Math.Lemmas.pow2_lt_compat 64 25; mod_mask_lemma s2 25ul; assert (v (mod_mask #U64 #SEC 25ul) == v (u64 0x1ffffff)); assert_norm (pow2 25 * pow2 26 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s2 % pow2 25) * pow2 26) (pow2 64); let f2h = s2 >>. 25ul in FStar.Math.Lemmas.lemma_div_lt (v s2) 64 25; let f3l = (s3 &. u64 0xfff) <<. 39ul in FStar.Math.Lemmas.pow2_lt_compat 64 12; mod_mask_lemma s3 12ul; assert (v (mod_mask #U64 #SEC 12ul) == v (u64 0xfff)); assert_norm (pow2 12 * pow2 39 = pow2 51); FStar.Math.Lemmas.modulo_lemma ((v s3 % pow2 12) * pow2 39) (pow2 64); let f3h = s3 >>. 12ul in let f0 = f0l in let f1 = f0h |. f1l in logor_disjoint f0h f1l 13; let f2 = f1h |. f2l in logor_disjoint f1h f2l 26; let f3 = f2h |. f3l in logor_disjoint f2h f3l 39; let f4 = f3h in let f = (f0, f1, f2, f3, f4) in lemma_load_felem_fits5 f u64s; lemma_load_felem5 f u64s

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_disj'

val free_vars_of_disj' (d: disj) : ML (list A.ident)

let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 66, "end_line": 168, "start_col": 0, "start_line": 164 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc'

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

d: InterpreterTarget.disj -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.disj", "FStar.List.Tot.Base.op_At", "Ast.ident", "Prims.list", "InterpreterTarget.free_vars_of_disj'", "InterpreterTarget.eloc", "Prims.b2t", "InterpreterTarget.uu___is_Eloc_copy_buf", "InterpreterTarget.free_vars_of_eloc'" ]

[ "recursion" ]

false

true

false

let rec free_vars_of_disj' (d: disj) : ML (list A.ident) =

match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j

false

InterpreterTarget.fst

InterpreterTarget.free_vars_of_inv'

val free_vars_of_inv' (i: inv) : ML (list A.ident)

let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 43, "end_line": 152, "start_col": 0, "start_line": 147 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.inv -> FStar.All.ML (Prims.list Ast.ident)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.inv", "FStar.List.Tot.Base.op_At", "Ast.ident", "Prims.list", "InterpreterTarget.free_vars_of_inv'", "InterpreterTarget.expr", "InterpreterTarget.free_vars_of_expr" ]

[ "recursion" ]

false

true

false

let rec free_vars_of_inv' (i: inv) : ML (list A.ident) =

match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x

false

InterpreterTarget.fst

InterpreterTarget.dtyp_of_app

val dtyp_of_app (en: env) (hd: A.ident) (args: list T.index) : ML dtyp

let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 15, "end_line": 223, "start_col": 0, "start_line": 208 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

en: InterpreterTarget.env -> hd: Ast.ident -> args: Prims.list Target.index -> FStar.All.ML InterpreterTarget.dtyp

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.env", "Ast.ident", "Prims.list", "Target.index", "FStar.Pervasives.Native.Mktuple2", "FStar.Pervasives.Native.option", "InterpreterTarget.itype", "InterpreterTarget.itype_of_ident", "InterpreterTarget.DT_IType", "InterpreterTarget.dtyp", "FStar.Pervasives.Native.tuple2", "InterpreterTarget.DT_App", "InterpreterTarget.expr", "FStar.List.map", "FStar.Pervasives.either", "Target.typ", "Target.expr", "FStar.All.failwith", "Prims.bool", "InterpreterTarget.type_decl", "InterpreterTarget.__proj__Mktype_decl__item__allow_reading", "Hashtable.try_find", "Ast.ident'", "Ast.__proj__Mkwith_meta_t__item__v" ]

[]

false

true

false

let dtyp_of_app (en: env) (hd: A.ident) (args: list T.index) : ML dtyp =

false

InterpreterTarget.fst

InterpreterTarget.allow_reading_of_typ

val allow_reading_of_typ (t: typ) : Tot bool

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 14, "end_line": 543, "start_col": 0, "start_line": 529 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

t: InterpreterTarget.typ -> Prims.bool

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.typ", "InterpreterTarget.non_empty_string", "Prims.string", "InterpreterTarget.allow_reading_of_typ", "InterpreterTarget.dtyp", "InterpreterTarget.itype", "InterpreterTarget.allow_reader_of_itype", "Prims.bool", "Ast.ident", "Prims.list", "InterpreterTarget.expr" ]

[ "recursion" ]

false

true

false

let rec allow_reading_of_typ (t: typ) : Tot bool =

false

InterpreterTarget.fst

InterpreterTarget.print_binders_as_args

val print_binders_as_args : mname: Prims.string -> binders: Prims.list (Ast.ident * _) -> FStar.All.ALL Prims.string

let print_binders_as_args mname binders = List.map (fun (i, _) -> print_ident mname i) binders |> String.concat " "

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 21, "end_line": 927, "start_col": 0, "start_line": 925 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x) | Eloc_copy_buf x -> Printf.sprintf "(A.copy_buffer_loc %s)" (T.print_expr mname x) let print_eloc mname = print_index (print_eloc' mname) let rec print_disj' mname (d:disj) : ML string = match d with | Disj_pair i j -> Printf.sprintf "(A.disjoint %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Disj_conj i j -> Printf.sprintf "(join_disj %s %s)" (print_disj' mname i) (print_disj' mname j) let print_disj mname = print_index (print_disj' mname) let print_td_iface is_entrypoint mname root_name binders args inv eloc disj ar pk_wk pk_nz = let kind_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ inline_for_extraction\n\ noextract\n\ val kind_%s : P.parser_kind %b P.%s" root_name pk_nz pk_wk in let def'_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ noextract\n\ val def'_%s %s: typ kind_%s %s %s %s %b" root_name binders root_name inv disj eloc ar in let validator_t = Printf.sprintf "val validate_%s %s : validator_of %s (def'_%s %s)" root_name binders (if is_entrypoint then "#false" else "") root_name args in let dtyp_t = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ val dtyp_%s %s : dtyp_of (def'_%s %s)" root_name binders root_name args in String.concat "\n\n" [kind_t; def'_t; validator_t; dtyp_t] let print_binders mname binders = List.map (print_param mname) binders |> String.concat " "

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> binders: Prims.list (Ast.ident * _) -> FStar.All.ALL Prims.string

FStar.All.ALL

[ "trivial_postcondition" ]

[]

[ "Prims.string", "Prims.list", "FStar.Pervasives.Native.tuple2", "Ast.ident", "FStar.String.concat", "FStar.List.map", "InterpreterTarget.print_ident" ]

[]

false

true

false

let print_binders_as_args mname binders =

List.map (fun (i, _) -> print_ident mname i) binders |> String.concat " "

false

InterpreterTarget.fst

InterpreterTarget.print_decls

val print_decls (e:env) (mname:string) (ds:list decl) : ML (string & string)

let print_decls en mname tds = let impl, iface = let impls, ifaces = List.map (print_decl mname) tds |> List.unzip in String.concat "\n\n" impls, String.concat "\n\n" ifaces in impl, iface

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 13, "end_line": 1103, "start_col": 0, "start_line": 1094 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x) | Eloc_copy_buf x -> Printf.sprintf "(A.copy_buffer_loc %s)" (T.print_expr mname x) let print_eloc mname = print_index (print_eloc' mname) let rec print_disj' mname (d:disj) : ML string = match d with | Disj_pair i j -> Printf.sprintf "(A.disjoint %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Disj_conj i j -> Printf.sprintf "(join_disj %s %s)" (print_disj' mname i) (print_disj' mname j) let print_disj mname = print_index (print_disj' mname) let print_td_iface is_entrypoint mname root_name binders args inv eloc disj ar pk_wk pk_nz = let kind_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ inline_for_extraction\n\ noextract\n\ val kind_%s : P.parser_kind %b P.%s" root_name pk_nz pk_wk in let def'_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ noextract\n\ val def'_%s %s: typ kind_%s %s %s %s %b" root_name binders root_name inv disj eloc ar in let validator_t = Printf.sprintf "val validate_%s %s : validator_of %s (def'_%s %s)" root_name binders (if is_entrypoint then "#false" else "") root_name args in let dtyp_t = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ val dtyp_%s %s : dtyp_of (def'_%s %s)" root_name binders root_name args in String.concat "\n\n" [kind_t; def'_t; validator_t; dtyp_t] let print_binders mname binders = List.map (print_param mname) binders |> String.concat " " let print_binders_as_args mname binders = List.map (fun (i, _) -> print_ident mname i) binders |> String.concat " " let print_binding mname (td:type_decl) : ML (string & string) = let tdn = td.name in let k = td.kind in let typ = td.typ in let root_name = print_ident mname tdn.td_name in let print_binders = print_binders mname in let print_args = print_binders_as_args mname in let binders = print_binders tdn.td_params in let args = print_args tdn.td_params in let def = print_type_decl mname td in let weak_kind = A.print_weak_kind k.pk_weak_kind in let pk_of_binding = Printf.sprintf "[@@noextract_to \"krml\"]\n\ inline_for_extraction noextract\n\ let kind_%s : P.parser_kind %s %s = coerce (_ by (T.norm [delta_only [`%%weak_kind_glb]; zeta; iota; primops]; T.trefl())) %s\n" root_name (string_of_bool k.pk_nz) weak_kind (T.print_kind mname k) in let inv, eloc, disj = let inv, eloc, disj, _ = td.typ_indexes in print_inv mname inv, print_eloc mname eloc, print_disj mname disj in let def' = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def'_%s %s\n\ : typ kind_%s %s %s %s %s\n\ = coerce (_ by (coerce_validator [`%%kind_%s])) (def_%s %s)" root_name binders root_name inv disj eloc (string_of_bool td.allow_reading) root_name root_name args in let as_type_or_parser tag = Printf.sprintf "[@@noextract_to \"krml\"]\n\ noextract\n let %s_%s %s = (as_%s (def'_%s %s))" tag root_name binders tag root_name args in let validate_binding = let cinline = if td.name.td_entrypoint || td.attrs.is_exported then "" else "; CInline" in Printf.sprintf "[@@normalize_for_extraction specialization_steps%s]\n\ let validate_%s %s = as_validator \"%s\" (def'_%s %s)\n" cinline root_name binders root_name root_name args in let dtyp : string = let reader = if td.allow_reading then Printf.sprintf "(Some (as_reader (def_%s %s)))" root_name args else "None" in let coerce_validator = Printf.sprintf "(T.norm [delta_only [`%%parser_%s; `%%type_%s; `%%coerce]]; T.trefl())" root_name root_name in Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let dtyp_%s %s\n\ : dtyp kind_%s %b %s %s %s\n\ = mk_dtyp_app\n\ kind_%s\n\ %s\n\ %s\n\ %s\n\ (type_%s %s)\n\ (coerce (_ by (T.norm [delta_only [`%%type_%s]]; T.trefl())) (parser_%s %s))\n\ %s\n\ %b\n\ (coerce (_ by %s) (validate_%s %s))\n\ (_ by (T.norm [delta_only [`%%Some?]; iota]; T.trefl()))\n" root_name binders root_name td.allow_reading inv disj eloc root_name inv disj eloc root_name args root_name root_name args reader td.allow_reading coerce_validator root_name args in let enum_typ_of_binding = match td.enum_typ with | None -> "" | Some t -> Printf.sprintf "let %s = %s\n" root_name (T.print_typ mname t) in let impl = String.concat "\n" [def; pk_of_binding; def'; (as_type_or_parser "type"); (as_type_or_parser "parser"); validate_binding; dtyp; enum_typ_of_binding] in // impl, "" if Some? td.enum_typ && (td.name.td_entrypoint || td.attrs.is_exported) then "", impl //exported enums are fully revealed else if td.name.td_entrypoint || td.attrs.is_exported then let iface = print_td_iface td.name.td_entrypoint mname root_name binders args inv eloc disj td.allow_reading weak_kind k.pk_nz in impl, iface else impl, "" let print_decl mname (d:decl) : ML (string & string) = match d with | Inl d -> begin match fst d with | T.Assumption _ -> T.print_assumption mname d, "" | T.Definition _ -> "", T.print_definition mname d | _ -> "", "" end | Inr td -> print_binding mname td let rec unzip (x: list ('a & 'b)) : list 'a & list 'b = match x with | [] -> [], [] | (x,y)::tl -> let xs, ys = unzip tl in x::xs, y::ys

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

e: InterpreterTarget.env -> mname: Prims.string -> ds: Prims.list InterpreterTarget.decl -> FStar.All.ML (Prims.string * Prims.string)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.env", "Prims.string", "Prims.list", "InterpreterTarget.decl", "FStar.Pervasives.Native.Mktuple2", "FStar.Pervasives.Native.tuple2", "FStar.String.concat", "FStar.List.Tot.Base.unzip", "FStar.List.map", "InterpreterTarget.print_decl" ]

[]

false

true

false

let print_decls en mname tds =

let impl, iface = let impls, ifaces = List.map (print_decl mname) tds |> List.unzip in String.concat "\n\n" impls, String.concat "\n\n" ifaces in impl, iface

false

InterpreterTarget.fst

InterpreterTarget.typ_indexes_of_action

val typ_indexes_of_action (a: T.action) : ML typ_indexes

let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 29, "end_line": 305, "start_col": 0, "start_line": 262 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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: Target.action -> FStar.All.ML InterpreterTarget.typ_indexes

FStar.All.ML

[ "ml" ]

[]

[ "Target.action", "Target.atomic_action", "InterpreterTarget.typ_indexes", "InterpreterTarget.typ_indexes_union", "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.option", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success", "InterpreterTarget.typ_indexes_of_action", "Ast.ident", "Target.expr", "InterpreterTarget.typ_indexes_nil", "FStar.Pervasives.Native.Mktuple4", "InterpreterTarget.index", "FStar.Pervasives.Native.Some", "InterpreterTarget.Inv_ptr", "InterpreterTarget.id_as_expr", "InterpreterTarget.Eloc_ptr", "FStar.Pervasives.Native.None", "InterpreterTarget.On_success", "InterpreterTarget.Eloc_output", "Prims.list" ]

[ "recursion" ]

false

true

false

let rec typ_indexes_of_action (a: T.action) : ML typ_indexes =

let open T in let of_atomic_action (a: T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a

false

InterpreterTarget.fst

InterpreterTarget.as_lam

val as_lam (x: T.lam 'a) : lam 'a

let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 12, "end_line": 258, "start_col": 0, "start_line": 251 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe"

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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: Target.lam 'a -> InterpreterTarget.lam 'a

Prims.Tot

[ "total" ]

[]

[ "Target.lam", "FStar.Pervasives.Native.Mktuple2", "Ast.ident", "FStar.Pervasives.Native.snd", "FStar.Pervasives.Native.option", "FStar.Pervasives.Native.fst", "Ast.with_dummy_range", "Ast.ident'", "Ast.to_ident'", "InterpreterTarget.lam" ]

[]

false

true

false

let as_lam (x: T.lam 'a) : lam 'a =

let i = match fst x with | None -> let open A in with_dummy_range (to_ident' "_") | Some i -> i in i, snd x

false

InterpreterTarget.fst

InterpreterTarget.print_ityp

val print_ityp : i: InterpreterTarget.itype -> Prims.string

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 26, "end_line": 626, "start_col": 0, "start_line": 614 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

i: InterpreterTarget.itype -> Prims.string

Prims.Tot

[ "total" ]

[]

[ "InterpreterTarget.itype", "Prims.string" ]

[]

false

true

false

let print_ityp (i: itype) =

false

InterpreterTarget.fst

InterpreterTarget.typ_of_parser

val typ_of_parser (en: env) : Tot (T.parser -> ML typ)

let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 16, "end_line": 527, "start_col": 0, "start_line": 394 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary"

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

en: InterpreterTarget.env -> _: Target.parser -> FStar.All.ML InterpreterTarget.typ

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.env", "Target.parser", "InterpreterTarget.typ", "Target.__proj__Mkparser__item__p_parser", "InterpreterTarget.T_false", "Ast.ident", "Prims.list", "Target.index", "InterpreterTarget.T_denoted", "InterpreterTarget.dtyp", "InterpreterTarget.T_pair", "InterpreterTarget.nes", "Target.__proj__Mkparser__item__p_fieldname", "Ast.comments", "InterpreterTarget.T_with_comment", "FStar.String.concat", "Target.expr", "InterpreterTarget.T_nlist", "InterpreterTarget.T_at_most", "InterpreterTarget.T_exact", "InterpreterTarget.T_if_else", "Target.lam", "InterpreterTarget.allow_reader_of_dtyp", "InterpreterTarget.T_dep_pair", "InterpreterTarget.lam", "FStar.Pervasives.Native.Mktuple2", "Prims.bool", "FStar.All.failwith", "InterpreterTarget.as_lam", "InterpreterTarget.T_dep_pair_with_refinement", "InterpreterTarget.expr", "Target.action", "InterpreterTarget.T_dep_pair_with_action", "InterpreterTarget.T_dep_pair_with_refinement_and_action", "InterpreterTarget.T_with_action", "InterpreterTarget.T_with_dep_action", "InterpreterTarget.T_string", "InterpreterTarget.T_refine", "InterpreterTarget.T_refine_with_action", "Target.parser_kind", "InterpreterTarget.T_probe_then_validate", "InterpreterTarget.non_empty_string", "InterpreterTarget.dtyp_of_app", "Target.parser'", "FStar.Printf.sprintf", "InterpreterTarget.tag_of_parser" ]

[]

false

true

false

let typ_of_parser (en: env) : Tot (T.parser -> ML typ) =

let rec typ_of_parser (p: T.parser) : ML typ = let rec dtyp_of_parser (p: T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let i, k = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser

false

InterpreterTarget.fst

InterpreterTarget.print_td_iface

val print_td_iface : is_entrypoint: Prims.bool -> mname: _ -> root_name: Prims.string -> binders: Prims.string -> args: Prims.string -> inv: Prims.string -> eloc: Prims.string -> disj: Prims.string -> ar: Prims.bool -> pk_wk: Prims.string -> pk_nz: Prims.bool -> Prims.string

let print_td_iface is_entrypoint mname root_name binders args inv eloc disj ar pk_wk pk_nz = let kind_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ inline_for_extraction\n\ noextract\n\ val kind_%s : P.parser_kind %b P.%s" root_name pk_nz pk_wk in let def'_t = Printf.sprintf "[@@noextract_to \"krml\"]\n\ noextract\n\ val def'_%s %s: typ kind_%s %s %s %s %b" root_name binders root_name inv disj eloc ar in let validator_t = Printf.sprintf "val validate_%s %s : validator_of %s (def'_%s %s)" root_name binders (if is_entrypoint then "#false" else "") root_name args in let dtyp_t = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ val dtyp_%s %s : dtyp_of (def'_%s %s)" root_name binders root_name args in String.concat "\n\n" [kind_t; def'_t; validator_t; dtyp_t]

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 60, "end_line": 919, "start_col": 0, "start_line": 883 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a) let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt) let print_param mname (p:T.param) = Printf.sprintf "(%s:%s)" (print_ident mname (fst p)) (T.print_typ mname (snd p)) let print_typedef_name mname (n:T.typedef_name) = Printf.sprintf "%s %s" (print_ident mname n.td_name) (List.map (print_param mname) n.td_params |> String.concat " ") let print_type_decl mname (td:type_decl) = FStar.Printf.sprintf "[@@specialize; noextract_to \"krml\"]\n\ noextract\n\ let def_%s = ( %s <: Tot (typ _ _ _ _ _) by (T.norm [delta_attr [`%%specialize]; zeta; iota; primops]; T.smt()))\n" (print_typedef_name mname td.name) (print_typ mname td.typ) let print_args mname (es:list expr) = List.map (T.print_expr mname) es |> String.concat " " let print_index (f: 'a -> ML string) (i:index 'a) : ML string = map_index "Trivial" (fun s -> Printf.sprintf "(NonTrivial %s)" (f s)) i let rec print_inv' mname (i:inv) : ML string = match i with | Inv_conj i j -> Printf.sprintf "(A.conj_inv %s %s)" (print_inv' mname i) (print_inv' mname j) | Inv_ptr x -> Printf.sprintf "(A.ptr_inv %s)" (T.print_expr mname x) | Inv_copy_buf x -> Printf.sprintf "(A.copy_buffer_inv %s)" (T.print_expr mname x) let print_inv mname = print_index (print_inv' mname) let rec print_eloc' mname (e:eloc) : ML string = match e with | Eloc_output -> "output_loc" //This is a bit sketchy | Eloc_union i j -> Printf.sprintf "(A.eloc_union %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Eloc_ptr x -> Printf.sprintf "(A.ptr_loc %s)" (T.print_expr mname x) | Eloc_copy_buf x -> Printf.sprintf "(A.copy_buffer_loc %s)" (T.print_expr mname x) let print_eloc mname = print_index (print_eloc' mname) let rec print_disj' mname (d:disj) : ML string = match d with | Disj_pair i j -> Printf.sprintf "(A.disjoint %s %s)" (print_eloc' mname i) (print_eloc' mname j) | Disj_conj i j -> Printf.sprintf "(join_disj %s %s)" (print_disj' mname i) (print_disj' mname j) let print_disj mname = print_index (print_disj' mname)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

is_entrypoint: Prims.bool -> mname: _ -> root_name: Prims.string -> binders: Prims.string -> args: Prims.string -> inv: Prims.string -> eloc: Prims.string -> disj: Prims.string -> ar: Prims.bool -> pk_wk: Prims.string -> pk_nz: Prims.bool -> Prims.string

Prims.Tot

[ "total" ]

[]

[ "Prims.bool", "Prims.string", "FStar.String.concat", "Prims.Cons", "Prims.Nil", "FStar.Printf.sprintf" ]

[]

false

true

false

let print_td_iface is_entrypoint mname root_name binders args inv eloc disj ar pk_wk pk_nz =

let kind_t = Printf.sprintf "[@@noextract_to \"krml\"]\ninline_for_extraction\nnoextract\nval kind_%s : P.parser_kind %b P.%s" root_name pk_nz pk_wk in let def'_t = Printf.sprintf "[@@noextract_to \"krml\"]\nnoextract\nval def'_%s %s: typ kind_%s %s %s %s %b" root_name binders root_name inv disj eloc ar in let validator_t = Printf.sprintf "val validate_%s %s : validator_of %s (def'_%s %s)" root_name binders (if is_entrypoint then "#false" else "") root_name args in let dtyp_t = Printf.sprintf "[@@specialize; noextract_to \"krml\"]\nnoextract\nval dtyp_%s %s : dtyp_of (def'_%s %s)" root_name binders root_name args in String.concat "\n\n" [kind_t; def'_t; validator_t; dtyp_t]

false

InterpreterTarget.fst

InterpreterTarget.tag_of_parser

val tag_of_parser : p: Target.parser -> Prims.string

let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe"

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 52, "end_line": 249, "start_col": 0, "start_line": 225 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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: Target.parser -> Prims.string

Prims.Tot

[ "total" ]

[]

[ "Target.parser", "Target.__proj__Mkparser__item__p_parser", "Target.expr", "Ast.ident", "Prims.list", "Target.index", "Target.lam", "Target.action", "Target.parser_kind", "Ast.comments", "Prims.string" ]

[]

false

true

false

let tag_of_parser p =

let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe"

false

InterpreterTarget.fst

InterpreterTarget.print_dtyp

val print_dtyp : mname: Prims.string -> dt: InterpreterTarget.dtyp -> FStar.All.ALL Prims.string

let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ")

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 63, "end_line": 645, "start_col": 0, "start_line": 637 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> dt: InterpreterTarget.dtyp -> FStar.All.ALL Prims.string

FStar.All.ALL

[]

[ "Prims.string", "InterpreterTarget.dtyp", "InterpreterTarget.itype", "FStar.Printf.sprintf", "InterpreterTarget.print_ityp", "Prims.bool", "Ast.ident", "Prims.list", "InterpreterTarget.expr", "InterpreterTarget.print_derived_name", "FStar.String.concat", "FStar.List.map", "Target.print_expr" ]

[]

false

true

false

let print_dtyp (mname: string) (dt: dtyp) =

match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ")

false

InterpreterTarget.fst

InterpreterTarget.typ_indexes_of_parser

val typ_indexes_of_parser (en: env) (p: T.parser) : ML typ_indexes

let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary"

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 48, "end_line": 392, "start_col": 0, "start_line": 307 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

en: InterpreterTarget.env -> p: Target.parser -> FStar.All.ML InterpreterTarget.typ_indexes

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.env", "Target.parser", "Target.__proj__Mkparser__item__p_parser", "InterpreterTarget.typ_indexes_nil", "InterpreterTarget.typ_indexes", "Ast.ident", "Prims.list", "Target.index", "InterpreterTarget.itype", "Prims.bool", "InterpreterTarget.expr", "InterpreterTarget.index", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.disj", "InterpreterTarget.on_success", "FStar.Pervasives.Native.Mktuple4", "InterpreterTarget.On_success_named", "InterpreterTarget.subst_disj", "FStar.Pervasives.Native.option", "InterpreterTarget.subst_eloc", "InterpreterTarget.subst_inv", "Target.subst", "FStar.All.failwith", "FStar.Printf.sprintf", "Ast.ident_to_string", "Target.__proj__Mktypedef_name__item__td_name", "InterpreterTarget.__proj__Mktype_decl__item__name", "Target.mk_subst", "Target.__proj__Mktypedef_name__item__td_params", "InterpreterTarget.__proj__Mktype_decl__item__typ_indexes", "InterpreterTarget.type_decl", "Hashtable.try_find", "Ast.ident'", "Ast.__proj__Mkwith_meta_t__item__v", "InterpreterTarget.dtyp", "InterpreterTarget.dtyp_of_app", "Target.expr", "InterpreterTarget.typ_indexes_union", "FStar.Pervasives.Native.tuple4", "Target.lam", "Target.parser_kind", "Ast.comments", "Target.action", "InterpreterTarget.typ_indexes_of_action", "FStar.Pervasives.Native.Some", "InterpreterTarget.Inv_copy_buf", "InterpreterTarget.id_as_expr", "InterpreterTarget.Eloc_copy_buf", "InterpreterTarget.disj_pair", "Prims.b2t", "InterpreterTarget.uu___is_Eloc_copy_buf", "InterpreterTarget.On_success", "InterpreterTarget.typ_indexes_of_parser" ]

[ "recursion" ]

false

true

false

let rec typ_indexes_of_parser (en: env) (p: T.parser) : ML typ_indexes =

let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in (match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args) | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary"

false

InterpreterTarget.fst

InterpreterTarget.check_validity_of_typ_indexes

val check_validity_of_typ_indexes : td: Target.type_decl -> indexes: (((_ * _) * FStar.Pervasives.Native.option InterpreterTarget.disj) * _) -> FStar.All.ALL Prims.unit

let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 32, "end_line": 576, "start_col": 0, "start_line": 545 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

td: Target.type_decl -> indexes: (((_ * _) * FStar.Pervasives.Native.option InterpreterTarget.disj) * _) -> FStar.All.ALL Prims.unit

FStar.All.ALL

[ "should_not_inline" ]

[]

[ "Target.type_decl", "FStar.Pervasives.Native.tuple4", "FStar.Pervasives.Native.option", "InterpreterTarget.disj", "Prims.unit", "Ast.ident", "Ast.range", "InterpreterTarget.eloc", "FStar.List.Tot.Base.existsb", "Ast.eq_idents", "Prims.bool", "Ast.error", "FStar.Printf.sprintf", "Target.print_ident", "Ast.__proj__Mkwith_meta_t__item__range", "Ast.ident'", "Target.__proj__Mktypedef_name__item__td_name", "Target.__proj__Mktype_decl__item__decl_name", "Prims.list", "Prims.Cons", "Prims.Nil", "FStar.List.Tot.Base.op_At", "InterpreterTarget.expr", "Prims.b2t", "Target.uu___is_Identifier", "FStar.Pervasives.Native.fst", "Target.expr'" ]

[]

false

true

false

let check_validity_of_typ_indexes (td: T.type_decl) indexes =

let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d: disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then (A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range) in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj

false

InterpreterTarget.fst

InterpreterTarget.translate_decls

val translate_decls (e:env) (ds:T.decls) : ML (list decl)

let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 8, "end_line": 612, "start_col": 0, "start_line": 578 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

e: InterpreterTarget.env -> ds: Target.decls -> FStar.All.ML (Prims.list InterpreterTarget.decl)

FStar.All.ML

[ "ml" ]

[]

[ "InterpreterTarget.env", "Target.decls", "FStar.List.map", "FStar.Pervasives.Native.tuple2", "Target.decl'", "Target.decl_attributes", "FStar.Pervasives.either", "InterpreterTarget.not_type_decl", "InterpreterTarget.type_decl", "Target.type_decl", "FStar.Pervasives.Inr", "Prims.unit", "Hashtable.insert", "Ast.ident'", "Ast.__proj__Mkwith_meta_t__item__v", "Target.__proj__Mktypedef_name__item__td_name", "InterpreterTarget.__proj__Mktype_decl__item__name", "InterpreterTarget.Mktype_decl", "Target.__proj__Mktype_decl__item__decl_name", "Target.__proj__Mkparser__item__p_kind", "Target.__proj__Mktype_decl__item__decl_parser", "InterpreterTarget.typ", "InterpreterTarget.typ_of_parser", "InterpreterTarget.check_validity_of_typ_indexes", "InterpreterTarget.index", "InterpreterTarget.inv", "InterpreterTarget.eloc", "InterpreterTarget.on_success", "InterpreterTarget.typ_indexes", "InterpreterTarget.typ_indexes_of_parser", "FStar.Pervasives.Native.option", "Target.typ", "Prims.b2t", "Target.uu___is_T_refine", "Target.__proj__Mktype_decl__item__decl_is_enum", "Target.__proj__Mktype_decl__item__decl_typ", "FStar.Pervasives.Native.Some", "Prims.bool", "FStar.Pervasives.Native.None", "Target.typedef_body", "InterpreterTarget.allow_reading_of_typ", "FStar.Pervasives.Inl", "Prims.list", "InterpreterTarget.decl" ]

[]

false

true

false

let translate_decls (en: env) (ds: T.decls) : ML (list decl) =

List.map (function | T.Type_decl td, attrs -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes = typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds

false

InterpreterTarget.fst

InterpreterTarget.print_action

val print_action (mname: string) (a: T.action) : ML string

let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 30, "end_line": 718, "start_col": 0, "start_line": 652 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x))

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> a: Target.action -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "Target.action", "Target.atomic_action", "FStar.Printf.sprintf", "InterpreterTarget.print_action", "Target.expr", "Target.print_expr", "Ast.ident", "InterpreterTarget.print_lam", "FStar.Pervasives.Native.Mktuple2", "Target.print_ident", "InterpreterTarget.print_ident", "Prims.list", "FStar.String.concat", "FStar.List.map" ]

[ "recursion" ]

false

true

false

let rec print_action (mname: string) (a: T.action) : ML string =

let print_atomic_action (a: T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a)

false

EverCrypt.AEAD.fst

EverCrypt.AEAD.invert_state_s

val invert_state_s (a: alg) : Lemma (requires True) (ensures (inversion (state_s a))) [SMTPat (state_s a)]

let invert_state_s (a: alg): Lemma (requires True) (ensures (inversion (state_s a))) [ SMTPat (state_s a) ] = allow_inversion (state_s a)

{ "file_name": "providers/evercrypt/fst/EverCrypt.AEAD.fst", "git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872", "git_url": "https://github.com/project-everest/hacl-star.git", "project_name": "hacl-star" }

{ "end_col": 29, "end_line": 61, "start_col": 0, "start_line": 56 }

module EverCrypt.AEAD module S = FStar.Seq module G = FStar.Ghost module HS = FStar.HyperStack module ST = FStar.HyperStack.ST module MB = LowStar.Monotonic.Buffer module B = LowStar.Buffer open FStar.HyperStack.ST open FStar.Integers open FStar.Int.Cast open Spec.Agile.AEAD open Spec.Cipher.Expansion open EverCrypt.CTR.Keys friend Spec.Agile.AEAD friend Spec.Cipher.Expansion friend EverCrypt.CTR.Keys #set-options "--z3rlimit 100 --max_fuel 0 --max_ifuel 0" /// Defining abstract predicates, invariants, footprint, etc. /// --------------------------------------------------------- let _: squash (inversion impl) = allow_inversion impl /// We now distinguish between an expanded key (as mandated by NIST spec) and a /// **concrete** expanded key, which may contain implementation-specific details /// and extra precomputations. In the rest of this module, we rely on concrete /// expanded keys, which are parameterized over an implementation, instead of /// regular expanded keys, which are parameterized over an algorithm. Helpers /// allow us to move from one notion to the other. let supported_alg_of_impl (i: impl): supported_alg = match i with | Vale_AES128 -> AES128_GCM | Vale_AES256 -> AES256_GCM | Hacl_CHACHA20 -> CHACHA20_POLY1305 inline_for_extraction noextract let alg_of_vale_impl (i: vale_impl) = match i with | Vale_AES128 -> AES128_GCM | Vale_AES256 -> AES256_GCM noeq type state_s a = | Ek: impl:impl -> kv:G.erased (kv a) -> ek:B.buffer UInt8.t -> // concrete expanded key state_s a

{ "checked_file": "/", "dependencies": [ "Vale.Wrapper.X64.GCMencryptOpt256.fsti.checked", "Vale.Wrapper.X64.GCMencryptOpt.fsti.checked", "Vale.Wrapper.X64.GCMdecryptOpt256.fsti.checked", "Vale.Wrapper.X64.GCMdecryptOpt.fsti.checked", "Vale.Wrapper.X64.GCM_IV.fsti.checked", "Vale.Def.Words_s.fsti.checked", "Vale.Def.Words.Seq_s.fsti.checked", "Vale.Def.Types_s.fst.checked", "Vale.Arch.Types.fsti.checked", "Vale.AES.OptPublic.fsti.checked", "Vale.AES.GCM_s.fst.checked", "Vale.AES.AES_s.fst.checked", "Spec.Cipher.Expansion.fst.checked", "Spec.Cipher.Expansion.fst.checked", "Spec.Agile.AEAD.fst.checked", "Spec.Agile.AEAD.fst.checked", "prims.fst.checked", "LowStar.Monotonic.Buffer.fsti.checked", "LowStar.Failure.fsti.checked", "LowStar.BufferOps.fst.checked", "LowStar.Buffer.fst.checked", "FStar.UInt8.fsti.checked", "FStar.UInt64.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Seq.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Integers.fst.checked", "FStar.Int.Cast.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked", "FStar.Ghost.fsti.checked", "FStar.Calc.fsti.checked", "EverCrypt.TargetConfig.fsti.checked", "EverCrypt.CTR.Keys.fst.checked", "EverCrypt.CTR.Keys.fst.checked", "EverCrypt.Chacha20Poly1305.fsti.checked", "EverCrypt.AutoConfig2.fsti.checked" ], "interface_file": true, "source_file": "EverCrypt.AEAD.fst" }

[ { "abbrev": false, "full_module": "EverCrypt.CTR.Keys", "short_module": null }, { "abbrev": false, "full_module": "Spec.Cipher.Expansion", "short_module": null }, { "abbrev": false, "full_module": "Spec.Agile.AEAD", "short_module": null }, { "abbrev": false, "full_module": "FStar.Int.Cast", "short_module": null }, { "abbrev": false, "full_module": "FStar.Integers", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": true, "full_module": "LowStar.Buffer", "short_module": "B" }, { "abbrev": true, "full_module": "LowStar.Monotonic.Buffer", "short_module": "MB" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "S" }, { "abbrev": false, "full_module": "EverCrypt.Error", "short_module": null }, { "abbrev": true, "full_module": "Spec.Agile.AEAD", "short_module": "Spec" }, { "abbrev": false, "full_module": "Spec.Agile.AEAD", "short_module": null }, { "abbrev": false, "full_module": "FStar.Integers", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": true, "full_module": "LowStar.Buffer", "short_module": "B" }, { "abbrev": true, "full_module": "LowStar.Monotonic.Buffer", "short_module": "MB" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "FStar.HyperStack", "short_module": "HS" }, { "abbrev": true, "full_module": "FStar.Ghost", "short_module": "G" }, { "abbrev": true, "full_module": "FStar.Seq", "short_module": "S" }, { "abbrev": false, "full_module": "EverCrypt", "short_module": null }, { "abbrev": false, "full_module": "EverCrypt", "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": 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

a: Spec.Agile.AEAD.alg -> FStar.Pervasives.Lemma (ensures FStar.Pervasives.inversion (EverCrypt.AEAD.state_s a)) [SMTPat (EverCrypt.AEAD.state_s a)]

FStar.Pervasives.Lemma

[ "lemma" ]

[]

[ "Spec.Agile.AEAD.alg", "FStar.Pervasives.allow_inversion", "EverCrypt.AEAD.state_s", "Prims.unit", "Prims.l_True", "Prims.squash", "FStar.Pervasives.inversion", "Prims.Cons", "FStar.Pervasives.pattern", "FStar.Pervasives.smt_pat", "Prims.Nil" ]

[]

true

false

true

false

let invert_state_s (a: alg) : Lemma (requires True) (ensures (inversion (state_s a))) [SMTPat (state_s a)] =

allow_inversion (state_s a)

false

InterpreterTarget.fst

InterpreterTarget.print_typ

val print_typ (mname: string) (t: typ) : ML string

let rec print_typ (mname:string) (t:typ) : ML string = match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt)

{ "file_name": "src/3d/InterpreterTarget.fst", "git_rev": "00217c4a89f5ba56002ba9aa5b4a9d5903bfe9fa", "git_url": "https://github.com/project-everest/everparse.git", "project_name": "everparse" }

{ "end_col": 42, "end_line": 832, "start_col": 0, "start_line": 720 }

(* Copyright 2021 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 InterpreterTarget (* The abstract syntax for the code produced by 3d, targeting prelude/Interpreter.fst *) open FStar.All open FStar.List.Tot module A = Ast module T = Target module H = Hashtable noeq type inv = | Inv_conj : inv -> inv -> inv | Inv_ptr : expr -> inv | Inv_copy_buf: expr -> inv noeq type eloc = | Eloc_output : eloc | Eloc_union : eloc -> eloc -> eloc | Eloc_ptr : expr -> eloc | Eloc_copy_buf: e:expr { T.Identifier? (fst e) } -> eloc noeq type disj = | Disj_pair : l:eloc{ Eloc_copy_buf? l } -> eloc -> disj | Disj_conj : disj -> disj -> disj let index a = option a let disj_pair l m : index disj = match l, m with | None, i | i, None -> None | Some l, Some m -> Some (Disj_pair l m) let subst_index (s:'a -> ML 'a) (i:index 'a) = match i with | None -> None | Some i -> Some (s i) let join_index j d0 d1 = match d0, d1 with | None, d | d, None -> d | Some d0, Some d1 -> Some (j d0 d1) let join_inv = join_index Inv_conj let join_eloc = join_index Eloc_union let join_disj = join_index Disj_conj let rec subst_inv' subst (i:inv) : inv = match i with | Inv_conj i j -> Inv_conj (subst_inv' subst i) (subst_inv' subst j) | Inv_ptr x -> Inv_ptr (T.subst_expr subst x) | Inv_copy_buf x -> Inv_copy_buf (T.subst_expr subst x) let subst_inv s = subst_index (subst_inv' s) let eq_tags e e' = match e, e' with | Eloc_output, Eloc_output | Eloc_union _ _, Eloc_union _ _ | Eloc_ptr _, Eloc_ptr _ | Eloc_copy_buf _, Eloc_copy_buf _ -> true | _ -> false let rec subst_eloc' subst (e:eloc) : ML (e':eloc { eq_tags e e' }) = match e with | Eloc_output -> e | Eloc_union i j -> Eloc_union (subst_eloc' subst i) (subst_eloc' subst j) | Eloc_ptr x -> Eloc_ptr (T.subst_expr subst x) | Eloc_copy_buf x -> let y = T.subst_expr subst x in if not (T.Identifier? (fst y)) then ( Ast.error "Unexpected non-identifier in subst_eloc" (snd x) ) else Eloc_copy_buf y let subst_eloc s = subst_index (subst_eloc' s) let rec subst_disj' subst (d:disj) : ML disj = match d with | Disj_pair e1 e2 -> Disj_pair (subst_eloc' subst e1) (subst_eloc' subst e2) | Disj_conj d1 d2 -> Disj_conj (subst_disj' subst d1) (subst_disj' subst d2) let subst_disj s = subst_index (subst_disj' s) noeq type on_success = | On_success : bool -> on_success | On_success_named : A.ident -> list expr -> on_success | On_success_union : on_success -> on_success -> on_success let typ_indexes = index inv & index eloc & index disj & on_success let typ_indexes_nil : typ_indexes = None, None, None, On_success false let typ_indexes_union (i, e, d, b) (i', e', d', b') = join_inv i i', join_eloc e e', join_disj d d', On_success_union b b' let env = H.t A.ident' type_decl let create_env (_:unit) : ML env = H.create 100 let rec free_vars_of_expr (e:T.expr) : ML (list A.ident) = let open T in match fst e with | Constant _ -> [] | Identifier i -> [i] | App _ args -> List.collect free_vars_of_expr args | Record _ args -> List.collect (fun (_, e) -> free_vars_of_expr e) args let map_index (def:'b) (f:'a -> ML 'b) (i:index 'a) : ML 'b = match i with | None -> def | Some i -> f i let rec free_vars_of_inv' (i:inv) : ML (list A.ident) = match i with | Inv_conj i j -> free_vars_of_inv' i @ free_vars_of_inv' j | Inv_ptr x -> free_vars_of_expr x | Inv_copy_buf x -> free_vars_of_expr x let free_vars_of_inv = map_index [] free_vars_of_inv' let rec free_vars_of_eloc' (e:eloc) : ML (list A.ident) = match e with | Eloc_output -> [] | Eloc_union i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j | Eloc_ptr x -> free_vars_of_expr x | Eloc_copy_buf x -> free_vars_of_expr x let free_vars_of_eloc = map_index [] free_vars_of_eloc' let rec free_vars_of_disj' (d:disj) : ML (list A.ident) = match d with | Disj_conj d0 d1 -> free_vars_of_disj' d0 @ free_vars_of_disj' d1 | Disj_pair i j -> free_vars_of_eloc' i @ free_vars_of_eloc' j let free_vars_of_disj = map_index [] free_vars_of_disj' let free_vars_of_typ_indexes (i:typ_indexes) = let i, j, d, _ = i in free_vars_of_inv i @ free_vars_of_eloc j @ free_vars_of_disj d let filter_args_for_inv (args:list expr) (td:type_decl) : ML (list expr) = let fvs = free_vars_of_typ_indexes td.typ_indexes in let args = List.map2 (fun (b, _) a -> if Some? (List.tryFind (fun j -> A.ident_name b = A.ident_name j) fvs) then [a] else []) td.name.td_params args in List.flatten args let itype_of_ident (hd:A.ident) : option itype = match hd.v.name with | "UINT8" -> Some UInt8 | "UINT16" -> Some UInt16 | "UINT32" -> Some UInt32 | "UINT64" -> Some UInt64 | "UINT8BE" -> Some UInt8BE | "UINT16BE" -> Some UInt16BE | "UINT32BE" -> Some UInt32BE | "UINT64BE" -> Some UInt64BE | "unit" -> Some Unit | "all_bytes" -> Some AllBytes | "all_zeros" -> Some AllZeros | _ -> None let dtyp_of_app (en: env) (hd:A.ident) (args:list T.index) : ML dtyp = match itype_of_ident hd, args with | Some i, [] -> DT_IType i | _ -> let readable = match H.try_find en hd.v with | None -> failwith "type not found" | Some td -> td.allow_reading in DT_App readable hd (List.map (function Inl _ -> failwith "Unexpected type application" | Inr e -> e) args) let tag_of_parser p = let open T in match p.p_parser with | Parse_return _ -> "Parse_return" | Parse_app _ _ -> "Parse_app" | Parse_nlist _ _ -> "Parse_nlist" | Parse_t_at_most _ _ -> "Parse_t_at_most" | Parse_t_exact _ _ -> "Parse_t_exact" | Parse_pair _ _ _ -> "Parse_pair" | Parse_dep_pair _ _ _ -> "Parse_dep_pair" | Parse_dep_pair_with_refinement _ _ _ _ -> "Parse_dep_pair_with_refinement" | Parse_dep_pair_with_action _ _ _ -> "Parse_dep_pair_with_action" | Parse_dep_pair_with_refinement_and_action _ _ _ _ _ -> "Parse_dep_pair_with_refinement_and_action" | Parse_map _ _ -> "Parse_map" | Parse_refinement _ _ _ -> "Parse_refinement" | Parse_refinement_with_action _ _ _ _ -> "Parse_refinement_with_action" | Parse_with_dep_action _ _ _ -> "Parse_with_dep_action" | Parse_with_action _ _ _ -> "Parse_with_action" | Parse_weaken_left _ _ -> "Parse_weaken_left" | Parse_weaken_right _ _ -> "Parse_weaken_right" | Parse_if_else _ _ _ -> "Parse_if_else" | Parse_impos -> "Parse_impos" | Parse_with_comment _ _ -> "Parse_with_comment" | Parse_string _ _ -> "Parse_string" | Parse_with_probe _ _ _ _ -> "Parse_with_probe" let as_lam (x:T.lam 'a) : lam 'a = let i = match fst x with | None -> A.(with_dummy_range (to_ident' "_")) | Some i -> i in i, snd x let id_as_expr (i:A.ident) = T.mk_expr (T.Identifier i) let rec typ_indexes_of_action (a:T.action) : ML typ_indexes = let open T in let of_atomic_action (a:T.atomic_action) : ML typ_indexes = match a with | Action_return _ | Action_abort | Action_field_pos_32 | Action_field_pos_64 -> typ_indexes_nil | Action_field_ptr_after _ write_to -> Some (Inv_ptr (id_as_expr write_to)), Some (Eloc_ptr (id_as_expr write_to)), None, On_success false | Action_field_ptr_after_with_setter _ _ _ -> None, Some Eloc_output, None, On_success false | Action_field_ptr -> None, None, None, On_success true | Action_deref x -> Some (Inv_ptr (id_as_expr x)), None, None, On_success false | Action_assignment x _ -> Some (Inv_ptr (id_as_expr x)), Some (Eloc_ptr (id_as_expr x)), None, On_success false | Action_call f args -> None, Some Eloc_output, None, On_success false in match a with | Atomic_action aa -> of_atomic_action aa | Action_seq hd tl | Action_let _ hd tl -> typ_indexes_union (of_atomic_action hd) (typ_indexes_of_action tl) | Action_ite _ a0 a1 -> typ_indexes_union (typ_indexes_of_action a0) (typ_indexes_of_action a1) | Action_act a -> typ_indexes_of_action a let rec typ_indexes_of_parser (en:env) (p:T.parser) : ML typ_indexes = let typ_indexes_of_parser = typ_indexes_of_parser en in match p.p_parser with | T.Parse_impos -> typ_indexes_nil | T.Parse_app hd args -> let dt = dtyp_of_app en hd args in begin match dt with | DT_IType _ -> typ_indexes_nil | DT_App _ hd args -> let td = match H.try_find en hd.v with | Some td -> td | _ -> failwith (Printf.sprintf "Type decl not found for %s" (A.ident_to_string hd)) in let inv, eloc, disj, _ = td.typ_indexes in let subst = match T.mk_subst td.name.td_params args with | None -> failwith (Printf.sprintf "Unexpected number of arguments to type %s" (A.ident_to_string td.name.td_name)) | Some s -> s in subst_inv subst inv, subst_eloc subst eloc, subst_disj subst disj, On_success_named hd args end | T.Parse_if_else _ p q | T.Parse_pair _ p q -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_dep_pair _ p (_, q) | T.Parse_dep_pair_with_refinement _ p _ (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_parser q) | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_refinement _ p _ | T.Parse_with_comment p _ | T.Parse_nlist _ p | T.Parse_t_at_most _ p | T.Parse_t_exact _ p -> typ_indexes_of_parser p | T.Parse_dep_pair_with_action p (_, a) (_, q) | T.Parse_dep_pair_with_refinement_and_action _ p _ (_, a) (_, q) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_union (typ_indexes_of_action a) (typ_indexes_of_parser q)) | T.Parse_with_action _ p a -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_dep_action _ p (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_string p _ -> typ_indexes_nil | T.Parse_refinement_with_action n p f (_, a) -> typ_indexes_union (typ_indexes_of_parser p) (typ_indexes_of_action a) | T.Parse_with_probe p _ _ dest -> let i, l, d, s = typ_indexes_of_parser p in typ_indexes_union (i, l, d, s) (Some (Inv_copy_buf (id_as_expr dest)), Some (Eloc_copy_buf (id_as_expr dest)), disj_pair (Some (Eloc_copy_buf (id_as_expr dest))) l, On_success true) | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" let typ_of_parser (en: env) : Tot (T.parser -> ML typ) = let rec typ_of_parser (p:T.parser) : ML typ = let rec dtyp_of_parser (p:T.parser) : ML dtyp = match p.p_parser with | T.Parse_app hd args -> dtyp_of_app en hd args | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ | T.Parse_with_comment p _ -> dtyp_of_parser p | _ -> failwith (Printf.sprintf "Expected a named type, got %s" (tag_of_parser p)) in let fn = nes p.p_fieldname in match p.p_parser with | T.Parse_impos -> T_false fn | T.Parse_app _ _ -> T_denoted fn (dtyp_of_parser p) | T.Parse_pair _ p q -> T_pair (nes p.p_fieldname) (typ_of_parser p) (typ_of_parser q) | T.Parse_with_comment p c -> T_with_comment fn (typ_of_parser p) (String.concat "; " c) | T.Parse_nlist n p -> T_nlist fn n (typ_of_parser p) | T.Parse_t_at_most n p -> T_at_most fn n (typ_of_parser p) | T.Parse_t_exact n p -> T_exact fn n (typ_of_parser p) | T.Parse_if_else e p1 p2 -> T_if_else e (typ_of_parser p1) (typ_of_parser p2) | T.Parse_dep_pair _ p k -> let i, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair (nes p.p_fieldname) d (i, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair: tag not readable" | T.Parse_dep_pair_with_refinement _ p r k -> let i, r = as_lam r in let j, k = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement fn d (i, r) (j, typ_of_parser k) else failwith "typ_of_parser: Parse_dep_pair_with_refinement: tag not readable" | T.Parse_dep_pair_with_action p a k -> let (i, k) = as_lam k in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_action fn d (i, typ_of_parser k) (as_lam a) else failwith "typ_of_parser: Parse_dep_pair_with_action: tag not readable" | T.Parse_dep_pair_with_refinement_and_action _ p r a k -> let a = as_lam a in let (i, k) = as_lam k in let r = as_lam r in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_dep_pair_with_refinement_and_action fn d r (i, typ_of_parser k) a else failwith "typ_of_parser: Parse_dep_pair_with_refinement_and_action: tag not readable" | T.Parse_with_action _ p a -> T_with_action fn (typ_of_parser p) a | T.Parse_with_dep_action _ p a -> let a = as_lam a in let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_with_dep_action fn d a else failwith "typ_of_parser: Parse_with_dep_action: tag not readable" | T.Parse_string p z -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_string fn d z else failwith "typ_of_parser: Parse_string: element not readable" | T.Parse_refinement _ p f -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine fn d (as_lam f) else failwith "typ_of_parser: Parse_refinement: element not readable" | T.Parse_refinement_with_action _ p f a -> let d = dtyp_of_parser p in if allow_reader_of_dtyp d then T_refine_with_action fn d (as_lam f) (as_lam a) else failwith "typ_of_parser: Parse_refinement_with_action: element not readable" | T.Parse_weaken_left p _ | T.Parse_weaken_right p _ -> typ_of_parser p | T.Parse_with_probe p probe_fn len dest -> let d = dtyp_of_parser p in T_probe_then_validate fn d probe_fn len dest | T.Parse_map _ _ | T.Parse_return _ -> failwith "Unnecessary" in typ_of_parser let rec allow_reading_of_typ (t:typ) : Tot bool = match t with | T_with_comment _ t _ -> allow_reading_of_typ t | T_denoted _ dt -> begin match dt with | DT_IType i -> allow_reader_of_itype i | DT_App readable _ _ -> readable end | _ -> false let check_validity_of_typ_indexes (td:T.type_decl) indexes = let rec atomic_locs_of l = match l with | Eloc_output -> [l] | Eloc_union l1 l2 -> atomic_locs_of l1 @ atomic_locs_of l2 | Eloc_ptr _ -> [l] | Eloc_copy_buf _ -> [l] in let rec valid_disj (d:disj) : ML unit = match d with | Disj_conj d1 d2 -> valid_disj d1; valid_disj d2 | Disj_pair (Eloc_copy_buf (T.Identifier x, rx)) l2 -> let l2_locs = atomic_locs_of l2 in if List.existsb (function | Eloc_copy_buf (T.Identifier y, ry) -> A.eq_idents x y | _ -> false) l2_locs then ( A.error (Printf.sprintf "Nested mutation of the copy buffer [%s]" (T.print_ident x)) td.decl_name.td_name.range ) else () in let _, _, disj, _ = indexes in match disj with | None -> () | Some disj -> valid_disj disj let translate_decls (en:env) (ds:T.decls) : ML (list decl) = List.map (fun d -> match d with | (T.Type_decl td, attrs) -> let t = typ_of_parser en td.decl_parser in let ar = allow_reading_of_typ t in let refined = if td.decl_is_enum then match td.decl_typ with | T.TD_abbrev t -> if T.T_refine? t then Some t else None | _ -> None else None in let typ_indexes = typ_indexes_of_parser en td.decl_parser in check_validity_of_typ_indexes td typ_indexes; let td = { name = td.decl_name; typ = typ_of_parser en td.decl_parser; kind = td.decl_parser.p_kind; typ_indexes; allow_reading = ar; attrs = attrs; enum_typ = refined } in H.insert en td.name.td_name.v td; Inr td | d -> Inl (d <: not_type_decl)) ds let print_ityp (i:itype) = match i with | UInt8 -> "UInt8" | UInt16 -> "UInt16" | UInt32 -> "UInt32" | UInt64 -> "UInt64" | UInt8BE -> "UInt8BE" | UInt16BE -> "UInt16BE" | UInt32BE -> "UInt32BE" | UInt64BE -> "UInt64BE" | Unit -> "Unit" | AllBytes -> "AllBytes" | AllZeros -> "AllZeros" let print_ident (mname:string) (i:A.ident) = T.print_maybe_qualified_ident mname i let print_derived_name (mname:string) (tag:string) (i:A.ident) = Printf.sprintf "%s%s_%s" (T.maybe_mname_prefix mname i) tag (T.print_ident i) let print_dtyp (mname:string) (dt:dtyp) = match dt with | DT_IType i -> Printf.sprintf "(DT_IType %s)" (print_ityp i) | DT_App _ hd args -> Printf.sprintf "(%s %s)" (print_derived_name mname "dtyp" hd) (List.map (T.print_expr mname) args |> String.concat " ") let print_lam (mname:string) (p:'a -> ML string) (x:lam 'a) = Printf.sprintf "(fun %s -> %s)" (print_ident mname (fst x)) (p (snd x)) let rec print_action (mname:string) (a:T.action) : ML string = let print_atomic_action (a:T.atomic_action) : ML string = match a with | T.Action_return e -> Printf.sprintf "(Action_return %s)" (T.print_expr mname e) | T.Action_abort -> "Action_abort" | T.Action_field_pos_64 -> "Action_field_pos_64" | T.Action_field_pos_32 -> "(Action_field_pos_32 EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr -> "(Action_field_ptr EverParse3d.Actions.BackendFlagValue.backend_flag_value)" | T.Action_field_ptr_after sz write_to -> Printf.sprintf "(Action_field_ptr_after EverParse3d.Actions.BackendFlagValue.backend_flag_value %s %s)" (T.print_expr mname sz) (T.print_ident write_to) | T.Action_field_ptr_after_with_setter sz write_to_field write_to_obj -> Printf.sprintf "(Action_field_ptr_after_with_setter EverParse3d.Actions.BackendFlagValue.backend_flag_value %s (%s %s))" (T.print_expr mname sz) (T.print_ident write_to_field) (T.print_expr mname write_to_obj) | T.Action_deref i -> Printf.sprintf "(Action_deref %s)" (print_ident mname i) | T.Action_assignment lhs rhs -> Printf.sprintf "(Action_assignment %s %s)" (print_ident mname lhs) (T.print_expr mname rhs) | T.Action_call hd args -> Printf.sprintf "(Action_call (mk_action_binding (%s %s)))" (print_ident mname hd) (List.map (T.print_expr mname) args |> String.concat " ") in match a with | T.Atomic_action a -> Printf.sprintf "(Atomic_action %s)" (print_atomic_action a) | T.Action_seq hd tl -> Printf.sprintf "(Action_seq %s %s)" (print_atomic_action hd) (print_action mname tl) | T.Action_ite hd then_ else_ -> Printf.sprintf "(Action_ite %s (fun _ -> %s) (fun _ -> %s))" (T.print_expr mname hd) (print_action mname then_) (print_action mname else_) | T.Action_let i a k -> Printf.sprintf "(Action_let %s %s)" (print_atomic_action a) (print_lam mname (print_action mname) (i, k)) | T.Action_act a -> Printf.sprintf "(Action_act %s)" (print_action mname a)

{ "checked_file": "/", "dependencies": [ "Target.fsti.checked", "prims.fst.checked", "Hashtable.fsti.checked", "FStar.String.fsti.checked", "FStar.Printf.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.List.Tot.fst.checked", "FStar.List.fst.checked", "FStar.All.fst.checked", "Ast.fst.checked" ], "interface_file": true, "source_file": "InterpreterTarget.fst" }

[ { "abbrev": true, "full_module": "Hashtable", "short_module": "H" }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.All", "short_module": null }, { "abbrev": false, "full_module": "Binding", "short_module": null }, { "abbrev": true, "full_module": "Target", "short_module": "T" }, { "abbrev": true, "full_module": "Ast", "short_module": "A" }, { "abbrev": false, "full_module": "FStar.All", "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

mname: Prims.string -> t: InterpreterTarget.typ -> FStar.All.ML Prims.string

FStar.All.ML

[ "ml" ]

[]

[ "Prims.string", "InterpreterTarget.typ", "InterpreterTarget.non_empty_string", "FStar.Printf.sprintf", "InterpreterTarget.dtyp", "InterpreterTarget.print_dtyp", "InterpreterTarget.print_typ", "InterpreterTarget.readable_dtyp", "InterpreterTarget.lam", "InterpreterTarget.print_lam", "InterpreterTarget.expr", "Target.print_expr", "InterpreterTarget.action", "InterpreterTarget.print_action", "Ast.ident", "Target.print_maybe_qualified_ident" ]

[ "recursion" ]

false

true

false

let rec print_typ (mname: string) (t: typ) : ML string =

match t with | T_false fn -> Printf.sprintf "(T_false \"%s\")" fn | T_denoted fn dt -> Printf.sprintf "(T_denoted \"%s\" %s)" fn (print_dtyp mname dt) | T_pair fn t1 t2 -> Printf.sprintf "(T_pair \"%s\" %s %s)" fn (print_typ mname t1) (print_typ mname t2) | T_dep_pair fn t k -> Printf.sprintf "(T_dep_pair \"%s\" %s %s)" fn (print_dtyp mname t) (print_lam mname (print_typ mname) k) | T_refine fn d r -> Printf.sprintf "(T_refine \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) | T_refine_with_action fn d r a -> Printf.sprintf "(T_refine_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement fn d r k -> Printf.sprintf "(T_dep_pair_with_refinement \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) | T_dep_pair_with_action fn d k a -> Printf.sprintf "(T_dep_pair_with_action \"%s\" %s %s %s)" fn (print_dtyp mname d) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_dep_pair_with_refinement_and_action fn d r k a -> Printf.sprintf "(T_dep_pair_with_refinement_and_action \"%s\" %s %s %s %s)" fn (print_dtyp mname d) (print_lam mname (T.print_expr mname) r) (print_lam mname (print_typ mname) k) (print_lam mname (print_action mname) a) | T_if_else e t1 t2 -> Printf.sprintf "(T_cases %s %s %s)" (T.print_expr mname e) (print_typ mname t1) (print_typ mname t2) | T_with_action fn p a -> Printf.sprintf "(T_with_action \"%s\" %s %s)" fn (print_typ mname p) (print_action mname a) | T_with_dep_action fn d a -> Printf.sprintf "(T_with_dep_action \"%s\" %s %s)" fn (print_dtyp mname d) (print_lam mname (print_action mname) a) | T_with_comment fn t c -> Printf.sprintf "(T_with_comment \"%s\" %s \"%s\")" fn (print_typ mname t) c | T_nlist fn n t -> Printf.sprintf "(T_nlist \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_at_most fn n t -> Printf.sprintf "(T_at_most \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_exact fn n t -> Printf.sprintf "(T_exact \"%s\" %s %s)" fn (T.print_expr mname n) (print_typ mname t) | T_string fn d z -> Printf.sprintf "(T_string \"%s\" %s %s)" fn (print_dtyp mname d) (T.print_expr mname z) | T_probe_then_validate fn dt probe_fn len dest -> Printf.sprintf "(t_probe_then_validate \"%s\" %s %s %s %s)" fn (T.print_maybe_qualified_ident mname probe_fn) (T.print_expr mname len) (T.print_maybe_qualified_ident mname dest) (print_dtyp mname dt)

false