Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
fact stringlengths 15 40.2k | statement stringlengths 1 5.3k | proof stringlengths 0 34.8k | type stringclasses 23
values | symbolic_name stringlengths 0 166 | library stringclasses 14
values | filename stringclasses 268
values | imports listlengths 0 57 | deps listlengths 0 63 | docstring stringclasses 641
values | line_start int64 1 5.25k | line_end int64 1 5.47k | has_proof bool 2
classes | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Lemma Z__range_add a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1)
: a0+b0 <= a+b < a1 + b1 - 1.
Proof. Lia.nia. Qed. | Z__range_add a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1)
: a0+b0 <= a+b < a1 + b1 - 1. | Proof. Lia.nia. Qed. | Lemma | Z__range_add | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"a0"
] | Bounds propagation | 9 | 11 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma Z__range_sub a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1)
: a0-b1+1 <= a-b < a1 - b0.
Proof. Lia.nia. Qed. | Z__range_sub a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1)
: a0-b1+1 <= a-b < a1 - b0. | Proof. Lia.nia. Qed. | Lemma | Z__range_sub | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"a0"
] | null | 13 | 15 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma Z__range_div_pos_const_r n0 n n1 (Hn : n0 <= n < n1) d (Hd : 0 < d)
: n0/d <= n/d < n1/d + 1.
Proof. Z.div_mod_to_equations. Lia.nia. Qed. | Z__range_div_pos_const_r n0 n n1 (Hn : n0 <= n < n1) d (Hd : 0 < d)
: n0/d <= n/d < n1/d + 1. | Proof. Z.div_mod_to_equations. Lia.nia. Qed. | Lemma | Z__range_div_pos_const_r | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"n1"
] | null | 16 | 18 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma Z__range_mul_nonneg a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1) (Ha0 : 0 <= a0) (Hb0 : 0 <= b0)
: a0*b0 <= a*b < (a1-1)*(b1-1) + 1.
Proof. Lia.nia. Qed. | Z__range_mul_nonneg a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1) (Ha0 : 0 <= a0) (Hb0 : 0 <= b0)
: a0*b0 <= a*b < (a1-1)*(b1-1) + 1. | Proof. Lia.nia. Qed. | Lemma | Z__range_mul_nonneg | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"a0"
] | null | 19 | 21 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma boundscheck {x0 x x1} (H: x0 <= x < x1) {X0 X1} (Hcheck : andb (X0 <=? x0) (x1 <=? X1) = true) : X0 <= x < X1.
Proof. eapply andb_prop in Hcheck; case Hcheck; intros H1 H2; eapply Z.leb_le in H1; eapply Z.leb_le in H2. blia. Qed. | boundscheck {x0 x x1} (H: x0 <= x < x1) {X0 X1} (Hcheck : andb (X0 <=? x0) (x1 <=? X1) = true) : X0 <= x < X1. | Proof. eapply andb_prop in Hcheck; case Hcheck; intros H1 H2; eapply Z.leb_le in H1; eapply Z.leb_le in H2. blia. Qed. | Lemma | boundscheck | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"x1"
] | null | 22 | 23 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma boundscheck_lt {x0 x x1} (H: x0 <= x < x1) {X1} (Hcheck: Z.ltb x1 X1 = true) : x < X1.
Proof. eapply Z.ltb_lt in Hcheck. blia. Qed. | boundscheck_lt {x0 x x1} (H: x0 <= x < x1) {X1} (Hcheck: Z.ltb x1 X1 = true) : x < X1. | Proof. eapply Z.ltb_lt in Hcheck. blia. Qed. | Lemma | boundscheck_lt | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"x1"
] | null | 24 | 25 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bounded_constant c : c <= c < c+1. Proof. blia. Qed. | bounded_constant c : c <= c < c+1. | Proof. blia. Qed. | Lemma | bounded_constant | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [] | null | 26 | 26 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac named_pose_proof pf :=
let H := fresh in
let __ := match constr:(Set) with _ => pose proof pf as H end in
H. | named_pose_proof pf | :=
let H := fresh in
let __ := match constr:(Set) with _ => pose proof pf as H end in
H. | Ltac | named_pose_proof | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set"
] | null | 28 | 31 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac named_pose pf :=
let H := fresh in
let __ := match constr:(Set) with _ => pose pf as H end in
H. | named_pose pf | :=
let H := fresh in
let __ := match constr:(Set) with _ => pose pf as H end in
H. | Ltac | named_pose | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set"
] | null | 32 | 35 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac named_pose_asfresh pf x :=
let H := fresh x in
let __ := match constr:(Set) with _ => pose pf as H end in
H. | named_pose_asfresh pf x | :=
let H := fresh x in
let __ := match constr:(Set) with _ => pose pf as H end in
H. | Ltac | named_pose_asfresh | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set"
] | null | 36 | 39 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac named_pose_asfresh_or_id x n :=
let y := match constr:(Set) with _ => named_pose_asfresh x n | _ => x end in
y. | named_pose_asfresh_or_id x n | :=
let y := match constr:(Set) with _ => named_pose_asfresh x n | _ => x end in
y. | Ltac | named_pose_asfresh_or_id | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set",
"named_pose_asfresh"
] | null | 41 | 43 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac requireZcst z :=
lazymatch Coq.setoid_ring.InitialRing.isZcst z with
| true => idtac
end. | requireZcst z | :=
lazymatch Coq.setoid_ring.InitialRing.isZcst z with
| true => idtac
end. | Ltac | requireZcst | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [] | null | 45 | 48 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac requireZcstExpr e :=
match e with
| Z.pred ?x => requireZcstExpr x
| Z.succ ?x => requireZcstExpr x
| Z.ones ?x => requireZcstExpr x
| Z.opp ?x => requireZcstExpr x
| Z.lnot ?x => requireZcstExpr x
| Z.log2 ?x => requireZcstExpr x
| Z.log2_up ?x => requireZcstExpr x
| Z.add ?x ?y => requireZcstEx... | requireZcstExpr e | :=
match e with
| Z.pred ?x => requireZcstExpr x
| Z.succ ?x => requireZcstExpr x
| Z.ones ?x => requireZcstExpr x
| Z.opp ?x => requireZcstExpr x
| Z.lnot ?x => requireZcstExpr x
| Z.log2 ?x => requireZcstExpr x
| Z.log2_up ?x => requireZcstExpr x
| Z.add ?x ?y => requireZcstExpr x; requireZcstExpr y... | Ltac | requireZcstExpr | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"requireZcst"
] | null | 49 | 79 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac zsimp x :=
match constr:(Set) with
| _ => let __ := requireZcstExpr x in let y := eval cbv in x in y
| _ => x
end. | zsimp x | :=
match constr:(Set) with
| _ => let __ := requireZcstExpr x in let y := eval cbv in x in y
| _ => x
end. | Ltac | zsimp | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set",
"eval",
"requireZcstExpr"
] | null | 81 | 85 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Local Notation "zbsimp! H" :=
(ltac:(
lazymatch type of H with
?L <= ?X < ?R =>
let L := zsimp L in
let R := zsimp R in
exact ((H : L <= X < R))
end
)) (at level 10, only parsing). | "zbsimp! H" | :=
(ltac:(
lazymatch type of H with
?L <= ?X < ?R =>
let L := zsimp L in
let R := zsimp R in
exact ((H : L <= X < R))
end
)) (at level 10, only parsing). | Notation | zbsimp! H | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Notation",
"R",
"zsimp"
] | null | 87 | 95 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac rbounded e :=
let re := rdelta e in
match goal with
| H : _ <= e < _ |- _ => H
| _ =>
match re with
| word.unsigned ?a =>
named_pose_proof (zbsimp! (Properties.word.unsigned_range a : _ <= e < _))
| Z.div ?a ?b => (* TODO: non-constant denominator? *)
let __ := match constr:(Set) w... | rbounded e | :=
let re := rdelta e in
match goal with
| H : _ <= e < _ |- _ => H
| _ =>
match re with
| word.unsigned ?a =>
named_pose_proof (zbsimp! (Properties.word.unsigned_range a : _ <= e < _))
| Z.div ?a ?b => (* TODO: non-constant denominator? *)
let __ := match constr:(Set) with _ => require... | Ltac | rbounded | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Set",
"TODO",
"Z",
"Z__range_add",
"Z__range_div_pos_const_r",
"Z__range_mul_nonneg",
"Z__range_sub",
"a0",
"bounded_constant",
"goal",
"named_pose_proof",
"requireZcstExpr",
"word"
] | null | 97 | 130 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_eq {T} := @eq T. | absint_eq {T} | := @eq T. | Definition | absint_eq | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [] | Abstract interpretation | 134 | 134 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_eq_refl {T} v := ((@eq_refl T v) : @absint_eq T v v). | absint_eq_refl {T} v | := ((@eq_refl T v) : @absint_eq T v v). | Definition | absint_eq_refl | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"absint_eq"
] | null | 135 | 135 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Local Notation "absint_lemma! pf" := (ltac:(
cbv [absint_eq] in *;
etransitivity; [ eapply pf | ]; cycle -1;
[unshelve (repeat match goal with
| |- _ => progress unfold word.wrap in *
| |-context [Z.shiftr ?x (word.unsigned ?y)] => assert_fails(is_evar x||is_evar y);
... | "absint_lemma! pf" | := (ltac:(
cbv [absint_eq] in *;
etransitivity; [ eapply pf | ]; cycle -1;
[unshelve (repeat match goal with
| |- _ => progress unfold word.wrap in *
| |-context [Z.shiftr ?x (word.unsigned ?y)] => assert_fails(is_evar x||is_evar y);
setoid_rewrite (Z.shiftr_div_pow2 ... | Notation | absint_lemma! pf | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Notation",
"P",
"Z",
"absint_eq",
"goal",
"word"
] | null | 141 | 161 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_add (x y : word.rep) ux Hx uy Hy Hbounds : _ =~> _ :=
absint_lemma! (word.unsigned_add x y). | absint_add (x y : word.rep) ux Hx uy Hy Hbounds : _ =~> _ | :=
absint_lemma! (word.unsigned_add x y). | Definition | absint_add | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 163 | 164 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_sub (x y : word.rep) ux Hx uy Hy Hbounds : word.unsigned _ =~> _ :=
absint_lemma! (word.unsigned_sub x y). | absint_sub (x y : word.rep) ux Hx uy Hy Hbounds : word.unsigned _ =~> _ | :=
absint_lemma! (word.unsigned_sub x y). | Definition | absint_sub | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 165 | 166 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_mul (x y : word.rep) ux Hx uy Hy Hbounds : word.unsigned _ =~> _ :=
absint_lemma! (word.unsigned_mul x y). | absint_mul (x y : word.rep) ux Hx uy Hy Hbounds : word.unsigned _ =~> _ | :=
absint_lemma! (word.unsigned_mul x y). | Definition | absint_mul | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 167 | 168 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_and (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_and_nowrap x y). | absint_and (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_and_nowrap x y). | Definition | absint_and | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 169 | 170 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_or (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_or_nowrap x y). | absint_or (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_or_nowrap x y). | Definition | absint_or | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 171 | 172 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_xor (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_xor_nowrap x y). | absint_xor (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_xor_nowrap x y). | Definition | absint_xor | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 173 | 174 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_ndn (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_ndn_nowrap x y). | absint_ndn (x y : word.rep) ux Hx uy Hy : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_ndn_nowrap x y). | Definition | absint_ndn | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 175 | 176 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_sru (x y : word.rep) ux Hx uy Hy Hshift : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_sru_nowrap x y). | absint_sru (x y : word.rep) ux Hx uy Hy Hshift : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_sru_nowrap x y). | Definition | absint_sru | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 177 | 178 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_slu (x y : word.rep) ux Hx uy Hy Hrange Hshift : word.unsigned _ =~> _ :=
absint_lemma! (word.unsigned_slu x y). | absint_slu (x y : word.rep) ux Hx uy Hy Hrange Hshift : word.unsigned _ =~> _ | :=
absint_lemma! (word.unsigned_slu x y). | Definition | absint_slu | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 179 | 180 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_divu (x y : word.rep) ux Hx uy Hy Hnz : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_divu_nowrap x y). | absint_divu (x y : word.rep) ux Hx uy Hy Hnz : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_divu_nowrap x y). | Definition | absint_divu | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 181 | 182 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition absint_modu (x y : word.rep) ux Hx uy Hy Hnz : word.unsigned _ =~> _ :=
absint_lemma! (Properties.word.unsigned_modu_nowrap x y). | absint_modu (x y : word.rep) ux Hx uy Hy Hnz : word.unsigned _ =~> _ | :=
absint_lemma! (Properties.word.unsigned_modu_nowrap x y). | Definition | absint_modu | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 183 | 184 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma absint_opp x (ux: Z) (Hx: word.unsigned x = ux) (Hnz: ux <> 0):
word.unsigned (word.opp x) =~> 2^width - ux.
Proof.
rewrite word.unsigned_opp. cbv [word.wrap].
rewrite Z_mod_nz_opp_full.
- rewrite Z.mod_small; [rewrite Hx; reflexivity|]. apply word.unsigned_range.
- rewrite Z.mod... | absint_opp x (ux: Z) (Hx: word.unsigned x = ux) (Hnz: ux <> 0):
word.unsigned (word.opp x) =~> 2^width - ux. | Proof.
rewrite word.unsigned_opp. cbv [word.wrap].
rewrite Z_mod_nz_opp_full.
- rewrite Z.mod_small; [rewrite Hx; reflexivity|]. apply word.unsigned_range.
- rewrite Z.mod_small; [rewrite Hx; apply Hnz|]. apply word.unsigned_range.
Qed. | Lemma | absint_opp | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"width",
"word"
] | TODO use it | 187 | 194 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma absint_mask_r x y ux (Hx : word.unsigned x = ux) uy (Hy : word.unsigned y = uy) (Huy : uy = Z.ones (Z.log2 uy+1)):
word.unsigned (word.and x y) =~> Z.modulo ux (uy+1).
Proof.
etransitivity; [eapply absint_and; eauto|].
rewrite Huy.
rewrite Z.land_ones, Z.ones_equiv; repeat (eapply f_e... | absint_mask_r x y ux (Hx : word.unsigned x = ux) uy (Hy : word.unsigned y = uy) (Huy : uy = Z.ones (Z.log2 uy+1)):
word.unsigned (word.and x y) =~> Z.modulo ux (uy+1). | Proof.
etransitivity; [eapply absint_and; eauto|].
rewrite Huy.
rewrite Z.land_ones, Z.ones_equiv; repeat (eapply f_equal2 || blia).
enough (Z.log2 0 <= Z.log2 uy) by (change (Z.log2 0) with 0 in *; blia).
eapply Z.log2_le_mono; subst uy; eapply word.unsigned_range.
Qed. | Lemma | absint_mask_r | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"absint_and",
"f_equal2",
"word"
] | null | 196 | 204 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma absint_mask_l y x uy (Hy : word.unsigned y = uy) ux (Hx : word.unsigned x = ux) (Huy : uy = Z.ones (Z.log2 uy+1)):
word.unsigned (word.and y x) =~> Z.modulo ux (uy+1).
Proof.
etransitivity; [eapply absint_and; eauto|].
rewrite Z.land_comm.
rewrite Huy.
rewrite Z.land_ones, Z.one... | absint_mask_l y x uy (Hy : word.unsigned y = uy) ux (Hx : word.unsigned x = ux) (Huy : uy = Z.ones (Z.log2 uy+1)):
word.unsigned (word.and y x) =~> Z.modulo ux (uy+1). | Proof.
etransitivity; [eapply absint_and; eauto|].
rewrite Z.land_comm.
rewrite Huy.
rewrite Z.land_ones, Z.ones_equiv; repeat (eapply f_equal2 || blia).
enough (Z.log2 0 <= Z.log2 uy) by (change (Z.log2 0) with 0 in *; blia).
eapply Z.log2_le_mono; subst uy; eapply word.unsigned_ran... | Lemma | absint_mask_l | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"Z",
"absint_and",
"f_equal2",
"word"
] | null | 205 | 214 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Ltac zify_expr e :=
let re := rdelta e in
lazymatch type of e with
| @word.rep ?width ?word_parameters =>
match re with
| _ => match goal with H: word.unsigned e =~> _ |- _ => H end
| word.of_Z ?a =>
let Ba := rbounded a in
named_pose_proof (word.unsigned_of_Z_nowrap a (bou... | zify_expr e | :=
let re := rdelta e in
lazymatch type of e with
| @word.rep ?width ?word_parameters =>
match re with
| _ => match goal with H: word.unsigned e =~> _ |- _ => H end
| word.of_Z ?a =>
let Ba := rbounded a in
named_pose_proof (word.unsigned_of_Z_nowrap a (boundscheck (X0:=0) ... | Ltac | zify_expr | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"TODO",
"Z",
"absint_add",
"absint_and",
"absint_eq",
"absint_eq_refl",
"absint_mask_l",
"absint_mask_r",
"absint_mul",
"absint_ndn",
"absint_or",
"absint_slu",
"absint_sru",
"absint_sub",
"absint_xor",
"boundscheck",
"boundscheck_lt",
"goal",
"named_pose_asfresh_or_id",
"named... | null | 217 | 289 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Fixpoint goal (x : word32) (n : nat) : Prop
:= match n with
| O => True
| S n' => let x := word.add x x in goal x n'
end. | goal (x : word32) (n : nat) : Prop | := match n with
| O => True
| S n' => let x := word.add x x in goal x n'
end. | Fixpoint | goal | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/AbsintWordToZ.v | [
"Coq.Strings.String",
"Coq.ZArith.ZArith",
"Word.Interface",
"Word.Properties",
"Tactics.rdelta",
"Z.div_mod_to_equations",
"Z.Lia",
"Word.Naive"
] | [
"word"
] | null | 295 | 299 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition anyval{word mem T: Type}(p: T -> word -> mem -> Prop)(a: word): mem -> Prop :=
ex1 (fun v => p v a). | anyval{word mem T: Type}(p: T -> word -> mem -> Prop)(a: word): mem -> Prop | :=
ex1 (fun v => p v a). | Definition | anyval | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/anyval.v | [
"Lift1Prop"
] | [
"Type",
"ex1",
"mem",
"word"
] | null | 3 | 4 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Notation "p ? a" := (anyval p a) (at level 20, a at level 9). | "p ? a" | := (anyval p a) (at level 20, a at level 9). | Notation | p ? a | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/anyval.v | [
"Lift1Prop"
] | [
"Notation",
"anyval"
] | makes __ a keyword, so "let __ := uselessvalue in blah" in Ltac
doesn't parse any more!
Notation "p '__' a" := (anyval p a) (at level 20, a at level 9).
Infix "__" := anyval (at level 20). | 12 | 12 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Fixpoint array (start : word) (xs : list T) :=
match xs with
| nil => emp True
| cons x xs => sep (element start x) (array (word.add start size) xs)
end. | array (start : word) (xs : list T) | :=
match xs with
| nil => emp True
| cons x xs => sep (element start x) (array (word.add start size) xs)
end. | Fixpoint | array | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"start",
"word"
] | null | 15 | 19 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_cons x xs start:
iff1 (array start (x :: xs)) (sep (element start x) (array (word.add start size) xs)).
Proof. reflexivity. Qed. | array_cons x xs start:
iff1 (array start (x :: xs)) (sep (element start x) (array (word.add start size) xs)). | Proof. reflexivity. Qed. | Lemma | array_cons | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"array",
"start",
"word"
] | null | 23 | 25 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_nil start:
iff1 (array start nil) (emp True).
Proof. reflexivity. Qed. | array_nil start:
iff1 (array start nil) (emp True). | Proof. reflexivity. Qed. | Lemma | array_nil | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"array",
"start"
] | null | 27 | 29 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_append xs ys start:
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start (word.of_Z (word.unsigned size * Z.of_nat (length xs)))) ys). | array_append xs ys start:
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start (word.of_Z (word.unsigned size * Z.of_nat (length xs)))) ys). | Lemma | array_append | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"start",
"word"
] | null | 31 | 33 | false | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 | |
Lemma array_append' xs ys start:
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start
(word.mul size (word.of_Z (Z.of_nat (length xs))))) ys).
Proof.
etransitivity; [eapply array_append|].
repeat Morphisms.f_equiv.
eapply word.unsign... | array_append' xs ys start:
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start
(word.mul size (word.of_Z (Z.of_nat (length xs))))) ys). | Proof.
etransitivity; [eapply array_append|].
repeat Morphisms.f_equiv.
eapply word.unsigned_inj.
repeat (rewrite ?word.unsigned_of_Z, ?word.unsigned_mul, ?Zdiv.Zmult_mod_idemp_r || unfold word.wrap).
reflexivity.
Qed. | Lemma | array_append' | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array_append",
"start",
"word"
] | null | 58 | 68 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma list__tl_skipn {A} n (xs : list A) : tl (skipn n xs) = skipn (S n) xs.
Proof. revert xs; induction n, xs; auto; []; eapply IHn. Qed. | list__tl_skipn {A} n (xs : list A) : tl (skipn n xs) = skipn (S n) xs. | Proof. revert xs; induction n, xs; auto; []; eapply IHn. Qed. | Lemma | list__tl_skipn | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [] | null | 70 | 71 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_index_nat xs start n :
iff1 (array start xs)
( array start (firstn n xs) * (
match hd_error (skipn n xs) with Some x => element (word.add start (word.of_Z (word.unsigned size*Z.of_nat n))) x | None => emp True end *
array (word.add (word.add start (word.of_Z (word.unsigned size*Z.o... | array_index_nat xs start n :
iff1 (array start xs)
( array start (firstn n xs) * (
match hd_error (skipn n xs) with Some x => element (word.add start (word.of_Z (word.unsigned size*Z.of_nat n))) x | None => emp True end *
array (word.add (word.add start (word.of_Z (word.unsigned size*Z.of_nat ... | Proof.
pose proof (firstn_skipn n xs) as H.
rewrite <-!list__tl_skipn.
remember (firstn n xs) as A in *; remember (skipn n xs) as B in *; rewrite <-H.
etransitivity; [eapply array_append|]; eapply iff1_sep_cancel.
destruct B; cbn [array hd_error tl]; [solve[cancel]|].
subst A; destruct (Compare_... | Lemma | array_index_nat | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array_append",
"list__tl_skipn",
"start",
"word"
] | null | 73 | 87 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_index_nat_inbounds xs start n (H : (n < length xs)%nat) :
iff1 (array start xs)
(array start (firstn n xs) *
(element (word.add start (word.of_Z (word.unsigned size * Z.of_nat n))) (hd default (skipn n xs)) *
array (word.add (word.add start (word.of_Z (word.unsigned size * Z.of_nat ... | array_index_nat_inbounds xs start n (H : (n < length xs)%nat) :
iff1 (array start xs)
(array start (firstn n xs) *
(element (word.add start (word.of_Z (word.unsigned size * Z.of_nat n))) (hd default (skipn n xs)) *
array (word.add (word.add start (word.of_Z (word.unsigned size * Z.of_nat n))) s... | Lemma | array_index_nat_inbounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"start",
"word"
] | null | 90 | 94 | false | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 | |
Lemma array_address_inbounds xs start a
(Hlen : word.unsigned (word.sub a start) < Z.mul (word.unsigned size) (Z.of_nat (length xs)))
(Hmod : word.unsigned (word.sub a start) mod (word.unsigned size) = 0)
n (Hn : n = Z.to_nat (word.unsigned (word.sub a start) / word.unsigned size))
: iff1 (array start x... | array_address_inbounds xs start a
(Hlen : word.unsigned (word.sub a start) < Z.mul (word.unsigned size) (Z.of_nat (length xs)))
(Hmod : word.unsigned (word.sub a start) mod (word.unsigned size) = 0)
n (Hn : n = Z.to_nat (word.unsigned (word.sub a start) / word.unsigned size))
: iff1 (array start xs)
... | Proof.
pose proof word.unsigned_range a.
pose proof word.unsigned_range size.
pose proof word.unsigned_range (word.sub a start).
destruct (Z.eq_dec (word.unsigned size) 0) as [Hz|Hnz].
{ rewrite Hz in *. blia. }
replace a with (word.add start (word.mul (word.of_Z (Z.of_nat n)) size)); cycle 1.
... | Lemma | array_address_inbounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array_index_nat_inbounds",
"start",
"word"
] | null | 103 | 135 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Local Coercion Z.of_nat : nat >-> Z. | Z.of_nat : nat >-> Z. | Coercion | Z | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [] | null | 142 | 142 | false | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 | |
Local Notation "xs $@ a" := (map.of_list_word_at a xs) (at level 10, format "xs $@ a"). | "xs $@ a" | := (map.of_list_word_at a xs) (at level 10, format "xs $@ a"). | Notation | xs $@ a | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Notation"
] | null | 144 | 144 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma sep_eq_of_list_word_at_app (a : word) (xs ys : list value)
lxs (Hlxs : Z.of_nat (length xs) = lxs) (Htotal : length xs + length ys <= 2^width)
: Lift1Prop.iff1 ((xs ++ ys)$@a) (sep (xs$@a) (ys$@(word.add a (word.of_Z lxs)))).
Proof.
etransitivity.
2: eapply sep_comm.
etransitivity.
2: ea... | sep_eq_of_list_word_at_app (a : word) (xs ys : list value)
lxs (Hlxs : Z.of_nat (length xs) = lxs) (Htotal : length xs + length ys <= 2^width)
: Lift1Prop.iff1 ((xs ++ ys)$@a) (sep (xs$@a) (ys$@(word.add a (word.of_Z lxs)))). | Proof.
etransitivity.
2: eapply sep_comm.
etransitivity.
2: eapply sep_eq_putmany, map.adjacent_arrays_disjoint_n; trivial.
erewrite map.of_list_word_at_app_n by eauto; reflexivity.
Qed. | Lemma | sep_eq_of_list_word_at_app | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"sep_eq_putmany",
"width",
"word"
] | null | 149 | 158 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma list_word_at_app_of_adjacent_eq (a b : word) (xs ys : list value)
(Hl: word.unsigned (word.sub b a) = Z.of_nat (length xs))
(Htotal : length xs + length ys <= 2^width)
: Lift1Prop.iff1 (xs$@a*ys$@b) ((xs++ys)$@a).
Proof.
etransitivity.
2:symmetry; eapply sep_eq_of_list_word_at_app; trivial.
... | list_word_at_app_of_adjacent_eq (a b : word) (xs ys : list value)
(Hl: word.unsigned (word.sub b a) = Z.of_nat (length xs))
(Htotal : length xs + length ys <= 2^width)
: Lift1Prop.iff1 (xs$@a*ys$@b) ((xs++ys)$@a). | Proof.
etransitivity.
2:symmetry; eapply sep_eq_of_list_word_at_app; trivial.
do 3 Morphisms.f_equiv. rewrite <-Hl, word.of_Z_unsigned. ring.
Qed. | Lemma | list_word_at_app_of_adjacent_eq | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"sep_eq_of_list_word_at_app",
"width",
"word"
] | null | 160 | 168 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma list_word_at_firstn_skipn (p : word) (l : list value) (n : nat) :
(length l >= n)%nat ->
(length l <= 2^width) ->
iff1 (l $@ p) ((firstn n l)$@p * (skipn n l)$@(word.add p (word.of_Z n))).
Proof.
intros.
transitivity ((firstn n l ++ skipn n l) $@ p).
{ rewrite (firstn_skipn n l). exact (... | list_word_at_firstn_skipn (p : word) (l : list value) (n : nat) :
(length l >= n)%nat ->
(length l <= 2^width) ->
iff1 (l $@ p) ((firstn n l)$@p * (skipn n l)$@(word.add p (word.of_Z n))). | Proof.
intros.
transitivity ((firstn n l ++ skipn n l) $@ p).
{ rewrite (firstn_skipn n l). exact (iff1_refl _). }
rewrite (map.of_list_word_at_app_n _ _ _ n) by (rewrite ?length_firstn, ?length_skipn; lia).
unshelve (epose proof (map.adjacent_arrays_disjoint_n p (firstn n l) (skipn n l) n _ _) as H... | Lemma | list_word_at_firstn_skipn | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"sep_eq_putmany",
"width",
"word"
] | null | 170 | 183 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma length_array_ptsto_1_le (default : value) bs (a : word) (m : map) (Hm : array ptsto (word.of_Z 1) a bs m) : Z.of_nat (length bs) <= 2 ^ width.
Proof.
pose proof word.width_pos.
destruct (Z.leb_spec (Z.of_nat (length bs)) (2^width)); trivial; exfalso.
case (@nth_split _ (Z.to_nat (2^width)) bs defaul... | length_array_ptsto_1_le (default : value) bs (a : word) (m : map) (Hm : array ptsto (word.of_Z 1) a bs m) : Z.of_nat (length bs) <= 2 ^ width. | Proof.
pose proof word.width_pos.
destruct (Z.leb_spec (Z.of_nat (length bs)) (2^width)); trivial; exfalso.
case (@nth_split _ (Z.to_nat (2^width)) bs default ltac:(lia)) as (xs&ys&E&L).
rewrite E in Hm;seprewrite_in @array_append Hm.
case xs in *; [simpl length in *; lia|].
rewrite word.unsigne... | Lemma | length_array_ptsto_1_le | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"add_0_r",
"array",
"array_append",
"ecancel_assumption",
"exfalso",
"width",
"word"
] | null | 185 | 195 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array1_iff_eq_of_list_word_at (a : word) (bs : list value)
(H : length bs <= 2 ^ width) : iff1 (array ptsto (word.of_Z 1) a bs) (bs$@a). | array1_iff_eq_of_list_word_at (a : word) (bs : list value)
(H : length bs <= 2 ^ width) : iff1 (array ptsto (word.of_Z 1) a bs) (bs$@a). | Lemma | array1_iff_eq_of_list_word_at | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"array",
"width",
"word"
] | null | 197 | 198 | false | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 | |
Lemma impl1_array : forall T (P Q: word->T->mem->Prop) p a l,
(forall a e, impl1 (P a e) (Q a e)) ->
impl1 (array P p a l) (array Q p a l).
Proof.
intros. generalize dependent a; revert p.
induction l; cbn [array]; eauto; intros; [reflexivity|].
eapply Proper_sep_impl1; eauto.
Qed. | impl1_array : forall T (P Q: word->T->mem->Prop) p a l,
(forall a e, impl1 (P a e) (Q a e)) ->
impl1 (array P p a l) (array Q p a l). | Proof.
intros. generalize dependent a; revert p.
induction l; cbn [array]; eauto; intros; [reflexivity|].
eapply Proper_sep_impl1; eauto.
Qed. | Lemma | impl1_array | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"P",
"Q",
"array",
"mem",
"word"
] | null | 229 | 236 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma impl1_array_with_offset : forall T (P Q: word->T->mem->Prop) sz l a,
(forall i e, List.nth_error l i = Some e ->
let a' := (word.add a (word.of_Z (Z.of_nat i * sz))) in
impl1 (P a' e) (Q a' e)) ->
impl1 (array P (word.of_Z sz) a l) (array Q (word.of_Z sz) a l).
... | impl1_array_with_offset : forall T (P Q: word->T->mem->Prop) sz l a,
(forall i e, List.nth_error l i = Some e ->
let a' := (word.add a (word.of_Z (Z.of_nat i * sz))) in
impl1 (P a' e) (Q a' e)) ->
impl1 (array P (word.of_Z sz) a l) (array Q (word.of_Z sz) a l). | Proof.
induction l; cbn [array]; intros; [reflexivity|].
rename a0 into addr.
eapply Proper_sep_impl1.
- specialize (H O). cbn in H. specialize (H _ eq_refl). rewrite word.add_0_r in H.
exact H.
- eapply IHl. cbv zeta. intros.
specialize (H (S i)). cbn -[Z.of_nat] in H. specialize (H _ H... | Lemma | impl1_array_with_offset | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"P",
"Q",
"Z",
"a0",
"add_0_r",
"addr",
"array",
"mem",
"rename",
"sz",
"word"
] | null | 238 | 255 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_map{T U: Type}(elem: word -> T -> mem -> Prop)(f: U -> T) addr vs sz:
impl1 (array (fun a x => elem a (f x)) sz addr vs)
(array elem sz addr (List.map f vs)).
Proof.
unfold impl1. revert addr. induction vs; intros.
- simpl in *. assumption.
- simpl in *.
destruct H as (... | array_map{T U: Type}(elem: word -> T -> mem -> Prop)(f: U -> T) addr vs sz:
impl1 (array (fun a x => elem a (f x)) sz addr vs)
(array elem sz addr (List.map f vs)). | Proof.
unfold impl1. revert addr. induction vs; intros.
- simpl in *. assumption.
- simpl in *.
destruct H as (m1 & m2 & D & Hm1 & Hm2).
exists m1, m2. eauto.
Qed. | Lemma | array_map | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Type",
"addr",
"array",
"mem",
"sz",
"word"
] | null | 257 | 266 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Local Notation array := (array (mem:=mem) ptsto (word.of_Z 1)). | array | := (array (mem:=mem) ptsto (word.of_Z 1)). | Notation | array | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Notation",
"mem",
"word"
] | null | 272 | 272 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma length_bytearray_le bs (a : word) m (Hm : array a bs m) : Z.of_nat (length bs) <= 2 ^ width.
Proof. eauto using length_array_ptsto_1_le, Byte.x00. Qed. | length_bytearray_le bs (a : word) m (Hm : array a bs m) : Z.of_nat (length bs) <= 2 ^ width. | Proof. eauto using length_array_ptsto_1_le, Byte.x00. Qed. | Lemma | length_bytearray_le | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"length_array_ptsto_1_le",
"width",
"word"
] | null | 275 | 276 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytearray_iff_bytes (a : word) (bs : list byte) :
iff1 (array a bs) ((bs$@a) * emp (Z.of_nat (length bs) <= 2 ^ width)).
Proof.
split; intros; extract_ex1_and_emp_in_hyps; extract_ex1_and_emp_in_goal; ssplit;
try eapply array1_iff_eq_of_list_word_at; eauto using length_bytearray_le.
Qed. | bytearray_iff_bytes (a : word) (bs : list byte) :
iff1 (array a bs) ((bs$@a) * emp (Z.of_nat (length bs) <= 2 ^ width)). | Proof.
split; intros; extract_ex1_and_emp_in_hyps; extract_ex1_and_emp_in_goal; ssplit;
try eapply array1_iff_eq_of_list_word_at; eauto using length_bytearray_le.
Qed. | Lemma | bytearray_iff_bytes | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array1_iff_eq_of_list_word_at",
"length_bytearray_le",
"split",
"width",
"word"
] | null | 278 | 283 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytearray_address_inbounds xs (start : word) a
(Hlen : word.unsigned (word.sub a start) < Z.of_nat (length xs))
(i := Z.to_nat (word.unsigned (word.sub a start)))
: iff1 (array start xs)
(array start (firstn i xs) * (
ptsto a (hd (byte.of_Z 0) (skipn i xs)) *
array (word.add a (w... | bytearray_address_inbounds xs (start : word) a
(Hlen : word.unsigned (word.sub a start) < Z.of_nat (length xs))
(i := Z.to_nat (word.unsigned (word.sub a start)))
: iff1 (array start xs)
(array start (firstn i xs) * (
ptsto a (hd (byte.of_Z 0) (skipn i xs)) *
array (word.add a (word.of... | Proof.
eapply array_address_inbounds;
rewrite ?word.unsigned_of_Z_1, ?Z.mul_1_l, ?Z.mod_1_r, ?Z.div_1_r; auto.
Qed. | Lemma | bytearray_address_inbounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array_address_inbounds",
"start",
"word"
] | null | 285 | 295 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytearray_index_inbounds xs (start iw : word)
(Hlen : word.unsigned iw < Z.of_nat (length xs))
(i := Z.to_nat (word.unsigned iw))
: iff1 (array start xs)
(array start (firstn i xs) * (
ptsto (word.add start iw) (hd (byte.of_Z 0) (skipn i xs)) *
array (word.add (word.add start iw)... | bytearray_index_inbounds xs (start iw : word)
(Hlen : word.unsigned iw < Z.of_nat (length xs))
(i := Z.to_nat (word.unsigned iw))
: iff1 (array start xs)
(array start (firstn i xs) * (
ptsto (word.add start iw) (hd (byte.of_Z 0) (skipn i xs)) *
array (word.add (word.add start iw) (word... | Proof.
rewrite (bytearray_address_inbounds xs start (word.add start iw));
replace (word.sub (word.add start iw) start) with iw; try (reflexivity || assumption).
all : rewrite word.word_sub_add_l_same_l; trivial.
Qed. | Lemma | bytearray_index_inbounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"all",
"array",
"bytearray_address_inbounds",
"start",
"word"
] | null | 297 | 308 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytearray_append xs ys start :
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start (word.of_Z (Z.of_nat (length xs)))) ys).
Proof.
replace (Z.of_nat (length xs))
with (Z.mul (word.unsigned (word.of_Z 1 : word)) (Z.of_nat (length xs)));
auto using array_append; [];... | bytearray_append xs ys start :
iff1 (array start (xs ++ ys))
(array start xs * array (word.add start (word.of_Z (Z.of_nat (length xs)))) ys). | Proof.
replace (Z.of_nat (length xs))
with (Z.mul (word.unsigned (word.of_Z 1 : word)) (Z.of_nat (length xs)));
auto using array_append; []; rewrite word.unsigned_of_Z_1; blia.
Qed. | Lemma | bytearray_append | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"array_append",
"start",
"word"
] | null | 310 | 317 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytearray_index_merge xs ys (start i : word)
(H : word.unsigned i = (Z.of_nat (length xs)))
: iff1 (array start xs * array (word.add start i) ys)
(array start (xs ++ ys)).
Proof.
pose proof word.of_Z_unsigned i as HH; rewrite H in HH.
subst i; symmetry; apply bytearray_append.
Q... | bytearray_index_merge xs ys (start i : word)
(H : word.unsigned i = (Z.of_nat (length xs)))
: iff1 (array start xs * array (word.add start i) ys)
(array start (xs ++ ys)). | Proof.
pose proof word.of_Z_unsigned i as HH; rewrite H in HH.
subst i; symmetry; apply bytearray_append.
Qed. | Lemma | bytearray_index_merge | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"array",
"bytearray_append",
"start",
"word"
] | null | 319 | 326 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma array_1_to_anybytes bs m (a: word) :
array a bs m -> bedrock2.Memory.anybytes a (Z.of_nat (List.length bs)) m.
Proof.
intros H; pose proof length_bytearray_le bs _ m H as Hl.
cbv [bedrock2.Memory.anybytes]; intros; exists bs; ssplit; try lia.
1:eapply array1_iff_eq_of_list_word_at in H; eauto.
... | array_1_to_anybytes bs m (a: word) :
array a bs m -> bedrock2.Memory.anybytes a (Z.of_nat (List.length bs)) m. | Proof.
intros H; pose proof length_bytearray_le bs _ m H as Hl.
cbv [bedrock2.Memory.anybytes]; intros; exists bs; ssplit; try lia.
1:eapply array1_iff_eq_of_list_word_at in H; eauto.
Qed. | Lemma | array_1_to_anybytes | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"anybytes",
"array",
"array1_iff_eq_of_list_word_at",
"length_bytearray_le",
"word"
] | null | 332 | 338 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma anybytes_to_array_1 m (addr : word) n :
bedrock2.Memory.anybytes addr n m ->
exists bs, array addr bs m /\ List.length bs = Z.to_nat n.
Proof.
intros [bs (?&?&?)]; subst m; subst n; exists bs; split; [|lia].
apply array1_iff_eq_of_list_word_at; eauto. reflexivity.
Qed. | anybytes_to_array_1 m (addr : word) n :
bedrock2.Memory.anybytes addr n m ->
exists bs, array addr bs m /\ List.length bs = Z.to_nat n. | Proof.
intros [bs (?&?&?)]; subst m; subst n; exists bs; split; [|lia].
apply array1_iff_eq_of_list_word_at; eauto. reflexivity.
Qed. | Lemma | anybytes_to_array_1 | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/Array.v | [
"Coq",
"ZArith",
"Ring",
"Lia",
"Map.Interface",
"Map.Memory",
"Map.Separation",
"Map.SeparationMemory",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Z.Lia",
"Byte",
"Tactics.eplace",
"Tactics.Tactics",... | [
"Z",
"addr",
"anybytes",
"array",
"array1_iff_eq_of_list_word_at",
"split",
"word"
] | null | 340 | 346 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bytes_per_range sz:
0 < Z.of_nat (Memory.bytes_per (width := width) sz) < 2 ^ width.
Proof using BW. (* Cop out by depending on BW; the previous proof was too bad: *)
clear -BW. destruct sz; simpl.
all: try (destruct width_cases as [-> | ->]; split; reflexivity).
Qed. | bytes_per_range sz:
0 < Z.of_nat (Memory.bytes_per (width := width) sz) < 2 ^ width. | Proof using BW. (* Cop out by depending on BW; the previous proof was too bad: *)
clear -BW. destruct sz; simpl.
all: try (destruct width_cases as [-> | ->]; split; reflexivity).
Qed. | Lemma | bytes_per_range | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"all",
"bytes_per",
"split",
"sz",
"width",
"width_cases"
] | null | 19 | 24 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma testbit_byte_unsigned_ge b n:
8 <= n ->
Z.testbit (byte.unsigned b) n = false.
Proof.
intros;
erewrite prove_Zeq_bitwise.testbit_above;
eauto using byte.unsigned_range;
lia.
Qed. | testbit_byte_unsigned_ge b n:
8 <= n ->
Z.testbit (byte.unsigned b) n = false. | Proof.
intros;
erewrite prove_Zeq_bitwise.testbit_above;
eauto using byte.unsigned_range;
lia.
Qed. | Lemma | testbit_byte_unsigned_ge | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 26 | 34 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma byte_unsigned_land (b1 b2: byte) :
byte.unsigned (byte.and b1 b2) =
Z.land (byte.unsigned b1) (byte.unsigned b2).
Proof.
unfold byte.and; rewrite byte.unsigned_of_Z.
unfold byte.wrap; rewrite <- Z.land_ones.
1: bitblast.Z.bitblast.
1: rewrite testbit_byte_unsigned_ge.
all: lia.
Qed... | byte_unsigned_land (b1 b2: byte) :
byte.unsigned (byte.and b1 b2) =
Z.land (byte.unsigned b1) (byte.unsigned b2). | Proof.
unfold byte.and; rewrite byte.unsigned_of_Z.
unfold byte.wrap; rewrite <- Z.land_ones.
1: bitblast.Z.bitblast.
1: rewrite testbit_byte_unsigned_ge.
all: lia.
Qed. | Lemma | byte_unsigned_land | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"all",
"testbit_byte_unsigned_ge"
] | null | 36 | 45 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma byte_unsigned_xor (b1 b2: byte) :
byte.unsigned (byte.xor b1 b2) =
Z.lxor (byte.unsigned b1) (byte.unsigned b2).
Proof.
unfold byte.xor; rewrite byte.unsigned_of_Z.
unfold byte.wrap; rewrite <- Z.land_ones.
1: bitblast.Z.bitblast.
1: rewrite !testbit_byte_unsigned_ge.
all: reflexiv... | byte_unsigned_xor (b1 b2: byte) :
byte.unsigned (byte.xor b1 b2) =
Z.lxor (byte.unsigned b1) (byte.unsigned b2). | Proof.
unfold byte.xor; rewrite byte.unsigned_of_Z.
unfold byte.wrap; rewrite <- Z.land_ones.
1: bitblast.Z.bitblast.
1: rewrite !testbit_byte_unsigned_ge.
all: reflexivity || lia.
Qed. | Lemma | byte_unsigned_xor | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"all",
"testbit_byte_unsigned_ge"
] | null | 47 | 56 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma byte_xor_comm b1 b2:
byte.xor b1 b2 = byte.xor b2 b1.
Proof. unfold byte.xor; rewrite Z.lxor_comm; reflexivity. Qed. | byte_xor_comm b1 b2:
byte.xor b1 b2 = byte.xor b2 b1. | Proof. unfold byte.xor; rewrite Z.lxor_comm; reflexivity. Qed. | Lemma | byte_xor_comm | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 58 | 60 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma Z_land_le_combine bs1 : forall bs2,
Z.land (le_combine bs1) (le_combine bs2) =
le_combine (List.map (fun '(x, y) => byte.and x y) (combine bs1 bs2)).
Proof.
induction bs1.
- reflexivity.
- destruct bs2; [ apply Z.land_0_r | ]; cbn -[Z.shiftl] in *.
rewrite <- IHbs1, !byte_unsigned_... | Z_land_le_combine bs1 : forall bs2,
Z.land (le_combine bs1) (le_combine bs2) =
le_combine (List.map (fun '(x, y) => byte.and x y) (combine bs1 bs2)). | Proof.
induction bs1.
- reflexivity.
- destruct bs2; [ apply Z.land_0_r | ]; cbn -[Z.shiftl] in *.
rewrite <- IHbs1, !byte_unsigned_land, !Z.shiftl_land.
bitblast.Z.bitblast.
assert (l < 0 \/ 8 <= i) as [Hlt | Hge] by lia.
+ rewrite !(Z.testbit_neg_r _ l) by assumption.
rewri... | Lemma | Z_land_le_combine | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"assert",
"byte_unsigned_land",
"testbit_byte_unsigned_ge"
] | null | 62 | 76 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition in_bounds n x :=
0 <= x < 2 ^ n. | in_bounds n x | :=
0 <= x < 2 ^ n. | Definition | in_bounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [] | null | 78 | 79 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma forall_in_bounds l n:
0 <= n ->
(Forall (in_bounds n) l) <-> (forall i, in_bounds n (nth i l 0)).
Proof.
intros; pose proof Z.pow_pos_nonneg 2 n.
rewrite List.Forall_nth_default' with (d := 0);
unfold in_bounds; reflexivity || lia.
Qed. | forall_in_bounds l n:
0 <= n ->
(Forall (in_bounds n) l) <-> (forall i, in_bounds n (nth i l 0)). | Proof.
intros; pose proof Z.pow_pos_nonneg 2 n.
rewrite List.Forall_nth_default' with (d := 0);
unfold in_bounds; reflexivity || lia.
Qed. | Lemma | forall_in_bounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"in_bounds",
"nth"
] | null | 81 | 88 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma le_combine_in_bounds bs n:
(length bs <= n)%nat ->
in_bounds (8 * Z.of_nat n) (le_combine bs).
Proof.
unfold in_bounds; intros.
pose proof le_combine_bound bs.
pose proof Zpow_facts.Zpower_le_monotone 2 (8 * Z.of_nat (length bs)) (8 * Z.of_nat n)
ltac:(lia) ltac:(lia); lia.
Qed. | le_combine_in_bounds bs n:
(length bs <= n)%nat ->
in_bounds (8 * Z.of_nat n) (le_combine bs). | Proof.
unfold in_bounds; intros.
pose proof le_combine_bound bs.
pose proof Zpow_facts.Zpower_le_monotone 2 (8 * Z.of_nat (length bs)) (8 * Z.of_nat n)
ltac:(lia) ltac:(lia); lia.
Qed. | Lemma | le_combine_in_bounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"in_bounds"
] | null | 90 | 98 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma Forall_le_combine_in_bounds n zs:
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) (List.map le_combine (List.chunk n zs)).
Proof.
intros; eapply Forall_map, Forall_impl.
- intros a; apply le_combine_in_bounds.
- eapply Forall_impl; [ | apply List.Forall_chunk_length_le ];
simpl; i... | Forall_le_combine_in_bounds n zs:
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) (List.map le_combine (List.chunk n zs)). | Proof.
intros; eapply Forall_map, Forall_impl.
- intros a; apply le_combine_in_bounds.
- eapply Forall_impl; [ | apply List.Forall_chunk_length_le ];
simpl; intros; lia.
Qed. | Lemma | Forall_le_combine_in_bounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"in_bounds",
"le_combine_in_bounds"
] | null | 100 | 108 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma le_split_0_l z:
le_split 0 z = nil.
Proof. reflexivity. Qed. | le_split_0_l z:
le_split 0 z = nil. | Proof. reflexivity. Qed. | Lemma | le_split_0_l | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [] | null | 110 | 112 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma le_split_0_r n:
le_split n 0 = repeat Byte.x00 n.
Proof.
induction n.
- reflexivity.
- unfold le_split; fold le_split.
rewrite Z.shiftr_0_l, IHn; reflexivity.
Qed. | le_split_0_r n:
le_split n 0 = repeat Byte.x00 n. | Proof.
induction n.
- reflexivity.
- unfold le_split; fold le_split.
rewrite Z.shiftr_0_l, IHn; reflexivity.
Qed. | Lemma | le_split_0_r | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 114 | 121 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma le_split_zeroes : forall m n z,
0 <= z < 2 ^ (8 * Z.of_nat n) ->
le_split (n + m) z = le_split n z ++ le_split m 0.
Proof.
induction n; cbn -[Z.pow Z.of_nat Z.shiftr]; intros * (Hle & Hlt).
- replace z with 0 by lia; reflexivity.
- rewrite IHn, !le_split_0_r; try reflexivity; [].
r... | le_split_zeroes : forall m n z,
0 <= z < 2 ^ (8 * Z.of_nat n) ->
le_split (n + m) z = le_split n z ++ le_split m 0. | Proof.
induction n; cbn -[Z.pow Z.of_nat Z.shiftr]; intros * (Hle & Hlt).
- replace z with 0 by lia; reflexivity.
- rewrite IHn, !le_split_0_r; try reflexivity; [].
rewrite Z.shiftr_div_pow2 by lia; split.
+ apply Z.div_pos; lia.
+ replace (8 * Z.of_nat (S n))%Z with (8 + 8 * Z.of_nat n)%Z... | Lemma | le_split_zeroes | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"le_split_0_r",
"split"
] | null | 125 | 137 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma flat_map_le_split_combine_chunk:
forall bs n,
(0 < n)%nat ->
(length bs mod n)%nat = 0%nat ->
flat_map (le_split n) (List.map le_combine (List.chunk n bs)) = bs.
Proof.
intros.
rewrite flat_map_concat_map, map_map, List.map_ext_id, List.concat_chunk; [reflexivity|].
intros * Hi... | flat_map_le_split_combine_chunk:
forall bs n,
(0 < n)%nat ->
(length bs mod n)%nat = 0%nat ->
flat_map (le_split n) (List.map le_combine (List.chunk n bs)) = bs. | Proof.
intros.
rewrite flat_map_concat_map, map_map, List.map_ext_id, List.concat_chunk; [reflexivity|].
intros * Hin;
pose proof (List.Forall_In (@List.Forall_chunk_length_mod _ n ltac:(lia) _) Hin);
pose proof (List.Forall_In (@List.Forall_chunk_length_le _ n ltac:(lia) _) Hin);
cbv beta... | Lemma | flat_map_le_split_combine_chunk | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [] | null | 139 | 152 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma map_le_combine_chunk_split:
forall zs n,
(0 < n)%nat ->
List.map le_combine (List.chunk n (flat_map (le_split n) zs)) =
List.map (fun z => z mod 2 ^ (Z.of_nat n * 8)) zs.
Proof.
induction zs; simpl; intros.
- reflexivity.
- rewrite List.chunk_app by (rewrite ?length_le_split, ?... | map_le_combine_chunk_split:
forall zs n,
(0 < n)%nat ->
List.map le_combine (List.chunk n (flat_map (le_split n) zs)) =
List.map (fun z => z mod 2 ^ (Z.of_nat n * 8)) zs. | Proof.
induction zs; simpl; intros.
- reflexivity.
- rewrite List.chunk_app by (rewrite ?length_le_split, ?Nat.Div0.mod_same; lia).
rewrite map_app, IHzs by lia.
rewrite le_combine_chunk_split by lia; reflexivity.
Qed. | Lemma | map_le_combine_chunk_split | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 154 | 165 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma map_le_combine_chunk_split_le:
forall zs n,
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) zs ->
List.map le_combine (List.chunk n (flat_map (le_split n) zs)) = zs.
Proof.
intros * Hlt Hle; rewrite map_le_combine_chunk_split by lia.
apply List.map_ext_id.
intros * Hin%(List... | map_le_combine_chunk_split_le:
forall zs n,
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) zs ->
List.map le_combine (List.chunk n (flat_map (le_split n) zs)) = zs. | Proof.
intros * Hlt Hle; rewrite map_le_combine_chunk_split by lia.
apply List.map_ext_id.
intros * Hin%(List.Forall_In Hle).
apply Z.mod_small.
rewrite Z.mul_comm; assumption.
Qed. | Lemma | map_le_combine_chunk_split_le | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"in_bounds",
"map_le_combine_chunk_split"
] | null | 167 | 178 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma map_unsigned_of_Z_le_combine bs:
let k := Z.to_nat (bytes_per_word width) in
List.map (fun z : Z => word.unsigned (word := word) (word.of_Z z))
(List.map le_combine (List.chunk k bs)) =
List.map le_combine (List.chunk k bs).
Proof.
cbv zeta. rewrite List.map_ext_id; [ reflexivity | ... | map_unsigned_of_Z_le_combine bs:
let k := Z.to_nat (bytes_per_word width) in
List.map (fun z : Z => word.unsigned (word := word) (word.of_Z z))
(List.map le_combine (List.chunk k bs)) =
List.map le_combine (List.chunk k bs). | Proof.
cbv zeta. rewrite List.map_ext_id; [ reflexivity | ].
intros * Hin.
apply word.unsigned_of_Z_nowrap.
pose proof word.width_pos.
eapply List.Forall_In in Hin.
2: eapply Forall_le_combine_in_bounds.
1: unfold in_bounds in Hin.
all: unfold bytes_per_word in *.
2: PreOmega.Z.to_eu... | Lemma | map_unsigned_of_Z_le_combine | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Forall_le_combine_in_bounds",
"Z",
"all",
"bytes_per_word",
"in_bounds",
"split",
"width",
"width_cases",
"word"
] | null | 180 | 200 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma le_combine_nth_chunk n (bs: list byte) idx dd:
n <> 0%nat ->
(idx < List.Nat.div_up (Datatypes.length bs) n)%nat ->
le_combine (nth idx (List.chunk n bs) dd) =
le_combine (List.map (fun idx => nth idx bs Byte.x00) (seq (idx * n) n)).
Proof.
intros.
rewrite List.nth_chunk by assumption.
... | le_combine_nth_chunk n (bs: list byte) idx dd:
n <> 0%nat ->
(idx < List.Nat.div_up (Datatypes.length bs) n)%nat ->
le_combine (nth idx (List.chunk n bs) dd) =
le_combine (List.map (fun idx => nth idx bs Byte.x00) (seq (idx * n) n)). | Proof.
intros.
rewrite List.nth_chunk by assumption.
rewrite List.map_seq_nth_slice, le_combine_app_0.
reflexivity.
Qed. | Lemma | le_combine_nth_chunk | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"nth"
] | null | 202 | 212 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma In_map_combine_in_bounds n (Hn: n <> 0%nat) bs a:
In a (List.map le_combine (List.chunk n bs)) ->
0 <= a < 2 ^ (8 * Z.of_nat n).
Proof.
intros; eapply (List.Forall_In (Forall_le_combine_in_bounds n bs ltac:(lia)));
eassumption.
Qed. | In_map_combine_in_bounds n (Hn: n <> 0%nat) bs a:
In a (List.map le_combine (List.chunk n bs)) ->
0 <= a < 2 ^ (8 * Z.of_nat n). | Proof.
intros; eapply (List.Forall_In (Forall_le_combine_in_bounds n bs ltac:(lia)));
eassumption.
Qed. | Lemma | In_map_combine_in_bounds | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Forall_le_combine_in_bounds",
"Z"
] | null | 214 | 220 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition bs2zs n (bs: list byte) : list Z :=
List.map le_combine (List.chunk n bs). | bs2zs n (bs: list byte) : list Z | :=
List.map le_combine (List.chunk n bs). | Definition | bs2zs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 222 | 223 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition zs2bs n (zs: list Z): list byte :=
List.flat_map (le_split n) zs. | zs2bs n (zs: list Z): list byte | :=
List.flat_map (le_split n) zs. | Definition | zs2bs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z"
] | null | 224 | 225 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bs2zs2bs n bs:
(0 < n)%nat ->
(List.length bs mod n = 0)%nat ->
zs2bs n (bs2zs n bs) = bs.
Proof. apply flat_map_le_split_combine_chunk. Qed. | bs2zs2bs n bs:
(0 < n)%nat ->
(List.length bs mod n = 0)%nat ->
zs2bs n (bs2zs n bs) = bs. | Proof. apply flat_map_le_split_combine_chunk. Qed. | Lemma | bs2zs2bs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"bs2zs",
"flat_map_le_split_combine_chunk",
"zs2bs"
] | null | 227 | 231 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma zs2bs2zs n zs:
(0 < n)%nat ->
bs2zs n (zs2bs n zs) =
List.map (fun z => z mod 2 ^ (Z.of_nat n * 8)) zs.
Proof. apply map_le_combine_chunk_split. Qed. | zs2bs2zs n zs:
(0 < n)%nat ->
bs2zs n (zs2bs n zs) =
List.map (fun z => z mod 2 ^ (Z.of_nat n * 8)) zs. | Proof. apply map_le_combine_chunk_split. Qed. | Lemma | zs2bs2zs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"bs2zs",
"map_le_combine_chunk_split",
"zs2bs"
] | null | 233 | 237 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma zs2bs2zs_le n zs:
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) zs ->
bs2zs n (zs2bs n zs) = zs.
Proof. apply map_le_combine_chunk_split_le. Qed. | zs2bs2zs_le n zs:
(0 < n)%nat ->
Forall (in_bounds (8 * Z.of_nat n)) zs ->
bs2zs n (zs2bs n zs) = zs. | Proof. apply map_le_combine_chunk_split_le. Qed. | Lemma | zs2bs2zs_le | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"Z",
"bs2zs",
"in_bounds",
"map_le_combine_chunk_split_le",
"zs2bs"
] | null | 239 | 243 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition zs2ws := List.map (word.of_Z (word := word)). | zs2ws | := List.map (word.of_Z (word := word)). | Definition | zs2ws | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"word"
] | null | 245 | 245 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition ws2zs := List.map (word.unsigned (word := word)). | ws2zs | := List.map (word.unsigned (word := word)). | Definition | ws2zs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"word"
] | null | 246 | 246 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma ws2zs2ws ws:
zs2ws (ws2zs ws) = ws.
Proof.
unfold zs2ws, ws2zs; rewrite map_map; apply List.map_ext_id.
intros; apply word.of_Z_unsigned.
Qed. | ws2zs2ws ws:
zs2ws (ws2zs ws) = ws. | Proof.
unfold zs2ws, ws2zs; rewrite map_map; apply List.map_ext_id.
intros; apply word.of_Z_unsigned.
Qed. | Lemma | ws2zs2ws | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"word",
"ws2zs",
"zs2ws"
] | null | 248 | 253 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma zs2ws2zs zs:
ws2zs (zs2ws zs) =
List.map word.wrap zs.
Proof.
unfold zs2ws, ws2zs; rewrite map_map; apply map_ext.
intros; apply word.unsigned_of_Z.
Qed. | zs2ws2zs zs:
ws2zs (zs2ws zs) =
List.map word.wrap zs. | Proof.
unfold zs2ws, ws2zs; rewrite map_map; apply map_ext.
intros; apply word.unsigned_of_Z.
Qed. | Lemma | zs2ws2zs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"word",
"ws2zs",
"zs2ws"
] | null | 255 | 261 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma zs2ws2zs_le zs:
Forall (in_bounds width) zs ->
ws2zs (zs2ws zs) = zs.
Proof.
unfold zs2ws, ws2zs; intros Hzs.
rewrite map_map; apply List.map_ext_id; intros z Hin%(List.Forall_In Hzs).
apply word.unsigned_of_Z_nowrap; assumption.
Qed. | zs2ws2zs_le zs:
Forall (in_bounds width) zs ->
ws2zs (zs2ws zs) = zs. | Proof.
unfold zs2ws, ws2zs; intros Hzs.
rewrite map_map; apply List.map_ext_id; intros z Hin%(List.Forall_In Hzs).
apply word.unsigned_of_Z_nowrap; assumption.
Qed. | Lemma | zs2ws2zs_le | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"in_bounds",
"width",
"word",
"ws2zs",
"zs2ws"
] | null | 263 | 270 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition bs2ws n (bs: list byte) : list word :=
zs2ws (bs2zs n bs). | bs2ws n (bs: list byte) : list word | :=
zs2ws (bs2zs n bs). | Definition | bs2ws | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"bs2zs",
"word",
"zs2ws"
] | null | 272 | 273 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Definition ws2bs n (ws: list word): list byte :=
zs2bs n (ws2zs ws). | ws2bs n (ws: list word): list byte | :=
zs2bs n (ws2zs ws). | Definition | ws2bs | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"word",
"ws2zs",
"zs2bs"
] | null | 274 | 275 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma zs2ws_length zs :
length (zs2ws zs) = length zs.
Proof. apply map_length. Qed. | zs2ws_length zs :
length (zs2ws zs) = length zs. | Proof. apply map_length. Qed. | Lemma | zs2ws_length | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"zs2ws"
] | null | 280 | 282 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bs2zs_length' n bs :
n <> 0 ->
length (bs2zs n bs) = List.Nat.div_up (length bs) n.
Proof.
unfold bs2zs; intros.
rewrite map_length, List.length_chunk, List.Nat.div_up_eqn.
all: auto.
Qed. | bs2zs_length' n bs :
n <> 0 ->
length (bs2zs n bs) = List.Nat.div_up (length bs) n. | Proof.
unfold bs2zs; intros.
rewrite map_length, List.length_chunk, List.Nat.div_up_eqn.
all: auto.
Qed. | Lemma | bs2zs_length' | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"all",
"bs2zs"
] | null | 284 | 291 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma div_up_mod_eq a b:
b <> 0 ->
a mod b = 0 ->
List.Nat.div_up a b = a / b.
Proof. intros H0 Hm; rewrite List.Nat.div_up_eqn, Hm; auto. Qed. | div_up_mod_eq a b:
b <> 0 ->
a mod b = 0 ->
List.Nat.div_up a b = a / b. | Proof. intros H0 Hm; rewrite List.Nat.div_up_eqn, Hm; auto. Qed. | Lemma | div_up_mod_eq | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [] | null | 293 | 297 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
Lemma bs2zs_length n bs :
(n <> 0)%nat ->
(length bs mod n = 0)%nat ->
length (bs2zs n bs) = (length bs / n)%nat.
Proof.
intros; rewrite bs2zs_length', div_up_mod_eq by assumption; reflexivity.
Qed. | bs2zs_length n bs :
(n <> 0)%nat ->
(length bs mod n = 0)%nat ->
length (bs2zs n bs) = (length bs / n)%nat. | Proof.
intros; rewrite bs2zs_length', div_up_mod_eq by assumption; reflexivity.
Qed. | Lemma | bs2zs_length | bedrock2.src.bedrock2 | bedrock2/src/bedrock2/ArrayCasts.v | [
"Map.Interface",
"Map.Separation",
"Map.SeparationLogic",
"Lift1Prop",
"Memory",
"Coq.Lists.List",
"Coq.ZArith.BinInt",
"Word.Interface",
"Word.Properties",
"Word.Bitwidth",
"Z.Lia",
"Coq.micromega.Lia",
"Byte",
"Coq.Arith.PeanoNat",
"Word.LittleEndianList",
"Array",
"Scalars",
"Zn... | [
"bs2zs",
"bs2zs_length'",
"div_up_mod_eq"
] | null | 299 | 305 | true | https://github.com/mit-plv/bedrock2 | c25e0e99557a6d71673d81c09b4fb24c048a2811 |
End of preview. Expand in Data Studio
Coq-Bedrock
A work-in-progress language and compiler for verified low-level programming targeting RISC-V.
Source
- Repository: https://github.com/mit-plv/bedrock2
- Commit:
c25e0e99557a6d71673d81c09b4fb24c048a2811 - Files: 290
- License: mit
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Complete verbatim declaration (keyword, signature, and body/proof) |
| statement | string | Signature with the leading keyword removed (verbatim slice) |
| proof | string | Verbatim proof/body, empty if none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level Require/Import modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, null if absent |
| line_start | int | First source line |
| line_end | int | Last source line |
| has_proof | bool | Whether a proof block was captured |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
Statistics
- Entries: 6,033
- With proof: 5,838 (96.8%)
- With docstring: 769 (12.7%)
- Libraries: 14
By type
| Type | Count |
|---|---|
| Lemma | 1,858 |
| Definition | 1,551 |
| Ltac | 894 |
| Notation | 822 |
| Instance | 325 |
| Fixpoint | 149 |
| Ltac2 | 141 |
| Inductive | 83 |
| Hypothesis | 50 |
| Record | 40 |
| Let | 33 |
| Axiom | 22 |
| Class | 18 |
| Coercion | 13 |
| Parameter | 7 |
| Example | 6 |
| Remark | 6 |
| Scheme | 5 |
| Theorem | 4 |
| Hypotheses | 3 |
| Variant | 1 |
| Parameters | 1 |
| Fact | 1 |
Example
Lemma Z__range_add a0 a a1 (Ha: a0 <= a < a1) b0 b b1 (Hb : b0 <= b < b1)
: a0+b0 <= a+b < a1 + b1 - 1.
Proof. Lia.nia. Qed.
- type: Lemma | symbolic_name:
Z__range_add| bedrock2/src/bedrock2/AbsintWordToZ.v:9
Use
Statement and proof are available both joined (fact) and split (statement, proof) for
proof-term modeling, autoformalization, retrieval, and dependency analysis via deps.
Citation
@misc{coq_bedrock_dataset,
title = {Coq-Bedrock},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/mit-plv/bedrock2, commit c25e0e99557a},
url = {https://huggingface.co/datasets/phanerozoic/Coq-Bedrock}
}
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