diff options
| -rw-r--r-- | backend/Duplicate.v | 24 | ||||
| -rw-r--r-- | backend/Duplicateproof.v | 7 | ||||
| -rw-r--r-- | common/AST.v | 19 | ||||
| -rw-r--r-- | lib/Floats.v | 63 | ||||
| -rw-r--r-- | lib/Integers.v | 38 |
5 files changed, 138 insertions, 13 deletions
diff --git a/backend/Duplicate.v b/backend/Duplicate.v index a5e7d92a..c313e3fa 100644 --- a/backend/Duplicate.v +++ b/backend/Duplicate.v @@ -53,6 +53,20 @@ Proof. intros H H'. intros. decide equality. Qed. +(** FIXME Ideally i would like to put this in AST.v but i get an "illegal application" + * error when doing so *) +Remark builtin_arg_eq_pos: forall (a b: builtin_arg positive), {a=b} + {a<>b}. +Proof. + intros. + apply (builtin_arg_eq Pos.eq_dec). +Defined. +Global Opaque builtin_arg_eq_pos. + +Remark builtin_res_eq_pos: forall (a b: builtin_res positive), {a=b} + {a<>b}. +Proof. intros. apply (builtin_res_eq Pos.eq_dec). Qed. +Global Opaque builtin_res_eq_pos. + + Definition verify_match_inst revmap inst tinst := match inst with | Inop n => match tinst with Inop n' => do u <- verify_is_copy revmap n n'; OK tt | _ => Error(msg "verify_match_inst Inop") end @@ -103,6 +117,16 @@ Definition verify_match_inst revmap inst tinst := else Error (msg "Different ri in Icall") else Error (msg "Different signatures in Icall") | _ => Error (msg "verify_match_inst Icall") end + | Ibuiltin ef lbar brr n => match tinst with + | Ibuiltin ef' lbar' brr' n' => + do u <- verify_is_copy revmap n n'; + if (external_function_eq ef ef') then + if (list_eq_dec builtin_arg_eq_pos lbar lbar') then + if (builtin_res_eq_pos brr brr') then OK tt + else Error (msg "Different brr in Ibuiltin") + else Error (msg "Different lbar in Ibuiltin") + else Error (msg "Different ef in Ibuiltin") + | _ => Error (msg "verify_match_inst Ibuiltin") end | _ => Error(msg "not implemented") end. diff --git a/backend/Duplicateproof.v b/backend/Duplicateproof.v index e9799f08..7369c3ea 100644 --- a/backend/Duplicateproof.v +++ b/backend/Duplicateproof.v @@ -114,6 +114,13 @@ Proof. destruct (Pos.eq_dec _ _); try discriminate. eapply verify_is_copy_correct_one. destruct x. eassumption. subst. constructor. +(* Ibuiltin *) + - destruct i'; try (inversion H; fail). monadInv H. + destruct (external_function_eq _ _); try discriminate. + destruct (list_eq_dec _ _ _); try discriminate. + destruct (builtin_res_eq_pos _ _); try discriminate. + eapply verify_is_copy_correct_one. destruct x. eassumption. subst. + constructor. Qed. Lemma verify_mapping_mn_correct: diff --git a/common/AST.v b/common/AST.v index a91138c9..7ffe355d 100644 --- a/common/AST.v +++ b/common/AST.v @@ -17,7 +17,7 @@ the abstract syntax trees of many of the intermediate languages. *) Require Import String. -Require Import Coqlib Maps Errors Integers Floats. +Require Import Coqlib Maps Errors Integers Floats BinPos. Require Archi. Set Implicit Arguments. @@ -630,11 +630,28 @@ Inductive builtin_arg (A: Type) : Type := | BA_splitlong (hi lo: builtin_arg A) | BA_addptr (a1 a2: builtin_arg A). +Definition builtin_arg_eq {A: Type}: + (forall x y : A, {x = y} + {x <> y}) -> + forall (ba1 ba2: (builtin_arg A)), {ba1=ba2} + {ba1<>ba2}. +Proof. + intro. generalize Integers.int_eq int64_eq float_eq float32_eq chunk_eq ptrofs_eq ident_eq. + decide equality. +Defined. +Global Opaque builtin_arg_eq. + Inductive builtin_res (A: Type) : Type := | BR (x: A) | BR_none | BR_splitlong (hi lo: builtin_res A). +Definition builtin_res_eq {A: Type}: + (forall x y : A, {x = y} + {x <> y}) -> + forall (a b: builtin_res A), {a=b} + {a<>b}. +Proof. + intro. decide equality. +Defined. +Global Opaque builtin_res_eq. + Fixpoint globals_of_builtin_arg (A: Type) (a: builtin_arg A) : list ident := match a with | BA_loadglobal chunk id ofs => id :: nil diff --git a/lib/Floats.v b/lib/Floats.v index 13350dd0..272efa52 100644 --- a/lib/Floats.v +++ b/lib/Floats.v @@ -16,7 +16,7 @@ (** Formalization of floating-point numbers, using the Flocq library. *) -Require Import Coqlib Zbits Integers. +Require Import Coqlib Zbits Integers Axioms. (*From Flocq*) Require Import Binary Bits Core. Require Import IEEE754_extra. @@ -27,8 +27,69 @@ Close Scope R_scope. Open Scope Z_scope. Definition float := binary64. (**r the type of IEE754 double-precision FP numbers *) + +Definition float_eq: forall (i1 i2: float), {i1=i2} + {i1<>i2}. +Proof. + intros. destruct i1. +(* B754_zero *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_infinity *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_nan *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + generalize (Pos.eq_dec pl pl0). intro. inv H. + ++ left. apply eqb_prop in BEQ. subst. + assert (e = e0) by (apply proof_irr). congruence. + ++ right. intro. inv H. contradiction. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_finite *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ; [apply eqb_prop in BEQ | apply eqb_false_iff in BEQ]. + generalize (Pos.eq_dec m m0). intro. inv H. + generalize (Z.eq_dec e e1). intro. inv H. + 1: { left. assert (e0 = e2) by (apply proof_irr). congruence. } + all: right; intro; inv H; contradiction. +Qed. + Definition float32 := binary32. (**r the type of IEE754 single-precision FP numbers *) +Definition float32_eq: forall (i1 i2: float32), {i1=i2} + {i1<>i2}. +Proof. + intros. destruct i1. +(* B754_zero *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_infinity *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + apply eqb_prop in BEQ. subst. left. reflexivity. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_nan *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ. + + generalize (Pos.eq_dec pl pl0). intro. inv H. + ++ left. apply eqb_prop in BEQ. subst. + assert (e = e0) by (apply proof_irr). congruence. + ++ right. intro. inv H. contradiction. + + apply eqb_false_iff in BEQ. right. intro. inv H. contradiction. +(* B754_finite *) + - destruct i2; try (right; discriminate). + destruct (eqb s s0) eqn:BEQ; [apply eqb_prop in BEQ | apply eqb_false_iff in BEQ]. + generalize (Pos.eq_dec m m0). intro. inv H. + generalize (Z.eq_dec e e1). intro. inv H. + 1: { left. assert (e0 = e2) by (apply proof_irr). congruence. } + all: right; intro; inv H; contradiction. +Qed. + (** Boolean-valued comparisons *) Definition cmp_of_comparison (c: comparison) (x: option Datatypes.comparison) : bool := diff --git a/lib/Integers.v b/lib/Integers.v index fca44b1e..9c6fcf1d 100644 --- a/lib/Integers.v +++ b/lib/Integers.v @@ -101,17 +101,6 @@ Hint Resolve modulus_pos: ints. Record int: Type := mkint { intval: Z; intrange: -1 < intval < modulus }. -Definition int_eq: forall (i1 i2: int), {i1=i2} + {i1<>i2}. -Proof. - generalize Z.eq_dec. intros. - destruct i1. destruct i2. generalize (H intval0 intval1). intro. - inversion H0. - - subst. left. assert (intrange0 = intrange1) by (apply proof_irr). congruence. - - right. intro. inversion H2. contradiction. -Qed. - -(* TODO - continue for the rest *) - (** Fast normalization modulo [2^wordsize] *) Definition Z_mod_modulus (x: Z) : Z := @@ -4167,8 +4156,26 @@ End Int64. Strategy 0 [Wordsize_64.wordsize]. +Definition int_eq: forall (i1 i2: int), {i1=i2} + {i1<>i2}. +Proof. + generalize Z.eq_dec. intros. + destruct i1. destruct i2. generalize (H intval intval0). intro. + inversion H0. + - subst. left. assert (intrange = intrange0) by (apply proof_irr). congruence. + - right. intro. inversion H2. contradiction. +Qed. + Notation int64 := Int64.int. +Definition int64_eq: forall (i1 i2: int64), {i1=i2} + {i1<>i2}. +Proof. + generalize Z.eq_dec. intros. + destruct i1. destruct i2. generalize (H intval intval0). intro. + inversion H0. + - subst. left. assert (intrange = intrange0) by (apply proof_irr). congruence. + - right. intro. inversion H2. contradiction. +Qed. + Global Opaque Int.repr Int64.repr Byte.repr. (** * Specialization to offsets in pointer values *) @@ -4445,6 +4452,15 @@ Strategy 0 [Wordsize_Ptrofs.wordsize]. Notation ptrofs := Ptrofs.int. +Definition ptrofs_eq: forall (i1 i2: ptrofs), {i1=i2} + {i1<>i2}. +Proof. + generalize Z.eq_dec. intros. + destruct i1. destruct i2. generalize (H intval intval0). intro. + inversion H0. + - subst. left. assert (intrange = intrange0) by (apply proof_irr). congruence. + - right. intro. inversion H2. contradiction. +Qed. + Global Opaque Ptrofs.repr. Hint Resolve Int.modulus_pos Int.eqm_refl Int.eqm_refl2 Int.eqm_sym Int.eqm_trans |