diff options
author | xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e> | 2006-09-18 15:52:24 +0000 |
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committer | xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e> | 2006-09-18 15:52:24 +0000 |
commit | 165407527b1be7df6a376791719321c788e55149 (patch) | |
tree | 35c2eb9603f007b033fced56f21fa49fd105562f /backend/Cmconstrproof.v | |
parent | 1346309fd03e19da52156a700d037c348f27af0d (diff) | |
download | compcert-165407527b1be7df6a376791719321c788e55149.tar.gz compcert-165407527b1be7df6a376791719321c788e55149.zip |
Simplification de Cminor: les affectations de variables locales ne sont
plus des expressions mais des statements (Eassign -> Sassign).
Cela simplifie les preuves et ameliore la qualite du RTL produit.
git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@111 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
Diffstat (limited to 'backend/Cmconstrproof.v')
-rw-r--r-- | backend/Cmconstrproof.v | 580 |
1 files changed, 290 insertions, 290 deletions
diff --git a/backend/Cmconstrproof.v b/backend/Cmconstrproof.v index b9976eec..35b3d8a0 100644 --- a/backend/Cmconstrproof.v +++ b/backend/Cmconstrproof.v @@ -67,38 +67,38 @@ Scheme eval_expr_ind_3 := Minimality for eval_expr Sort Prop with eval_condexpr_ind_3 := Minimality for eval_condexpr Sort Prop with eval_exprlist_ind_3 := Minimality for eval_exprlist Sort Prop. -Hint Resolve eval_Evar eval_Eassign eval_Eop eval_Eload eval_Estore +Hint Resolve eval_Evar eval_Eop eval_Eload eval_Estore eval_Ecall eval_Econdition eval_Ealloc eval_Elet eval_Eletvar eval_CEtrue eval_CEfalse eval_CEcond eval_CEcondition eval_Enil eval_Econs: evalexpr. Lemma eval_list_one: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_exprlist ge sp le e1 m1 (a ::: Enil) t e2 m2 (v :: nil). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_exprlist ge sp le e m1 (a ::: Enil) t m2 (v :: nil). Proof. intros. econstructor. eauto. constructor. traceEq. Qed. Lemma eval_list_two: - forall sp le e1 m1 a1 t1 e2 m2 v1 a2 t2 e3 m3 v2 t, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 -> + forall sp le e m1 a1 t1 m2 v1 a2 t2 m3 v2 t, + eval_expr ge sp le e m1 a1 t1 m2 v1 -> + eval_expr ge sp le e m2 a2 t2 m3 v2 -> t = t1 ** t2 -> - eval_exprlist ge sp le e1 m1 (a1 ::: a2 ::: Enil) t e3 m3 (v1 :: v2 :: nil). + eval_exprlist ge sp le e m1 (a1 ::: a2 ::: Enil) t m3 (v1 :: v2 :: nil). Proof. intros. econstructor. eauto. econstructor. eauto. constructor. reflexivity. traceEq. Qed. Lemma eval_list_three: - forall sp le e1 m1 a1 t1 e2 m2 v1 a2 t2 e3 m3 v2 a3 t3 e4 m4 v3 t, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 -> - eval_expr ge sp le e3 m3 a3 t3 e4 m4 v3 -> + forall sp le e m1 a1 t1 m2 v1 a2 t2 m3 v2 a3 t3 m4 v3 t, + eval_expr ge sp le e m1 a1 t1 m2 v1 -> + eval_expr ge sp le e m2 a2 t2 m3 v2 -> + eval_expr ge sp le e m3 a3 t3 m4 v3 -> t = t1 ** t2 ** t3 -> - eval_exprlist ge sp le e1 m1 (a1 ::: a2 ::: a3 ::: Enil) t e4 m4 (v1 :: v2 :: v3 :: nil). + eval_exprlist ge sp le e m1 (a1 ::: a2 ::: a3 ::: Enil) t m4 (v1 :: v2 :: v3 :: nil). Proof. intros. econstructor. eauto. econstructor. eauto. econstructor. eauto. constructor. reflexivity. reflexivity. traceEq. @@ -107,22 +107,22 @@ Qed. Hint Resolve eval_list_one eval_list_two eval_list_three: evalexpr. Lemma eval_lift_expr: - forall w sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall w sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> forall p le', insert_lenv le p w le' -> - eval_expr ge sp le' e1 m1 (lift_expr p a) t e2 m2 v. + eval_expr ge sp le' e m1 (lift_expr p a) t m2 v. Proof. intros w. apply (eval_expr_ind_3 ge - (fun sp le e1 m1 a t e2 m2 v => + (fun sp le e m1 a t m2 v => forall p le', insert_lenv le p w le' -> - eval_expr ge sp le' e1 m1 (lift_expr p a) t e2 m2 v) - (fun sp le e1 m1 a t e2 m2 vb => + eval_expr ge sp le' e m1 (lift_expr p a) t m2 v) + (fun sp le e m1 a t m2 vb => forall p le', insert_lenv le p w le' -> - eval_condexpr ge sp le' e1 m1 (lift_condexpr p a) t e2 m2 vb) - (fun sp le e1 m1 al t e2 m2 vl => + eval_condexpr ge sp le' e m1 (lift_condexpr p a) t m2 vb) + (fun sp le e m1 al t m2 vl => forall p le', insert_lenv le p w le' -> - eval_exprlist ge sp le' e1 m1 (lift_exprlist p al) t e2 m2 vl)); + eval_exprlist ge sp le' e m1 (lift_exprlist p al) t m2 vl)); simpl; intros; eauto with evalexpr. destruct v1; eapply eval_Econdition; @@ -139,9 +139,9 @@ Proof. Qed. Lemma eval_lift: - forall sp le e1 m1 a t e2 m2 v w, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp (w::le) e1 m1 (lift a) t e2 m2 v. + forall sp le e m1 a t m2 v w, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp (w::le) e m1 (lift a) t m2 v. Proof. intros. unfold lift. eapply eval_lift_expr. eexact H. apply insert_lenv_0. @@ -160,69 +160,69 @@ Ltac TrivialOp cstr := of operator applications. *) Lemma inv_eval_Eop_0: - forall sp le e1 m1 op t e2 m2 v, - eval_expr ge sp le e1 m1 (Eop op Enil) t e2 m2 v -> - t = E0 /\ e2 = e1 /\ m2 = m1 /\ eval_operation ge sp op nil = Some v. + forall sp le e m1 op t m2 v, + eval_expr ge sp le e m1 (Eop op Enil) t m2 v -> + t = E0 /\ m2 = m1 /\ eval_operation ge sp op nil = Some v. Proof. intros. inversion H. inversion H6. intuition. congruence. Qed. Lemma inv_eval_Eop_1: - forall sp le e1 m1 op t a1 e2 m2 v, - eval_expr ge sp le e1 m1 (Eop op (a1 ::: Enil)) t e2 m2 v -> + forall sp le e m1 op t a1 m2 v, + eval_expr ge sp le e m1 (Eop op (a1 ::: Enil)) t m2 v -> exists v1, - eval_expr ge sp le e1 m1 a1 t e2 m2 v1 /\ + eval_expr ge sp le e m1 a1 t m2 v1 /\ eval_operation ge sp op (v1 :: nil) = Some v. Proof. intros. - inversion H. inversion H6. inversion H19. + inversion H. inversion H6. inversion H18. subst. exists v1; intuition. rewrite E0_right. auto. Qed. Lemma inv_eval_Eop_2: - forall sp le e1 m1 op a1 a2 t3 e3 m3 v, - eval_expr ge sp le e1 m1 (Eop op (a1 ::: a2 ::: Enil)) t3 e3 m3 v -> - exists t1, exists t2, exists e2, exists m2, exists v1, exists v2, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 /\ - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 /\ + forall sp le e m1 op a1 a2 t3 m3 v, + eval_expr ge sp le e m1 (Eop op (a1 ::: a2 ::: Enil)) t3 m3 v -> + exists t1, exists t2, exists m2, exists v1, exists v2, + eval_expr ge sp le e m1 a1 t1 m2 v1 /\ + eval_expr ge sp le e m2 a2 t2 m3 v2 /\ t3 = t1 ** t2 /\ eval_operation ge sp op (v1 :: v2 :: nil) = Some v. Proof. intros. inversion H. subst. inversion H6. subst. inversion H8. subst. - inversion H10. subst. - exists t1; exists t0; exists e0; exists m0; exists v0; exists v1. + inversion H11. subst. + exists t1; exists t0; exists m0; exists v0; exists v1. intuition. traceEq. Qed. Ltac SimplEval := match goal with - | [ |- (eval_expr _ ?sp ?le ?e1 ?m1 (Eop ?op Enil) ?t ?e2 ?m2 ?v) -> _] => + | [ |- (eval_expr _ ?sp ?le ?e ?m1 (Eop ?op Enil) ?t ?m2 ?v) -> _] => intro XX1; - generalize (inv_eval_Eop_0 sp le e1 m1 op t e2 m2 v XX1); + generalize (inv_eval_Eop_0 sp le e m1 op t m2 v XX1); clear XX1; - intros [XX1 [XX2 [XX3 XX4]]]; - subst t e2 m2; simpl in XX4; - try (simplify_eq XX4; clear XX4; + intros [XX1 [XX2 XX3]]; + subst t m2; simpl in XX3; + try (simplify_eq XX3; clear XX3; let EQ := fresh "EQ" in (intro EQ; rewrite EQ)) - | [ |- (eval_expr _ ?sp ?le ?e1 ?m1 (Eop ?op (?a1 ::: Enil)) ?t ?e2 ?m2 ?v) -> _] => + | [ |- (eval_expr _ ?sp ?le ?e ?m1 (Eop ?op (?a1 ::: Enil)) ?t ?m2 ?v) -> _] => intro XX1; - generalize (inv_eval_Eop_1 sp le e1 m1 op t a1 e2 m2 v XX1); + generalize (inv_eval_Eop_1 sp le e m1 op t a1 m2 v XX1); clear XX1; let v1 := fresh "v" in let EV := fresh "EV" in let EQ := fresh "EQ" in (intros [v1 [EV EQ]]; simpl in EQ) - | [ |- (eval_expr _ ?sp ?le ?e1 ?m1 (Eop ?op (?a1 ::: ?a2 ::: Enil)) ?t ?e2 ?m2 ?v) -> _] => + | [ |- (eval_expr _ ?sp ?le ?e ?m1 (Eop ?op (?a1 ::: ?a2 ::: Enil)) ?t ?m2 ?v) -> _] => intro XX1; - generalize (inv_eval_Eop_2 sp le e1 m1 op a1 a2 t e2 m2 v XX1); + generalize (inv_eval_Eop_2 sp le e m1 op a1 a2 t m2 v XX1); clear XX1; let t1 := fresh "t" in let t2 := fresh "t" in - let e := fresh "e" in let m := fresh "m" in + let m := fresh "m" in let v1 := fresh "v" in let v2 := fresh "v" in let EV1 := fresh "EV" in let EV2 := fresh "EV" in let EQ := fresh "EQ" in let TR := fresh "TR" in - (intros [t1 [t2 [e [m [v1 [v2 [EV1 [EV2 [TR EQ]]]]]]]]]; simpl in EQ) + (intros [t1 [t2 [m [v1 [v2 [EV1 [EV2 [TR EQ]]]]]]]]; simpl in EQ) | _ => idtac end. @@ -245,57 +245,57 @@ Ltac InvEval H := *) Theorem eval_negint: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (negint a) t e2 m2 (Vint (Int.neg x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (negint a) t m2 (Vint (Int.neg x)). Proof. TrivialOp negint. Qed. Theorem eval_negfloat: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vfloat x) -> - eval_expr ge sp le e1 m1 (negfloat a) t e2 m2 (Vfloat (Float.neg x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vfloat x) -> + eval_expr ge sp le e m1 (negfloat a) t m2 (Vfloat (Float.neg x)). Proof. TrivialOp negfloat. Qed. Theorem eval_absfloat: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vfloat x) -> - eval_expr ge sp le e1 m1 (absfloat a) t e2 m2 (Vfloat (Float.abs x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vfloat x) -> + eval_expr ge sp le e m1 (absfloat a) t m2 (Vfloat (Float.abs x)). Proof. TrivialOp absfloat. Qed. Theorem eval_intoffloat: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vfloat x) -> - eval_expr ge sp le e1 m1 (intoffloat a) t e2 m2 (Vint (Float.intoffloat x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vfloat x) -> + eval_expr ge sp le e m1 (intoffloat a) t m2 (Vint (Float.intoffloat x)). Proof. TrivialOp intoffloat. Qed. Theorem eval_floatofint: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (floatofint a) t e2 m2 (Vfloat (Float.floatofint x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (floatofint a) t m2 (Vfloat (Float.floatofint x)). Proof. TrivialOp floatofint. Qed. Theorem eval_floatofintu: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (floatofintu a) t e2 m2 (Vfloat (Float.floatofintu x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (floatofintu a) t m2 (Vfloat (Float.floatofintu x)). Proof. TrivialOp floatofintu. Qed. Theorem eval_notint: - forall sp le e1 m1 a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (notint a) t e2 m2 (Vint (Int.not x)). + forall sp le e m1 a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (notint a) t m2 (Vint (Int.not x)). Proof. unfold notint; intros until x; case (notint_match a); intros. InvEval H. FuncInv. EvalOp. simpl. congruence. @@ -310,10 +310,10 @@ Proof. Qed. Lemma eval_notbool_base: - forall sp le e1 m1 a t e2 m2 v b, - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall sp le e m1 a t m2 v b, + eval_expr ge sp le e m1 a t m2 v -> Val.bool_of_val v b -> - eval_expr ge sp le e1 m1 (notbool_base a) t e2 m2 (Val.of_bool (negb b)). + eval_expr ge sp le e m1 (notbool_base a) t m2 (Val.of_bool (negb b)). Proof. TrivialOp notbool_base. simpl. inversion H0. @@ -326,10 +326,10 @@ Hint Resolve Val.bool_of_true_val Val.bool_of_false_val Val.bool_of_true_val_inv Val.bool_of_false_val_inv: valboolof. Theorem eval_notbool: - forall a sp le e1 m1 t e2 m2 v b, - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall a sp le e m1 t m2 v b, + eval_expr ge sp le e m1 a t m2 v -> Val.bool_of_val v b -> - eval_expr ge sp le e1 m1 (notbool a) t e2 m2 (Val.of_bool (negb b)). + eval_expr ge sp le e m1 (notbool a) t m2 (Val.of_bool (negb b)). Proof. assert (N1: forall v b, Val.is_false v -> Val.bool_of_val v b -> Val.is_true (Val.of_bool (negb b))). intros. inversion H0; simpl; auto; subst v; simpl in H. @@ -341,33 +341,33 @@ Proof. induction a; simpl; intros; try (eapply eval_notbool_base; eauto). destruct o; try (eapply eval_notbool_base; eauto). - destruct e. InvEval H. injection XX4; clear XX4; intro; subst v. + destruct e. InvEval H. injection XX3; clear XX3; intro; subst v. inversion H0. rewrite Int.eq_false; auto. simpl; eauto with evalexpr. rewrite Int.eq_true; simpl; eauto with evalexpr. eapply eval_notbool_base; eauto. inversion H. subst. - simpl in H12. eapply eval_Eop; eauto. + simpl in H11. eapply eval_Eop; eauto. simpl. caseEq (eval_condition c vl); intros. - rewrite H1 in H12. + rewrite H1 in H11. assert (b0 = b). - destruct b0; inversion H12; subst v; inversion H0; auto. + destruct b0; inversion H11; subst v; inversion H0; auto. subst b0. rewrite (Op.eval_negate_condition _ _ H1). destruct b; reflexivity. - rewrite H1 in H12; discriminate. + rewrite H1 in H11; discriminate. inversion H; eauto 10 with evalexpr valboolof. inversion H; eauto 10 with evalexpr valboolof. - inversion H. subst. eapply eval_Econdition with (t2 := t8). eexact H36. + inversion H. subst. eapply eval_Econdition with (t2 := t8). eexact H34. destruct v4; eauto. auto. Qed. Theorem eval_addimm: - forall sp le e1 m1 n a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (addimm n a) t e2 m2 (Vint (Int.add x n)). + forall sp le e m1 n a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (addimm n a) t m2 (Vint (Int.add x n)). Proof. unfold addimm; intros until x. generalize (Int.eq_spec n Int.zero). case (Int.eq n Int.zero); intro. @@ -376,16 +376,16 @@ Proof. InvEval H0. EvalOp. simpl. rewrite Int.add_commut. auto. InvEval H0. destruct (Genv.find_symbol ge s); discriminate. InvEval H0. - destruct sp; simpl in XX4; discriminate. + destruct sp; simpl in XX3; discriminate. InvEval H0. FuncInv. EvalOp. simpl. subst x. rewrite Int.add_assoc. decEq; decEq; decEq. apply Int.add_commut. EvalOp. Qed. Theorem eval_addimm_ptr: - forall sp le e1 m1 n t a e2 m2 b ofs, - eval_expr ge sp le e1 m1 a t e2 m2 (Vptr b ofs) -> - eval_expr ge sp le e1 m1 (addimm n a) t e2 m2 (Vptr b (Int.add ofs n)). + forall sp le e m1 n t a m2 b ofs, + eval_expr ge sp le e m1 a t m2 (Vptr b ofs) -> + eval_expr ge sp le e m1 (addimm n a) t m2 (Vptr b (Int.add ofs n)). Proof. unfold addimm; intros until ofs. generalize (Int.eq_spec n Int.zero). case (Int.eq n Int.zero); intro. @@ -396,8 +396,8 @@ Proof. destruct (Genv.find_symbol ge s). rewrite Int.add_commut. congruence. discriminate. - InvEval H0. destruct sp; simpl in XX4; try discriminate. - inversion XX4. EvalOp. simpl. decEq. decEq. + InvEval H0. destruct sp; simpl in XX3; try discriminate. + inversion XX3. EvalOp. simpl. decEq. decEq. rewrite Int.add_assoc. decEq. apply Int.add_commut. InvEval H0. FuncInv. subst b0; subst ofs. EvalOp. simpl. rewrite (Int.add_commut n m). rewrite Int.add_assoc. auto. @@ -405,10 +405,10 @@ Proof. Qed. Theorem eval_add: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (add a b) (t1**t2) e3 m3 (Vint (Int.add x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (add a b) (t1**t2) m3 (Vint (Int.add x y)). Proof. intros until y. unfold add; case (add_match a b); intros. InvEval H. rewrite Int.add_commut. apply eval_addimm. @@ -432,10 +432,10 @@ Proof. Qed. Theorem eval_add_ptr: - forall sp le e1 m1 a t1 e2 m2 p x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vptr p x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (add a b) (t1**t2) e3 m3 (Vptr p (Int.add x y)). + forall sp le e m1 a t1 m2 p x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vptr p x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (add a b) (t1**t2) m3 (Vptr p (Int.add x y)). Proof. intros until y. unfold add; case (add_match a b); intros. InvEval H. @@ -457,10 +457,10 @@ Proof. Qed. Theorem eval_add_ptr_2: - forall sp le e1 m1 a t1 e2 m2 p x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vptr p y) -> - eval_expr ge sp le e1 m1 (add a b) (t1**t2) e3 m3 (Vptr p (Int.add y x)). + forall sp le e m1 a t1 m2 p x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vptr p y) -> + eval_expr ge sp le e m1 (add a b) (t1**t2) m3 (Vptr p (Int.add y x)). Proof. intros until y. unfold add; case (add_match a b); intros. InvEval H. @@ -484,10 +484,10 @@ Proof. Qed. Theorem eval_sub: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (sub a b) (t1**t2) e3 m3 (Vint (Int.sub x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (sub a b) (t1**t2) m3 (Vint (Int.sub x y)). Proof. intros until y. unfold sub; case (sub_match a b); intros. @@ -512,10 +512,10 @@ Proof. Qed. Theorem eval_sub_ptr_int: - forall sp le e1 m1 a t1 e2 m2 p x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vptr p x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (sub a b) (t1**t2) e3 m3 (Vptr p (Int.sub x y)). + forall sp le e m1 a t1 m2 p x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vptr p x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (sub a b) (t1**t2) m3 (Vptr p (Int.sub x y)). Proof. intros until y. unfold sub; case (sub_match a b); intros. @@ -541,10 +541,10 @@ Proof. Qed. Theorem eval_sub_ptr_ptr: - forall sp le e1 m1 a t1 e2 m2 p x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vptr p x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vptr p y) -> - eval_expr ge sp le e1 m1 (sub a b) (t1**t2) e3 m3 (Vint (Int.sub x y)). + forall sp le e m1 a t1 m2 p x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vptr p x) -> + eval_expr ge sp le e m2 b t2 m3 (Vptr p y) -> + eval_expr ge sp le e m1 (sub a b) (t1**t2) m3 (Vint (Int.sub x y)). Proof. intros until y. unfold sub; case (sub_match a b); intros. @@ -571,9 +571,9 @@ Proof. Qed. Lemma eval_rolm: - forall sp le e1 m1 a amount mask t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (rolm a amount mask) t e2 m2 (Vint (Int.rolm x amount mask)). + forall sp le e m1 a amount mask t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (rolm a amount mask) t m2 (Vint (Int.rolm x amount mask)). Proof. intros until x. unfold rolm; case (rolm_match a); intros. InvEval H. eauto with evalexpr. @@ -590,10 +590,10 @@ Proof. Qed. Theorem eval_shlimm: - forall sp le e1 m1 a n t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> + forall sp le e m1 a n t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> Int.ltu n (Int.repr 32) = true -> - eval_expr ge sp le e1 m1 (shlimm a n) t e2 m2 (Vint (Int.shl x n)). + eval_expr ge sp le e m1 (shlimm a n) t m2 (Vint (Int.shl x n)). Proof. intros. unfold shlimm. generalize (Int.eq_spec n Int.zero); case (Int.eq n Int.zero); intro. @@ -604,10 +604,10 @@ Proof. Qed. Theorem eval_shruimm: - forall sp le e1 m1 a n t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> + forall sp le e m1 a n t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> Int.ltu n (Int.repr 32) = true -> - eval_expr ge sp le e1 m1 (shruimm a n) t e2 m2 (Vint (Int.shru x n)). + eval_expr ge sp le e m1 (shruimm a n) t m2 (Vint (Int.shru x n)). Proof. intros. unfold shruimm. generalize (Int.eq_spec n Int.zero); case (Int.eq n Int.zero); intro. @@ -618,9 +618,9 @@ Proof. Qed. Lemma eval_mulimm_base: - forall sp le e1 m1 a t n e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (mulimm_base n a) t e2 m2 (Vint (Int.mul x n)). + forall sp le e m1 a t n m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (mulimm_base n a) t m2 (Vint (Int.mul x n)). Proof. intros; unfold mulimm_base. generalize (Int.one_bits_decomp n). @@ -633,7 +633,7 @@ Proof. rewrite Int.add_zero. rewrite <- Int.shl_mul. apply eval_shlimm. auto. auto with coqlib. destruct l. - intros. apply eval_Elet with t e2 m2 (Vint x) E0. auto. + intros. apply eval_Elet with t m2 (Vint x) E0. auto. rewrite H1. simpl. rewrite Int.add_zero. rewrite Int.mul_add_distr_r. rewrite <- Int.shl_mul. @@ -650,9 +650,9 @@ Proof. Qed. Theorem eval_mulimm: - forall sp le e1 m1 a n t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (mulimm n a) t e2 m2 (Vint (Int.mul x n)). + forall sp le e m1 a n t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (mulimm n a) t m2 (Vint (Int.mul x n)). Proof. intros until x; unfold mulimm. generalize (Int.eq_spec n Int.zero); case (Int.eq n Int.zero); intro. @@ -670,10 +670,10 @@ Proof. Qed. Theorem eval_mul: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (mul a b) (t1**t2) e3 m3 (Vint (Int.mul x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (mul a b) (t1**t2) m3 (Vint (Int.mul x y)). Proof. intros until y. unfold mul; case (mul_match a b); intros. @@ -684,11 +684,11 @@ Proof. Qed. Theorem eval_divs: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (divs a b) (t1**t2) e3 m3 (Vint (Int.divs x y)). + eval_expr ge sp le e m1 (divs a b) (t1**t2) m3 (Vint (Int.divs x y)). Proof. TrivialOp divs. simpl. predSpec Int.eq Int.eq_spec y Int.zero. contradiction. auto. @@ -700,11 +700,11 @@ Lemma eval_mod_aux: y <> Int.zero -> eval_operation ge sp divop (Vint x :: Vint y :: nil) = Some (Vint (semdivop x y))) -> - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (mod_aux divop a b) (t1**t2) e3 m3 + eval_expr ge sp le e m1 (mod_aux divop a b) (t1**t2) m3 (Vint (Int.sub x (Int.mul (semdivop x y) y))). Proof. intros; unfold mod_aux. @@ -726,11 +726,11 @@ Proof. Qed. Theorem eval_mods: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (mods a b) (t1**t2) e3 m3 (Vint (Int.mods x y)). + eval_expr ge sp le e m1 (mods a b) (t1**t2) m3 (Vint (Int.mods x y)). Proof. intros; unfold mods. rewrite Int.mods_divs. @@ -740,22 +740,22 @@ Proof. Qed. Lemma eval_divu_base: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (Eop Odivu (a ::: b ::: Enil)) (t1**t2) e3 m3 (Vint (Int.divu x y)). + eval_expr ge sp le e m1 (Eop Odivu (a ::: b ::: Enil)) (t1**t2) m3 (Vint (Int.divu x y)). Proof. intros. EvalOp. simpl. predSpec Int.eq Int.eq_spec y Int.zero. contradiction. auto. Qed. Theorem eval_divu: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (divu a b) (t1**t2) e3 m3 (Vint (Int.divu x y)). + eval_expr ge sp le e m1 (divu a b) (t1**t2) m3 (Vint (Int.divu x y)). Proof. intros until y. unfold divu; case (divu_match b); intros. @@ -768,11 +768,11 @@ Proof. Qed. Theorem eval_modu: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> y <> Int.zero -> - eval_expr ge sp le e1 m1 (modu a b) (t1**t2) e3 m3 (Vint (Int.modu x y)). + eval_expr ge sp le e m1 (modu a b) (t1**t2) m3 (Vint (Int.modu x y)). Proof. intros until y; unfold modu; case (divu_match b); intros. InvEval H0. caseEq (Int.is_power2 y). @@ -789,9 +789,9 @@ Proof. Qed. Theorem eval_andimm: - forall sp le e1 m1 n a t e2 m2 x, - eval_expr ge sp le e1 m1 a t e2 m2 (Vint x) -> - eval_expr ge sp le e1 m1 (andimm n a) t e2 m2 (Vint (Int.and x n)). + forall sp le e m1 n a t m2 x, + eval_expr ge sp le e m1 a t m2 (Vint x) -> + eval_expr ge sp le e m1 (andimm n a) t m2 (Vint (Int.and x n)). Proof. intros. unfold andimm. case (Int.is_rlw_mask n). rewrite <- Int.rolm_zero. apply eval_rolm; auto. @@ -799,10 +799,10 @@ Proof. Qed. Theorem eval_and: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (and a b) (t1**t2) e3 m3 (Vint (Int.and x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (and a b) (t1**t2) m3 (Vint (Int.and x y)). Proof. intros until y; unfold and; case (mul_match a b); intros. InvEval H. rewrite Int.and_commut. @@ -812,11 +812,11 @@ Proof. Qed. Remark eval_same_expr_pure: - forall a1 a2 sp le e1 m1 t1 e2 m2 v1 t2 e3 m3 v2, + forall a1 a2 sp le e m1 t1 m2 v1 t2 m3 v2, same_expr_pure a1 a2 = true -> - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 -> - t1 = E0 /\ t2 = E0 /\ a2 = a1 /\ v2 = v1 /\ e2 = e1 /\ m2 = m1. + eval_expr ge sp le e m1 a1 t1 m2 v1 -> + eval_expr ge sp le e m2 a2 t2 m3 v2 -> + t1 = E0 /\ t2 = E0 /\ a2 = a1 /\ v2 = v1 /\ m2 = m1. Proof. intros until v2. destruct a1; simpl; try (intros; discriminate). @@ -828,18 +828,18 @@ Proof. Qed. Lemma eval_or: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (or a b) (t1**t2) e3 m3 (Vint (Int.or x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (or a b) (t1**t2) m3 (Vint (Int.or x y)). Proof. intros until y; unfold or; case (or_match a b); intros. generalize (Int.eq_spec amount1 amount2); case (Int.eq amount1 amount2); intro. case (Int.is_rlw_mask (Int.or mask1 mask2)). caseEq (same_expr_pure t0 t3); intro. simpl. InvEval H. FuncInv. InvEval H0. FuncInv. - generalize (eval_same_expr_pure _ _ _ _ _ _ _ _ _ _ _ _ _ _ H2 EV EV0). - intros [EQ1 [EQ2 [EQ3 [EQ4 [EQ5 EQ6]]]]]. + generalize (eval_same_expr_pure _ _ _ _ _ _ _ _ _ _ _ _ H2 EV EV0). + intros [EQ1 [EQ2 [EQ3 [EQ4 EQ5]]]]. injection EQ4; intro EQ7. subst. EvalOp. simpl. rewrite Int.or_rolm. auto. simpl. EvalOp. @@ -849,18 +849,18 @@ Proof. Qed. Theorem eval_xor: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (xor a b) (t1**t2) e3 m3 (Vint (Int.xor x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (xor a b) (t1**t2) m3 (Vint (Int.xor x y)). Proof. TrivialOp xor. Qed. Theorem eval_shl: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> Int.ltu y (Int.repr 32) = true -> - eval_expr ge sp le e1 m1 (shl a b) (t1**t2) e3 m3 (Vint (Int.shl x y)). + eval_expr ge sp le e m1 (shl a b) (t1**t2) m3 (Vint (Int.shl x y)). Proof. intros until y; unfold shl; case (shift_match b); intros. InvEval H0. rewrite E0_right. apply eval_shlimm; auto. @@ -868,21 +868,21 @@ Proof. Qed. Theorem eval_shr: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> Int.ltu y (Int.repr 32) = true -> - eval_expr ge sp le e1 m1 (shr a b) (t1**t2) e3 m3 (Vint (Int.shr x y)). + eval_expr ge sp le e m1 (shr a b) (t1**t2) m3 (Vint (Int.shr x y)). Proof. TrivialOp shr. simpl. rewrite H1. auto. Qed. Theorem eval_shru: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> Int.ltu y (Int.repr 32) = true -> - eval_expr ge sp le e1 m1 (shru a b) (t1**t2) e3 m3 (Vint (Int.shru x y)). + eval_expr ge sp le e m1 (shru a b) (t1**t2) m3 (Vint (Int.shru x y)). Proof. intros until y; unfold shru; case (shift_match b); intros. InvEval H0. rewrite E0_right; apply eval_shruimm; auto. @@ -890,10 +890,10 @@ Proof. Qed. Theorem eval_addf: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vfloat x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vfloat y) -> - eval_expr ge sp le e1 m1 (addf a b) (t1**t2) e3 m3 (Vfloat (Float.add x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vfloat x) -> + eval_expr ge sp le e m2 b t2 m3 (Vfloat y) -> + eval_expr ge sp le e m1 (addf a b) (t1**t2) m3 (Vfloat (Float.add x y)). Proof. intros until y; unfold addf; case (addf_match a b); intros. InvEval H. FuncInv. EvalOp. @@ -909,10 +909,10 @@ Proof. Qed. Theorem eval_subf: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vfloat x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vfloat y) -> - eval_expr ge sp le e1 m1 (subf a b) (t1**t2) e3 m3 (Vfloat (Float.sub x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vfloat x) -> + eval_expr ge sp le e m2 b t2 m3 (Vfloat y) -> + eval_expr ge sp le e m1 (subf a b) (t1**t2) m3 (Vfloat (Float.sub x y)). Proof. intros until y; unfold subf; case (subf_match a b); intros. InvEval H. FuncInv. EvalOp. @@ -922,23 +922,23 @@ Proof. Qed. Theorem eval_mulf: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vfloat x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vfloat y) -> - eval_expr ge sp le e1 m1 (mulf a b) (t1**t2) e3 m3 (Vfloat (Float.mul x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vfloat x) -> + eval_expr ge sp le e m2 b t2 m3 (Vfloat y) -> + eval_expr ge sp le e m1 (mulf a b) (t1**t2) m3 (Vfloat (Float.mul x y)). Proof. TrivialOp mulf. Qed. Theorem eval_divf: - forall sp le e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vfloat x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vfloat y) -> - eval_expr ge sp le e1 m1 (divf a b) (t1**t2) e3 m3 (Vfloat (Float.div x y)). + forall sp le e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vfloat x) -> + eval_expr ge sp le e m2 b t2 m3 (Vfloat y) -> + eval_expr ge sp le e m1 (divf a b) (t1**t2) m3 (Vfloat (Float.div x y)). Proof. TrivialOp divf. Qed. Theorem eval_cast8signed: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp le e1 m1 (cast8signed a) t e2 m2 (Val.cast8signed v). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp le e m1 (cast8signed a) t m2 (Val.cast8signed v). Proof. intros until v; unfold cast8signed; case (cast8signed_match a); intros. replace (Val.cast8signed v) with v. auto. @@ -947,9 +947,9 @@ Proof. Qed. Theorem eval_cast8unsigned: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp le e1 m1 (cast8unsigned a) t e2 m2 (Val.cast8unsigned v). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp le e m1 (cast8unsigned a) t m2 (Val.cast8unsigned v). Proof. intros until v; unfold cast8unsigned; case (cast8unsigned_match a); intros. replace (Val.cast8unsigned v) with v. auto. @@ -958,9 +958,9 @@ Proof. Qed. Theorem eval_cast16signed: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp le e1 m1 (cast16signed a) t e2 m2 (Val.cast16signed v). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp le e m1 (cast16signed a) t m2 (Val.cast16signed v). Proof. intros until v; unfold cast16signed; case (cast16signed_match a); intros. replace (Val.cast16signed v) with v. auto. @@ -969,9 +969,9 @@ Proof. Qed. Theorem eval_cast16unsigned: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp le e1 m1 (cast16unsigned a) t e2 m2 (Val.cast16unsigned v). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp le e m1 (cast16unsigned a) t m2 (Val.cast16unsigned v). Proof. intros until v; unfold cast16unsigned; case (cast16unsigned_match a); intros. replace (Val.cast16unsigned v) with v. auto. @@ -980,9 +980,9 @@ Proof. Qed. Theorem eval_singleoffloat: - forall sp le e1 m1 a t e2 m2 v, - eval_expr ge sp le e1 m1 a t e2 m2 v -> - eval_expr ge sp le e1 m1 (singleoffloat a) t e2 m2 (Val.singleoffloat v). + forall sp le e m1 a t m2 v, + eval_expr ge sp le e m1 a t m2 v -> + eval_expr ge sp le e m1 (singleoffloat a) t m2 (Val.singleoffloat v). Proof. intros until v; unfold singleoffloat; case (singleoffloat_match a); intros. replace (Val.singleoffloat v) with v. auto. @@ -991,42 +991,42 @@ Proof. Qed. Theorem eval_cmp: - forall sp le c e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (cmp c a b) (t1**t2) e3 m3 (Val.of_bool (Int.cmp c x y)). + forall sp le c e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (cmp c a b) (t1**t2) m3 (Val.of_bool (Int.cmp c x y)). Proof. TrivialOp cmp. simpl. case (Int.cmp c x y); auto. Qed. Theorem eval_cmp_null_r: - forall sp le c e1 m1 a t1 e2 m2 p x b t2 e3 m3 v, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vptr p x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint Int.zero) -> + forall sp le c e m1 a t1 m2 p x b t2 m3 v, + eval_expr ge sp le e m1 a t1 m2 (Vptr p x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint Int.zero) -> (c = Ceq /\ v = Vfalse) \/ (c = Cne /\ v = Vtrue) -> - eval_expr ge sp le e1 m1 (cmp c a b) (t1**t2) e3 m3 v. + eval_expr ge sp le e m1 (cmp c a b) (t1**t2) m3 v. Proof. TrivialOp cmp. simpl. elim H1; intros [EQ1 EQ2]; subst c; subst v; reflexivity. Qed. Theorem eval_cmp_null_l: - forall sp le c e1 m1 a t1 e2 m2 p x b t2 e3 m3 v, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint Int.zero) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vptr p x) -> + forall sp le c e m1 a t1 m2 p x b t2 m3 v, + eval_expr ge sp le e m1 a t1 m2 (Vint Int.zero) -> + eval_expr ge sp le e m2 b t2 m3 (Vptr p x) -> (c = Ceq /\ v = Vfalse) \/ (c = Cne /\ v = Vtrue) -> - eval_expr ge sp le e1 m1 (cmp c a b) (t1**t2) e3 m3 v. + eval_expr ge sp le e m1 (cmp c a b) (t1**t2) m3 v. Proof. TrivialOp cmp. simpl. elim H1; intros [EQ1 EQ2]; subst c; subst v; reflexivity. Qed. Theorem eval_cmp_ptr: - forall sp le c e1 m1 a t1 e2 m2 p x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vptr p x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vptr p y) -> - eval_expr ge sp le e1 m1 (cmp c a b) (t1**t2) e3 m3 (Val.of_bool (Int.cmp c x y)). + forall sp le c e m1 a t1 m2 p x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vptr p x) -> + eval_expr ge sp le e m2 b t2 m3 (Vptr p y) -> + eval_expr ge sp le e m1 (cmp c a b) (t1**t2) m3 (Val.of_bool (Int.cmp c x y)). Proof. TrivialOp cmp. simpl. unfold eq_block. rewrite zeq_true. @@ -1034,32 +1034,32 @@ Proof. Qed. Theorem eval_cmpu: - forall sp le c e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vint x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vint y) -> - eval_expr ge sp le e1 m1 (cmpu c a b) (t1**t2) e3 m3 (Val.of_bool (Int.cmpu c x y)). + forall sp le c e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vint x) -> + eval_expr ge sp le e m2 b t2 m3 (Vint y) -> + eval_expr ge sp le e m1 (cmpu c a b) (t1**t2) m3 (Val.of_bool (Int.cmpu c x y)). Proof. TrivialOp cmpu. simpl. case (Int.cmpu c x y); auto. Qed. Theorem eval_cmpf: - forall sp le c e1 m1 a t1 e2 m2 x b t2 e3 m3 y, - eval_expr ge sp le e1 m1 a t1 e2 m2 (Vfloat x) -> - eval_expr ge sp le e2 m2 b t2 e3 m3 (Vfloat y) -> - eval_expr ge sp le e1 m1 (cmpf c a b) (t1**t2) e3 m3 (Val.of_bool (Float.cmp c x y)). + forall sp le c e m1 a t1 m2 x b t2 m3 y, + eval_expr ge sp le e m1 a t1 m2 (Vfloat x) -> + eval_expr ge sp le e m2 b t2 m3 (Vfloat y) -> + eval_expr ge sp le e m1 (cmpf c a b) (t1**t2) m3 (Val.of_bool (Float.cmp c x y)). Proof. TrivialOp cmpf. simpl. case (Float.cmp c x y); auto. Qed. Lemma eval_base_condition_of_expr: - forall sp le a e1 m1 t e2 m2 v (b: bool), - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall sp le a e m1 t m2 v (b: bool), + eval_expr ge sp le e m1 a t m2 v -> Val.bool_of_val v b -> - eval_condexpr ge sp le e1 m1 + eval_condexpr ge sp le e m1 (CEcond (Ccompuimm Cne Int.zero) (a ::: Enil)) - t e2 m2 b. + t m2 b. Proof. intros. eapply eval_CEcond. eauto with evalexpr. @@ -1067,60 +1067,60 @@ Proof. Qed. Lemma eval_condition_of_expr: - forall a sp le e1 m1 t e2 m2 v (b: bool), - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall a sp le e m1 t m2 v (b: bool), + eval_expr ge sp le e m1 a t m2 v -> Val.bool_of_val v b -> - eval_condexpr ge sp le e1 m1 (condexpr_of_expr a) t e2 m2 b. + eval_condexpr ge sp le e m1 (condexpr_of_expr a) t m2 b. Proof. induction a; simpl; intros; try (eapply eval_base_condition_of_expr; eauto; fail). destruct o; try (eapply eval_base_condition_of_expr; eauto; fail). - destruct e. InvEval H. inversion XX4; subst v. + destruct e. InvEval H. inversion XX3; subst v. inversion H0. rewrite Int.eq_false; auto. constructor. subst i; rewrite Int.eq_true. constructor. eapply eval_base_condition_of_expr; eauto. - inversion H. subst. eapply eval_CEcond; eauto. simpl in H12. + inversion H. subst. eapply eval_CEcond; eauto. simpl in H11. destruct (eval_condition c vl); try discriminate. - destruct b0; inversion H12; subst; inversion H0; congruence. + destruct b0; inversion H11; subst; inversion H0; congruence. inversion H. subst. destruct v1; eauto with evalexpr. Qed. Theorem eval_conditionalexpr_true: - forall sp le e1 m1 a1 t1 e2 m2 v1 t2 a2 e3 m3 v2 a3, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> + forall sp le e m1 a1 t1 m2 v1 t2 a2 m3 v2 a3, + eval_expr ge sp le e m1 a1 t1 m2 v1 -> Val.is_true v1 -> - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 -> - eval_expr ge sp le e1 m1 (conditionalexpr a1 a2 a3) (t1**t2) e3 m3 v2. + eval_expr ge sp le e m2 a2 t2 m3 v2 -> + eval_expr ge sp le e m1 (conditionalexpr a1 a2 a3) (t1**t2) m3 v2. Proof. intros; unfold conditionalexpr. - apply eval_Econdition with t1 e2 m2 true t2; auto. + apply eval_Econdition with t1 m2 true t2; auto. eapply eval_condition_of_expr; eauto with valboolof. Qed. Theorem eval_conditionalexpr_false: - forall sp le e1 m1 a1 t1 e2 m2 v1 a2 t2 e3 m3 v2 a3, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> + forall sp le e m1 a1 t1 m2 v1 a2 t2 m3 v2 a3, + eval_expr ge sp le e m1 a1 t1 m2 v1 -> Val.is_false v1 -> - eval_expr ge sp le e2 m2 a3 t2 e3 m3 v2 -> - eval_expr ge sp le e1 m1 (conditionalexpr a1 a2 a3) (t1**t2) e3 m3 v2. + eval_expr ge sp le e m2 a3 t2 m3 v2 -> + eval_expr ge sp le e m1 (conditionalexpr a1 a2 a3) (t1**t2) m3 v2. Proof. intros; unfold conditionalexpr. - apply eval_Econdition with t1 e2 m2 false t2; auto. + apply eval_Econdition with t1 m2 false t2; auto. eapply eval_condition_of_expr; eauto with valboolof. Qed. Lemma eval_addressing: - forall sp le e1 m1 a t e2 m2 v b ofs, - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall sp le e m1 a t m2 v b ofs, + eval_expr ge sp le e m1 a t m2 v -> v = Vptr b ofs -> match addressing a with (mode, args) => exists vl, - eval_exprlist ge sp le e1 m1 args t e2 m2 vl /\ + eval_exprlist ge sp le e m1 args t m2 vl /\ eval_addressing ge sp mode vl = Some v end. Proof. @@ -1151,54 +1151,54 @@ Proof. Qed. Theorem eval_load: - forall sp le e1 m1 a t e2 m2 v chunk v', - eval_expr ge sp le e1 m1 a t e2 m2 v -> + forall sp le e m1 a t m2 v chunk v', + eval_expr ge sp le e m1 a t m2 v -> Mem.loadv chunk m2 v = Some v' -> - eval_expr ge sp le e1 m1 (load chunk a) t e2 m2 v'. + eval_expr ge sp le e m1 (load chunk a) t m2 v'. Proof. intros. generalize H0; destruct v; simpl; intro; try discriminate. unfold load. - generalize (eval_addressing _ _ _ _ _ _ _ _ _ _ _ H (refl_equal _)). + generalize (eval_addressing _ _ _ _ _ _ _ _ _ _ H (refl_equal _)). destruct (addressing a). intros [vl [EV EQ]]. eapply eval_Eload; eauto. Qed. Theorem eval_store: - forall sp le e1 m1 a1 t1 e2 m2 v1 a2 t2 e3 m3 v2 chunk m4, - eval_expr ge sp le e1 m1 a1 t1 e2 m2 v1 -> - eval_expr ge sp le e2 m2 a2 t2 e3 m3 v2 -> + forall sp le e m1 a1 t1 m2 v1 a2 t2 m3 v2 chunk m4, + eval_expr ge sp le e m1 a1 t1 m2 v1 -> + eval_expr ge sp le e m2 a2 t2 m3 v2 -> Mem.storev chunk m3 v1 v2 = Some m4 -> - eval_expr ge sp le e1 m1 (store chunk a1 a2) (t1**t2) e3 m4 v2. + eval_expr ge sp le e m1 (store chunk a1 a2) (t1**t2) m4 v2. Proof. intros. generalize H1; destruct v1; simpl; intro; try discriminate. unfold store. - generalize (eval_addressing _ _ _ _ _ _ _ _ _ _ _ H (refl_equal _)). + generalize (eval_addressing _ _ _ _ _ _ _ _ _ _ H (refl_equal _)). destruct (addressing a1). intros [vl [EV EQ]]. eapply eval_Estore; eauto. Qed. Theorem exec_ifthenelse_true: - forall sp e1 m1 a t1 e2 m2 v ifso ifnot t2 e3 m3 out, - eval_expr ge sp nil e1 m1 a t1 e2 m2 v -> + forall sp e m1 a t1 m2 v ifso ifnot t2 e3 m3 out, + eval_expr ge sp nil e m1 a t1 m2 v -> Val.is_true v -> - exec_stmt ge sp e2 m2 ifso t2 e3 m3 out -> - exec_stmt ge sp e1 m1 (ifthenelse a ifso ifnot) (t1**t2) e3 m3 out. + exec_stmt ge sp e m2 ifso t2 e3 m3 out -> + exec_stmt ge sp e m1 (ifthenelse a ifso ifnot) (t1**t2) e3 m3 out. Proof. intros. unfold ifthenelse. - apply exec_Sifthenelse with t1 e2 m2 true t2. + apply exec_Sifthenelse with t1 m2 true t2. eapply eval_condition_of_expr; eauto with valboolof. auto. auto. Qed. Theorem exec_ifthenelse_false: - forall sp e1 m1 a t1 e2 m2 v ifso ifnot t2 e3 m3 out, - eval_expr ge sp nil e1 m1 a t1 e2 m2 v -> + forall sp e m1 a t1 m2 v ifso ifnot t2 e3 m3 out, + eval_expr ge sp nil e m1 a t1 m2 v -> Val.is_false v -> - exec_stmt ge sp e2 m2 ifnot t2 e3 m3 out -> - exec_stmt ge sp e1 m1 (ifthenelse a ifso ifnot) (t1**t2) e3 m3 out. + exec_stmt ge sp e m2 ifnot t2 e3 m3 out -> + exec_stmt ge sp e m1 (ifthenelse a ifso ifnot) (t1**t2) e3 m3 out. Proof. intros. unfold ifthenelse. - apply exec_Sifthenelse with t1 e2 m2 false t2. + apply exec_Sifthenelse with t1 m2 false t2. eapply eval_condition_of_expr; eauto with valboolof. auto. auto. Qed. |