diff options
Diffstat (limited to 'arm/CombineOpproof.v')
| -rw-r--r-- | arm/CombineOpproof.v | 53 |
1 files changed, 32 insertions, 21 deletions
diff --git a/arm/CombineOpproof.v b/arm/CombineOpproof.v index c95b19c..485857b 100644 --- a/arm/CombineOpproof.v +++ b/arm/CombineOpproof.v @@ -21,8 +21,8 @@ Require Import Memory. Require Import Op. Require Import Registers. Require Import RTL. +Require Import CSEdomain. Require Import CombineOp. -Require Import CSE. Section COMBINE. @@ -31,8 +31,20 @@ Variable sp: val. Variable m: mem. Variable get: valnum -> option rhs. Variable valu: valnum -> val. -Hypothesis get_sound: forall v rhs, get v = Some rhs -> equation_holds valu ge sp m v rhs. +Hypothesis get_sound: forall v rhs, get v = Some rhs -> rhs_eval_to valu ge sp m rhs (valu v). +Lemma get_op_sound: + forall v op vl, get v = Some (Op op vl) -> eval_operation ge sp op (map valu vl) m = Some (valu v). +Proof. + intros. exploit get_sound; eauto. intros REV; inv REV; auto. +Qed. + +Ltac UseGetSound := + match goal with + | [ H: get _ = Some _ |- _ ] => + let x := fresh "EQ" in (generalize (get_op_sound _ _ _ H); intros x; simpl in x; FuncInv) + end. + Lemma combine_compimm_ne_0_sound: forall x cond args, combine_compimm_ne_0 get x = Some(cond, args) -> @@ -41,7 +53,7 @@ Lemma combine_compimm_ne_0_sound: Proof. intros until args. functional induction (combine_compimm_ne_0 get x); intros EQ; inv EQ. (* of cmp *) - exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + UseGetSound. rewrite <- H. destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. Qed. @@ -53,7 +65,7 @@ Lemma combine_compimm_eq_0_sound: Proof. intros until args. functional induction (combine_compimm_eq_0 get x); intros EQ; inv EQ. (* of cmp *) - exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + UseGetSound. rewrite <- H. rewrite eval_negate_condition. destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. Qed. @@ -66,7 +78,7 @@ Lemma combine_compimm_eq_1_sound: Proof. intros until args. functional induction (combine_compimm_eq_1 get x); intros EQ; inv EQ. (* of cmp *) - exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + UseGetSound. rewrite <- H. destruct (eval_condition cond (map valu args) m); simpl; auto. destruct b; auto. Qed. @@ -78,7 +90,7 @@ Lemma combine_compimm_ne_1_sound: Proof. intros until args. functional induction (combine_compimm_ne_1 get x); intros EQ; inv EQ. (* of cmp *) - exploit get_sound; eauto. unfold equation_holds. simpl. intro EQ; inv EQ. + UseGetSound. rewrite <- H. rewrite eval_negate_condition. destruct (eval_condition c (map valu args) m); simpl; auto. destruct b; auto. Qed. @@ -114,8 +126,7 @@ Theorem combine_addr_sound: Proof. intros. functional inversion H; subst. (* indexed - addimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intro EQ. FuncInv. - rewrite <- H0. rewrite Val.add_assoc. auto. + UseGetSound. simpl. rewrite <- H0. rewrite Val.add_assoc. auto. Qed. Theorem combine_op_sound: @@ -125,28 +136,28 @@ Theorem combine_op_sound: Proof. intros. functional inversion H; subst. (* addimm - addimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. rewrite Val.add_assoc. auto. + UseGetSound. FuncInv. simpl. + rewrite <- H0. rewrite Val.add_assoc. auto. (* addimm - subimm *) Opaque Val.sub. - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. change (Vint (Int.add m0 n)) with (Val.add (Vint m0) (Vint n)). - rewrite Val.sub_add_l. auto. + UseGetSound. FuncInv. simpl. + change (Vint (Int.add m0 n)) with (Val.add (Vint m0) (Vint n)). + rewrite <- H0. rewrite Val.sub_add_l. auto. (* subimm - addimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. + UseGetSound. FuncInv. simpl. rewrite <- H0. Transparent Val.sub. destruct v; simpl; auto. repeat rewrite Int.sub_add_opp. rewrite Int.add_assoc. rewrite Int.neg_add_distr. decEq. decEq. decEq. apply Int.add_commut. (* andimm - andimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. rewrite Val.and_assoc. auto. + UseGetSound; simpl. + generalize (Int.eq_spec p m0); rewrite H7; intros. + rewrite <- H0. rewrite Val.and_assoc. simpl. fold p. rewrite H1. auto. + UseGetSound; simpl. + rewrite <- H0. rewrite Val.and_assoc. auto. (* orimm - orimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. rewrite Val.or_assoc. auto. + UseGetSound. simpl. rewrite <- H0. rewrite Val.or_assoc. auto. (* xorimm - xorimm *) - exploit get_sound; eauto. unfold equation_holds; simpl; intros. FuncInv. - rewrite <- H1. rewrite Val.xor_assoc. auto. + UseGetSound. simpl. rewrite <- H0. rewrite Val.xor_assoc. auto. (* cmp *) simpl. decEq; decEq. eapply combine_cond_sound; eauto. Qed. |