diff options
Diffstat (limited to 'mppa_k1c/SelectOpproof.v')
| -rw-r--r-- | mppa_k1c/SelectOpproof.v | 89 |
1 files changed, 87 insertions, 2 deletions
diff --git a/mppa_k1c/SelectOpproof.v b/mppa_k1c/SelectOpproof.v index 89af39ee..d35c4b6d 100644 --- a/mppa_k1c/SelectOpproof.v +++ b/mppa_k1c/SelectOpproof.v @@ -92,7 +92,7 @@ Let ge := Genv.globalenv prog. Variable sp: val. Variable e: env. Variable m: mem. - + (* Helper lemmas - from SplitLongproof.v *) Ltac UseHelper := decompose [Logic.and] arith_helpers_correct; eauto. @@ -162,7 +162,7 @@ Definition binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> va eval_expr ge sp e m le a x -> eval_expr ge sp e m le b y -> exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. - + Theorem eval_addrsymbol: forall le id ofs, exists v, eval_expr ge sp e m le (addrsymbol id ofs) v /\ Val.lessdef (Genv.symbol_address ge id ofs) v. @@ -526,6 +526,15 @@ Proof. discriminate. Qed. +Lemma int_eq_commut: forall x y : int, + (Int.eq x y) = (Int.eq y x). +Proof. + intros. + predSpec Int.eq Int.eq_spec x y; + predSpec Int.eq Int.eq_spec y x; + congruence. +Qed. + Theorem eval_or: binary_constructor_sound or Val.or. Proof. unfold or; red; intros. @@ -553,6 +562,82 @@ Proof. exists (Val.ror v1 (Vint n2)); split. EvalOp. rewrite Val.or_commut. apply ROR; auto. - (*orn*) TrivialExists; simpl; congruence. - (*orn reversed*) rewrite Val.or_commut. TrivialExists; simpl; congruence. + - (* select *) + destruct (same_expr_pure y0 y1) eqn:PURE; simpl; try exact DEFAULT. + predSpec Int.eq Int.eq_spec zero0 Int.zero; simpl; try exact DEFAULT. + predSpec Int.eq Int.eq_spec zero1 Int.zero; simpl; try exact DEFAULT. + TrivialExists. + simpl in *. + unfold select. + f_equal. + inv H6. + inv H7. + inv H9. + inv H11. + unfold same_expr_pure in PURE. + destruct y0; try congruence. + destruct y1; try congruence. + destruct (ident_eq i i0); try congruence. + rewrite <- e0 in *. clear e0. clear PURE. + inv H2. inv H5. + replace v8 with v4 in * by congruence. + rename v4 into vselect. + destruct vselect; simpl; trivial. + rewrite (Val.and_commut _ v5). + destruct v5; simpl; trivial. + rewrite (Val.and_commut _ v9). + rewrite Val.or_commut. + destruct v9; simpl; trivial. + rewrite int_eq_commut. + destruct (Int.eq i1 Int.zero); simpl. + + rewrite Int.and_zero. + rewrite Int.or_commut. + rewrite Int.or_zero. + rewrite Int.and_mone. + reflexivity. + + rewrite Int.and_mone. + rewrite Int.neg_zero. + rewrite Int.and_zero. + rewrite Int.or_zero. + reflexivity. + - (* select unsigned *) + destruct (same_expr_pure y0 y1) eqn:PURE; simpl; try exact DEFAULT. + predSpec Int.eq Int.eq_spec zero0 Int.zero; simpl; try exact DEFAULT. + predSpec Int.eq Int.eq_spec zero1 Int.zero; simpl; try exact DEFAULT. + TrivialExists. + simpl in *. + unfold select. + f_equal. + inv H6. + inv H7. + inv H9. + inv H11. + unfold same_expr_pure in PURE. + destruct y0; try congruence. + destruct y1; try congruence. + destruct (ident_eq i i0); try congruence. + rewrite <- e0 in *. clear e0. clear PURE. + inv H2. inv H5. + replace v8 with v4 in * by congruence. + rename v4 into vselect. + destruct vselect; simpl; trivial. + rewrite (Val.and_commut _ v5). + destruct v5; simpl; trivial. + rewrite (Val.and_commut _ v9). + rewrite Val.or_commut. + destruct v9; simpl; trivial. + rewrite int_eq_commut. + destruct (Int.eq i1 Int.zero); simpl. + + rewrite Int.and_zero. + rewrite Int.or_commut. + rewrite Int.or_zero. + rewrite Int.and_mone. + reflexivity. + + rewrite Int.and_mone. + rewrite Int.neg_zero. + rewrite Int.and_zero. + rewrite Int.or_zero. + reflexivity. - apply DEFAULT. Qed. |