diff options
Diffstat (limited to 'ia32/SelectLongproof.v')
| -rw-r--r-- | ia32/SelectLongproof.v | 87 |
1 files changed, 44 insertions, 43 deletions
diff --git a/ia32/SelectLongproof.v b/ia32/SelectLongproof.v index fced9a07..4cd15fd3 100644 --- a/ia32/SelectLongproof.v +++ b/ia32/SelectLongproof.v @@ -64,7 +64,7 @@ Proof. unfold longconst; intros; destruct Archi.splitlong. apply SplitLongproof.eval_longconst. EvalOp. -Qed. +Qed. Lemma is_longconst_sound_1: forall a n, is_longconst a = Some n -> a = Eop (Olongconst n) Enil. @@ -83,46 +83,46 @@ Theorem eval_intoflong: unary_constructor_sound intoflong Val.loword. Proof. unfold intoflong; destruct Archi.splitlong. apply SplitLongproof.eval_intoflong. red; intros. destruct (is_longconst a) as [n|] eqn:C. -- TrivialExists. simpl. erewrite (is_longconst_sound x) by eauto. auto. -- TrivialExists. -Qed. +- TrivialExists. simpl. erewrite (is_longconst_sound x) by eauto. auto. +- TrivialExists. +Qed. Theorem eval_longofintu: unary_constructor_sound longofintu Val.longofintu. Proof. unfold longofintu; destruct Archi.splitlong. apply SplitLongproof.eval_longofintu. red; intros. destruct (is_intconst a) as [n|] eqn:C. -- econstructor; split. apply eval_longconst. +- econstructor; split. apply eval_longconst. exploit is_intconst_sound; eauto. intros; subst x. auto. -- TrivialExists. -Qed. +- TrivialExists. +Qed. Theorem eval_longofint: unary_constructor_sound longofint Val.longofint. Proof. unfold longofint; destruct Archi.splitlong. apply SplitLongproof.eval_longofint. red; intros. destruct (is_intconst a) as [n|] eqn:C. -- econstructor; split. apply eval_longconst. +- econstructor; split. apply eval_longconst. exploit is_intconst_sound; eauto. intros; subst x. auto. -- TrivialExists. -Qed. +- TrivialExists. +Qed. Theorem eval_notl: unary_constructor_sound notl Val.notl. Proof. unfold notl; destruct Archi.splitlong. apply SplitLongproof.eval_notl. - red; intros. destruct (notl_match a). + red; intros. destruct (notl_match a). - InvEval. econstructor; split. apply eval_longconst. auto. - InvEval. subst. exists v1; split; auto. destruct v1; simpl; auto. rewrite Int64.not_involutive; auto. -- TrivialExists. -Qed. +- TrivialExists. +Qed. Theorem eval_andlimm: forall n, unary_constructor_sound (andlimm n) (fun v => Val.andl v (Vlong n)). Proof. - unfold andlimm; intros; red; intros. + unfold andlimm; intros; red; intros. predSpec Int64.eq Int64.eq_spec n Int64.zero. - exists (Vlong Int64.zero); split. apply eval_longconst. - subst. destruct x; simpl; auto. rewrite Int64.and_zero; auto. + exists (Vlong Int64.zero); split. apply eval_longconst. + subst. destruct x; simpl; auto. rewrite Int64.and_zero; auto. predSpec Int64.eq Int64.eq_spec n Int64.mone. exists x; split. assumption. - subst. destruct x; simpl; auto. rewrite Int64.and_mone; auto. + subst. destruct x; simpl; auto. rewrite Int64.and_mone; auto. destruct (andlimm_match a); InvEval; subst. - econstructor; split. apply eval_longconst. simpl. rewrite Int64.and_commut; auto. - TrivialExists. simpl. rewrite Val.andl_assoc. rewrite Int64.and_commut; auto. @@ -131,7 +131,7 @@ Qed. Theorem eval_andl: binary_constructor_sound andl Val.andl. Proof. - unfold andl; destruct Archi.splitlong. apply SplitLongproof.eval_andl. + unfold andl; destruct Archi.splitlong. apply SplitLongproof.eval_andl. red; intros. destruct (andl_match a b). - InvEval. rewrite Val.andl_commut. apply eval_andlimm; auto. - InvEval. apply eval_andlimm; auto. @@ -140,7 +140,7 @@ Qed. Theorem eval_orlimm: forall n, unary_constructor_sound (orlimm n) (fun v => Val.orl v (Vlong n)). Proof. - unfold orlimm; intros; red; intros. + unfold orlimm; intros; red; intros. predSpec Int64.eq Int64.eq_spec n Int64.zero. exists x; split; auto. subst. destruct x; simpl; auto. rewrite Int64.or_zero; auto. predSpec Int64.eq Int64.eq_spec n Int64.mone. @@ -153,7 +153,7 @@ Qed. Theorem eval_orl: binary_constructor_sound orl Val.orl. Proof. - unfold orl; destruct Archi.splitlong. apply SplitLongproof.eval_orl. + unfold orl; destruct Archi.splitlong. apply SplitLongproof.eval_orl. red; intros. assert (DEFAULT: exists v, eval_expr ge sp e m le (Eop Oorl (a:::b:::Enil)) v /\ Val.lessdef (Val.orl x y) v) by TrivialExists. assert (ROR: forall v n1 n2, @@ -180,23 +180,24 @@ Qed. Theorem eval_xorlimm: forall n, unary_constructor_sound (xorlimm n) (fun v => Val.xorl v (Vlong n)). Proof. - unfold xorlimm; intros; red; intros. + unfold xorlimm; intros; red; intros. predSpec Int64.eq Int64.eq_spec n Int64.zero. exists x; split; auto. subst. destruct x; simpl; auto. rewrite Int64.xor_zero; auto. predSpec Int64.eq Int64.eq_spec n Int64.mone. replace (Val.xorl x (Vlong n)) with (Val.notl x). apply eval_notl; auto. - subst n. destruct x; simpl; auto. + subst n. destruct x; simpl; auto. destruct (xorlimm_match a); InvEval; subst. - econstructor; split. apply eval_longconst. simpl. rewrite Int64.xor_commut; auto. - TrivialExists. simpl. rewrite Val.xorl_assoc. rewrite Int64.xor_commut; auto. - TrivialExists. simpl. destruct v1; simpl; auto. unfold Int64.not. - rewrite Int64.xor_assoc. do 3 f_equal. apply Int64.xor_commut. + rewrite Int64.xor_assoc. apply f_equal. apply f_equal. apply f_equal. + apply Int64.xor_commut. - TrivialExists. Qed. Theorem eval_xorl: binary_constructor_sound xorl Val.xorl. Proof. - unfold xorl; destruct Archi.splitlong. apply SplitLongproof.eval_xorl. + unfold xorl; destruct Archi.splitlong. apply SplitLongproof.eval_xorl. red; intros. destruct (xorl_match a b). - InvEval. rewrite Val.xorl_commut. apply eval_xorlimm; auto. - InvEval. apply eval_xorlimm; auto. @@ -305,19 +306,19 @@ Theorem eval_negl: unary_constructor_sound negl Val.negl. Proof. unfold negl. destruct Archi.splitlong eqn:SL. apply SplitLongproof.eval_negl; auto. red; intros. destruct (is_longconst a) as [n|] eqn:C. -- exploit is_longconst_sound; eauto. intros EQ; subst x. +- exploit is_longconst_sound; eauto. intros EQ; subst x. econstructor; split. apply eval_longconst. auto. - TrivialExists. -Qed. +Qed. Theorem eval_addlimm: forall n, unary_constructor_sound (addlimm n) (fun v => Val.addl v (Vlong n)). Proof. - unfold addlimm; intros; red; intros. + unfold addlimm; intros; red; intros. predSpec Int64.eq Int64.eq_spec n Int64.zero. subst. exists x; split; auto. destruct x; simpl; auto. rewrite Int64.add_zero; auto. - destruct Archi.ptr64; auto. rewrite Ptrofs.add_zero; auto. + destruct Archi.ptr64; auto. rewrite Ptrofs.add_zero; auto. destruct (addlimm_match a); InvEval. - econstructor; split. apply eval_longconst. rewrite Int64.add_commut; auto. - inv H. simpl in H6. TrivialExists. simpl. @@ -332,10 +333,10 @@ Proof. assert (B: forall id ofs n, Archi.ptr64 = true -> Genv.symbol_address ge id (Ptrofs.add ofs (Ptrofs.repr n)) = Val.addl (Genv.symbol_address ge id ofs) (Vlong (Int64.repr n))). - { intros. replace (Ptrofs.repr n) with (Ptrofs.of_int64 (Int64.repr n)) by auto with ptrofs. + { intros. replace (Ptrofs.repr n) with (Ptrofs.of_int64 (Int64.repr n)) by auto with ptrofs. apply Genv.shift_symbol_address_64; auto. } unfold addl. destruct Archi.splitlong eqn:SL. - apply SplitLongproof.eval_addl. apply Archi.splitlong_ptr32; auto. + apply SplitLongproof.eval_addl. apply Archi.splitlong_ptr32; auto. red; intros; destruct (addl_match a b); InvEval. - rewrite Val.addl_commut. apply eval_addlimm; auto. - apply eval_addlimm; auto. @@ -373,7 +374,7 @@ Qed. Theorem eval_mullimm_base: forall n, unary_constructor_sound (mullimm_base n) (fun v => Val.mull v (Vlong n)). Proof. - intros; unfold mullimm_base. red; intros. + intros; unfold mullimm_base. red; intros. generalize (Int64.one_bits'_decomp n); intros D. destruct (Int64.one_bits' n) as [ | i [ | j [ | ? ? ]]] eqn:B. - TrivialExists. @@ -416,7 +417,7 @@ Proof. rewrite (Int64.mul_commut n). auto. destruct Archi.ptr64; auto. - apply eval_mullimm_base; auto. -Qed. +Qed. Theorem eval_mull: binary_constructor_sound mull Val.mull. Proof. @@ -442,28 +443,28 @@ Proof. Qed. Theorem eval_divls_base: partial_binary_constructor_sound divls_base Val.divls. -Proof. +Proof. unfold divls_base; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_divls_base; eauto. TrivialExists. Qed. Theorem eval_modls_base: partial_binary_constructor_sound modls_base Val.modls. -Proof. +Proof. unfold modls_base; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_modls_base; eauto. TrivialExists. Qed. - + Theorem eval_divlu_base: partial_binary_constructor_sound divlu_base Val.divlu. -Proof. +Proof. unfold divlu_base; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_divlu_base; eauto. TrivialExists. Qed. Theorem eval_modlu_base: partial_binary_constructor_sound modlu_base Val.modlu. -Proof. +Proof. unfold modlu_base; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_modlu_base; eauto. TrivialExists. @@ -476,7 +477,7 @@ Theorem eval_cmplu: Val.cmplu (Mem.valid_pointer m) c x y = Some v -> eval_expr ge sp e m le (cmplu c a b) v. Proof. - unfold cmplu; intros. destruct Archi.splitlong eqn:SL. + unfold cmplu; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_cmplu; eauto. apply Archi.splitlong_ptr32; auto. unfold Val.cmplu in H1. destruct (Val.cmplu_bool (Mem.valid_pointer m) c x y) as [vb|] eqn:C; simpl in H1; inv H1. @@ -497,7 +498,7 @@ Theorem eval_cmpl: Val.cmpl c x y = Some v -> eval_expr ge sp e m le (cmpl c a b) v. Proof. - unfold cmpl; intros. destruct Archi.splitlong eqn:SL. + unfold cmpl; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_cmpl; eauto. unfold Val.cmpl in H1. destruct (Val.cmpl_bool c x y) as [vb|] eqn:C; simpl in H1; inv H1. @@ -516,27 +517,27 @@ Proof. unfold longoffloat; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_longoffloat; eauto. TrivialExists. -Qed. +Qed. Theorem eval_floatoflong: partial_unary_constructor_sound floatoflong Val.floatoflong. Proof. unfold floatoflong; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_floatoflong; eauto. TrivialExists. -Qed. +Qed. Theorem eval_longofsingle: partial_unary_constructor_sound longofsingle Val.longofsingle. Proof. unfold longofsingle; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_longofsingle; eauto. TrivialExists. -Qed. +Qed. Theorem eval_singleoflong: partial_unary_constructor_sound singleoflong Val.singleoflong. Proof. unfold singleoflong; red; intros. destruct Archi.splitlong eqn:SL. eapply SplitLongproof.eval_singleoflong; eauto. TrivialExists. -Qed. +Qed. End CMCONSTR. |