diff options
Diffstat (limited to 'common/Memory.v')
| -rw-r--r-- | common/Memory.v | 155 |
1 files changed, 155 insertions, 0 deletions
diff --git a/common/Memory.v b/common/Memory.v index b68a5049..cd8a2001 100644 --- a/common/Memory.v +++ b/common/Memory.v @@ -38,6 +38,10 @@ Require Import Floats. Require Import Values. Require Export Memdata. Require Export Memtype. +Require Import Lia. + +Definition default_notrap_load_value (chunk : memory_chunk) := Vundef. + (* To avoid useless definitions of inductors in extracted code. *) Local Unset Elimination Schemes. @@ -538,6 +542,48 @@ Proof. induction vl; simpl; intros. auto. rewrite IHvl. auto. Qed. +Remark set_setN_swap_disjoint: + forall vl: list memval, + forall v: memval, + forall m : ZMap.t memval, + forall p pl: Z, + ~ (Intv.In p (pl, pl + Z.of_nat (length vl))) -> + (setN vl pl (ZMap.set p v m)) = (ZMap.set p v (setN vl pl m)). +Proof. + induction vl; simpl; trivial. + intros. + unfold Intv.In in *; simpl in *. + rewrite ZMap.set_disjoint by lia. + apply IHvl. + lia. +Qed. + +Lemma setN_swap_disjoint: + forall vl1 vl2: list memval, + forall m : ZMap.t memval, + forall p1 p2: Z, + Intv.disjoint (p1, p1 + Z.of_nat (length vl1)) + (p2, p2 + Z.of_nat (length vl2)) -> + (setN vl1 p1 (setN vl2 p2 m)) = (setN vl2 p2 (setN vl1 p1 m)). +Proof. + induction vl1; simpl; trivial. + intros until p2. intro DISJOINT. + rewrite <- set_setN_swap_disjoint. + { rewrite IHvl1. + reflexivity. + unfold Intv.disjoint, Intv.In in *. + simpl in *. + intro. + intro BOUNDS. + apply DISJOINT. + lia. + } + unfold Intv.disjoint, Intv.In in *. + simpl in *. + apply DISJOINT. + lia. +Qed. + (** [store chunk m b ofs v] perform a write in memory state [m]. Value [v] is stored at address [b] and offset [ofs]. Return the updated memory store, or [None] if the accessed bytes @@ -682,6 +728,15 @@ Proof. apply decode_val_type. Qed. +Theorem load_rettype: + forall m chunk b ofs v, + load chunk m b ofs = Some v -> + Val.has_rettype v (rettype_of_chunk chunk). +Proof. + intros. exploit load_result; eauto; intros. rewrite H0. + apply decode_val_rettype. +Qed. + Theorem load_cast: forall m chunk b ofs v, load chunk m b ofs = Some v -> @@ -1169,6 +1224,106 @@ Local Hint Resolve store_valid_block_1 store_valid_block_2: mem. Local Hint Resolve store_valid_access_1 store_valid_access_2 store_valid_access_3: mem. +Remark mem_same_proof_irr : + forall m1 m2 : mem, + (mem_contents m1) = (mem_contents m2) -> + (mem_access m1) = (mem_access m2) -> + (nextblock m1) = (nextblock m2) -> + m1 = m2. +Proof. + destruct m1 as [contents1 access1 nextblock1 access_max1 nextblock_noaccess1 default1]. + destruct m2 as [contents2 access2 nextblock2 access_max2 nextblock_noaccess2 default2]. + simpl. + intros. + subst contents2. + subst access2. + subst nextblock2. + f_equal; apply proof_irr. +Qed. + +Theorem store_store_other: + forall chunk b ofs v chunk' b' ofs' v' m0 m1 m1', + b' <> b + \/ ofs' + size_chunk chunk' <= ofs + \/ ofs + size_chunk chunk <= ofs' -> + store chunk m0 b ofs v = Some m1 -> + store chunk' m0 b' ofs' v' = Some m1' -> + store chunk' m1 b' ofs' v' = + store chunk m1' b ofs v. +Proof. + intros until m1'. + intro DISJOINT. + intros W0 W0'. + assert (valid_access m1' chunk b ofs Writable) as WRITEABLE1' by eauto with mem. + (* { + eapply store_valid_access_1. + apply W0'. + eapply store_valid_access_3. + apply W0. + } *) + assert (valid_access m1 chunk' b' ofs' Writable) as WRITABLE1 by eauto with mem. + (* { + eapply store_valid_access_1. + apply W0. + eapply store_valid_access_3. + apply W0'. + } *) + unfold store in *. + destruct (valid_access_dec m0 chunk b ofs Writable). + 2: congruence. + destruct (valid_access_dec m1 chunk' b' ofs' Writable). + 2: contradiction. + destruct (valid_access_dec m0 chunk' b' ofs' Writable). + 2: congruence. + destruct (valid_access_dec m1' chunk b ofs Writable). + 2: contradiction. + f_equal. + inv W0; simpl in *. + inv W0'; simpl in *. + apply mem_same_proof_irr; simpl; trivial. + destruct (eq_block b b'). + { subst b'. + rewrite PMap.gss. + rewrite PMap.gss. + rewrite PMap.set2. + rewrite PMap.set2. + f_equal. + apply setN_swap_disjoint. + unfold Intv.disjoint. + rewrite encode_val_length. + rewrite <- size_chunk_conv. + rewrite encode_val_length. + rewrite <- size_chunk_conv. + unfold Intv.In; simpl. + intros. + destruct DISJOINT. contradiction. + lia. + } + { + rewrite PMap.set_disjoint by congruence. + rewrite PMap.gso by congruence. + rewrite PMap.gso by congruence. + reflexivity. + } +Qed. + +Section STOREV. +Variable chunk: memory_chunk. +Variable m1: mem. +Variables addr v: val. +Variable m2: mem. +Hypothesis STORE: storev chunk m1 addr v = Some m2. + + +Theorem loadv_storev_same: + loadv chunk m2 addr = Some (Val.load_result chunk v). +Proof. + destruct addr; simpl in *; try discriminate. + eapply load_store_same. + eassumption. +Qed. +End STOREV. + Lemma load_store_overlap: forall chunk m1 b ofs v m2 chunk' ofs' v', store chunk m1 b ofs v = Some m2 -> |