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Proofreading SeparationLogic
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2 changed files with 19 additions and 19 deletions
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@ -143,12 +143,12 @@ Module Import S <: SEP.
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Qed.
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Local Ltac t := (unfold himp, heq, lift, star, exis; propositional; subst);
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repeat (match goal with
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| [ H : forall x, _ <-> _ |- _ ] =>
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apply iff_two in H
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| [ H : ex _ |- _ ] => destruct H
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| [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H
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end; propositional; subst); eauto 15.
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repeat (match goal with
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| [ H : forall x, _ <-> _ |- _ ] =>
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apply iff_two in H
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| [ H : ex _ |- _ ] => destruct H
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| [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H
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end; propositional; subst); eauto 15.
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Theorem himp_heq : forall p q, p === q
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<-> (p ===> q /\ q ===> p).
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@ -327,11 +327,11 @@ Inductive hoare_triple : forall {result}, hprop -> cmd result -> (result -> hpro
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| HtFrame : forall {result} (c : cmd result) P Q R,
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hoare_triple P c Q
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-> hoare_triple (P * R)%sep c (fun r => Q r * R)%sep.
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(* The *frame rule* is the other big idea of separation. We can extend any
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* Hoare triple by starring an arbitrary assertion [R] into both precondition
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* and postcondition. Note that rule [HtRead] built in a variant of the frame
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* rule, where the frame predicate [R] may depend on the value [v] being read.
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* The other operations can use this generic frame rule instead. *)
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(* The *frame rule* is the other big idea of separation logic. We can extend
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* any Hoare triple by starring an arbitrary assertion [R] into both
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* precondition and postcondition. Note that rule [HtRead] built in a variant
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* of the frame rule, where the frame predicate [R] may depend on the value [v]
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* being read. The other operations can use this generic frame rule instead. *)
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Notation "{{ P }} c {{ r ~> Q }}" :=
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@ -1266,7 +1266,7 @@ Qed.
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Fixpoint linkedListSegment (p : nat) (ls : list nat) (q : nat) :=
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match ls with
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| nil => [| p = q |]
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| x :: ls' => [| p <> 0 |] * exists p', p |-> x * (p+1) |-> p' * linkedListSegment p' ls' q
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| x :: ls' => [| p <> 0 |] * exists p', p |--> [x; p'] * linkedListSegment p' ls' q
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end%sep.
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(* Next, two [linkedListSegment] lemmas analogous to those for [linkedList]
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@ -1280,7 +1280,7 @@ Qed.
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Lemma linkedListSegment_append : forall q r x ls p,
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q <> 0
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-> linkedListSegment p ls q * q |-> x * (q+1) |-> r ===> linkedListSegment p (ls ++ x :: nil) r.
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-> linkedListSegment p ls q * q |--> [x; r] ===> linkedListSegment p (ls ++ x :: nil) r.
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Proof.
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induct ls; cancel; auto.
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subst; cancel.
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@ -127,12 +127,12 @@ Module Import S <: SEP.
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Qed.
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Local Ltac t := (unfold himp, heq, lift, star, exis; propositional; subst);
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repeat (match goal with
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| [ H : forall x, _ <-> _ |- _ ] =>
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apply iff_two in H
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| [ H : ex _ |- _ ] => destruct H
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| [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H
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end; propositional; subst); eauto 15.
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repeat (match goal with
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| [ H : forall x, _ <-> _ |- _ ] =>
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apply iff_two in H
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| [ H : ex _ |- _ ] => destruct H
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| [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H
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end; propositional; subst); eauto 15.
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Theorem himp_heq : forall p q, p === q
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<-> (p ===> q /\ q ===> p).
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