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Proofreading SeparationLogic

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Adam Chlipala 2018-04-22 14:32:38 -04:00
parent 7c06dc3541
commit b7fd72f309
2 changed files with 19 additions and 19 deletions
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26
SeparationLogic.v
View file

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

12
SeparationLogic_template.v
View file

@ -127,12 +127,12 @@ Module Import S <: SEP.
Qed. Qed.
Local Ltac t := (unfold himp, heq, lift, star, exis; propositional; subst); Local Ltac t := (unfold himp, heq, lift, star, exis; propositional; subst);
repeat (match goal with repeat (match goal with
| [ H : forall x, _ <-> _ |- _ ] => | [ H : forall x, _ <-> _ |- _ ] =>
apply iff_two in H apply iff_two in H
| [ H : ex _ |- _ ] => destruct H | [ H : ex _ |- _ ] => destruct H
| [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H | [ H : split _ _ $0 |- _ ] => apply split_empty_fwd in H
end; propositional; subst); eauto 15. end; propositional; subst); eauto 15.
Theorem himp_heq : forall p q, p === q Theorem himp_heq : forall p q, p === q
<-> (p ===> q /\ q ===> p). <-> (p ===> q /\ q ===> p).