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SharedMemory: stronger notAboutToFail

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Adam Chlipala 2016-04-21 20:35:34 -04:00
parent a8a8ff0bc6
commit e9849b9e9c
1 changed files with 34 additions and 21 deletions
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55
SharedMemory.v
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@ -98,17 +98,18 @@ Example two_increments :=
else else
Fail. Fail.
Fixpoint notAboutToFail (c : cmd) : Prop := Fixpoint notAboutToFail (c : cmd) : bool :=
match c with match c with
| Fail => False | Fail => false
| Bind c1 _ => notAboutToFail c1 | Bind c1 _ => notAboutToFail c1
| _ => True | Par c1 c2 => notAboutToFail c1 && notAboutToFail c2
| _ => true
end. end.
Theorem two_increments_ok : Theorem two_increments_ok :
invariantFor (trsys_of $0 {} two_increments) invariantFor (trsys_of $0 {} two_increments)
(fun p => let '(_, _, c) := p in (fun p => let '(_, _, c) := p in
notAboutToFail c). notAboutToFail c = true).
Proof. Proof.
unfold two_increments, two_increments_thread. unfold two_increments, two_increments_thread.
simplify. simplify.
@ -136,7 +137,7 @@ Proof.
model_check_done. model_check_done.
simplify. simplify.
propositional; subst; simplify; propositional. propositional; subst; equality.
Qed. Qed.
@ -268,6 +269,16 @@ Proof.
equality. equality.
Qed. Qed.
Lemma runLocal_left : forall c1 c2,
(forall r, runLocal c1 <> Return r)
-> runLocal (c1 || c2) = runLocal c1 || runLocal c2.
Proof.
simplify.
cases (runLocal c1); eauto.
unfold not in *.
exfalso; eauto.
Qed.
Lemma step_runLocal : forall h l c h' l' c', Lemma step_runLocal : forall h l c h' l' c',
step (h, l, c) (h', l', c') step (h, l, c) (h', l', c')
-> (runLocal c = runLocal c' /\ h = h' /\ l = l') -> (runLocal c = runLocal c' /\ h = h' /\ l = l')
@ -391,16 +402,6 @@ Proof.
eexists; propositional. eexists; propositional.
eauto. eauto.
Lemma runLocal_left : forall c1 c2,
(forall r, runLocal c1 <> Return r)
-> runLocal (c1 || c2) = runLocal c1 || runLocal c2.
Proof.
simplify.
cases (runLocal c1); eauto.
unfold not in *.
exfalso; eauto.
Qed.
rewrite runLocal_left. rewrite runLocal_left.
rewrite <- Heq. rewrite <- Heq.
rewrite runLocal_idem. rewrite runLocal_idem.
@ -494,19 +495,31 @@ Proof.
Qed. Qed.
Theorem notAboutToFail_runLocal : forall c, Theorem notAboutToFail_runLocal : forall c,
notAboutToFail (runLocal c) notAboutToFail (runLocal c) = true
-> notAboutToFail c. -> notAboutToFail c = true.
Proof. Proof.
induct c; simplify; auto. induct c; simplify; auto.
cases (runLocal c); simplify; auto. cases (runLocal c); simplify; auto.
Ltac bool := simplify; auto; propositional;
repeat match goal with
| [ H : _ |- _ ] => apply andb_true_iff in H; propositional
| [ H : _ = _ |- _ ] => rewrite H
end; try equality.
cases (runLocal c1); bool.
cases (runLocal c2); bool.
cases r; bool.
cases r; bool.
cases r; bool.
Qed. Qed.
Theorem step_stepL : forall h l c , Theorem step_stepL : forall h l c ,
invariantFor (trsys_ofL h l c) (fun p => let '(_, _, c) := p in invariantFor (trsys_ofL h l c) (fun p => let '(_, _, c) := p in
notAboutToFail c) notAboutToFail c = true)
-> invariantFor (trsys_of h l c) (fun p => -> invariantFor (trsys_of h l c) (fun p =>
let '(_, _, c) := p in let '(_, _, c) := p in
notAboutToFail c). notAboutToFail c = true).
Proof. Proof.
unfold invariantFor; simplify. unfold invariantFor; simplify.
propositional; subst. propositional; subst.
@ -520,7 +533,7 @@ Qed.
Theorem two_increments_ok_again : Theorem two_increments_ok_again :
invariantFor (trsys_of $0 {} two_increments) invariantFor (trsys_of $0 {} two_increments)
(fun p => let '(_, _, c) := p in (fun p => let '(_, _, c) := p in
notAboutToFail c). notAboutToFail c = true).
Proof. Proof.
apply step_stepL. apply step_stepL.
unfold two_increments, two_increments_thread. unfold two_increments, two_increments_thread.
@ -540,5 +553,5 @@ Proof.
model_check_done. model_check_done.
simplify. simplify.
propositional; subst; simplify; propositional. propositional; subst; equality.
Qed. Qed.