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ConcurrentSeparationLogic_template: extend to match last change

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Adam Chlipala 2021-01-03 15:27:46 -05:00
parent b7f248e099
commit f73e30817b
1 changed files with 25 additions and 19 deletions
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44
ConcurrentSeparationLogic_template.v
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@ -323,11 +323,13 @@ Inductive hoare_triple (linvs : list hprop) : forall {result}, hprop -> cmd resu
nth_error linvs a = Some I
-> hoare_triple linvs I (Unlock a) (fun _ => emp)%sep
(* When forking into two threads, divide the (local) heap among them. *)
(* When forking into two threads, divide the (local) heap among them.
* For simplicity, we never let parallel compositions terminate,
* so it is appropriate to assign a contradictory overall postcondition. *)
| HtPar : forall P1 c1 Q1 P2 c2 Q2,
hoare_triple linvs P1 c1 Q1
-> hoare_triple linvs P2 c2 Q2
-> hoare_triple linvs (P1 * P2)%sep (Par c1 c2) (fun _ => Q1 tt * Q2 tt)%sep
-> hoare_triple linvs (P1 * P2)%sep (Par c1 c2) (fun _ => [| False |])%sep
(* Now we repeat these two structural rules from before. *)
| HtConsequence : forall {result} (c : cmd result) P Q (P' : hprop) (Q' : _ -> hprop),
@ -353,6 +355,18 @@ Proof.
reflexivity.
Qed.
Lemma HtStrengthenFalse : forall linvs {result} (c : cmd result) P (Q' : _ -> hprop),
hoare_triple linvs P c (fun _ => [| False |])%sep
-> hoare_triple linvs P c Q'.
Proof.
simplify.
eapply HtStrengthen; eauto.
simplify.
unfold himp; simplify.
cases H0.
tauto.
Qed.
Lemma HtWeaken : forall linvs {result} (c : cmd result) P Q (P' : hprop),
hoare_triple linvs P c Q
-> P' ===> P
@ -432,8 +446,8 @@ Ltac use_IH H := conseq; [ apply H | .. ]; ht.
Ltac loop_inv0 Inv := (eapply HtWeaken; [ apply HtLoop with (I := Inv) | .. ])
|| (eapply HtConsequence; [ apply HtLoop with (I := Inv) | .. ]).
Ltac loop_inv Inv := loop_inv0 Inv; ht.
Ltac fork0 P1 P2 := apply HtWeaken with (P := (P1 * P2)%sep); [ apply HtPar | ].
Ltac fork P1 P2 := fork0 P1 P2 || (eapply HtStrengthen; [ fork0 P1 P2 | ]).
Ltac fork0 P1 P2 := apply HtWeaken with (P := (P1 * P2)%sep); [ eapply HtPar | ].
Ltac fork P1 P2 := fork0 P1 P2 || (eapply HtStrengthenFalse; fork0 P1 P2).
Ltac use H := (eapply use_lemma; [ eapply H | cancel ])
|| (eapply HtStrengthen; [ eapply use_lemma; [ eapply H | cancel ] | ]).
@ -733,8 +747,6 @@ Proof.
cancel.
cancel.
cancel.
cancel.
Qed.
@ -1095,10 +1107,9 @@ Lemma invert_Par : forall linvs c1 c2 P Q,
-> exists P1 P2 Q1 Q2,
hoare_triple linvs P1 c1 Q1
/\ hoare_triple linvs P2 c2 Q2
/\ P ===> P1 * P2
/\ Q1 tt * Q2 tt ===> Q tt.
/\ P ===> P1 * P2.
Proof.
induct 1; simp; eauto 10.
induct 1; simp; eauto 7.
symmetry in x0.
apply unit_not_nat in x0; simp.
@ -1106,11 +1117,10 @@ Proof.
symmetry in x0.
apply unit_not_nat in x0; simp.
eauto 10 using himp_trans.
eauto 8 using himp_trans.
exists (x * R)%sep, x0, (fun r => x1 r * R)%sep, x2; simp; eauto.
rewrite H2; cancel.
rewrite <- H4; cancel.
rewrite H3; cancel.
Qed.
Transparent heq himp lift star exis ptsto.
@ -1421,12 +1431,10 @@ Proof.
eapply IHstep in H2.
simp.
eexists; propositional.
eapply HtStrengthen.
apply HtStrengthenFalse.
econstructor.
eassumption.
eassumption.
simp.
cases r; auto.
eapply use_himp; try eassumption.
cancel.
eapply use_himp; try eassumption.
@ -1437,16 +1445,14 @@ Proof.
eapply IHstep in H0.
simp.
eexists; propositional.
eapply HtStrengthen.
apply HtStrengthenFalse.
econstructor.
eassumption.
eassumption.
simp.
cases r; auto.
eapply use_himp; try eassumption.
cancel.
eapply use_himp; try eassumption.
rewrite H3.
rewrite H4.
cancel.
Qed.