Commit 4d2398aa authored by Ralf Jung's avatar Ralf Jung

Merge branch 'robbert/invariant_weaken' into 'master'

Make invariants closed under weakening.

See merge request FP/iris-coq!85
parents 59fbe96b 7c9f06f7
Pipeline #6395 passed with stages
in 9 minutes and 59 seconds
......@@ -7,7 +7,7 @@ Import uPred.
(** Derived forms and lemmas about them. *)
Definition inv_def `{invG Σ} (N : namespace) (P : iProp Σ) : iProp Σ :=
( i, i (N:coPset) ownI i P)%I.
( i P', i (N:coPset) (P' P) ownI i P')%I.
Definition inv_aux : seal (@inv_def). by eexists. Qed.
Definition inv {Σ i} := unseal inv_aux Σ i.
Definition inv_eq : @inv = @inv_def := seal_eq inv_aux.
......@@ -21,19 +21,25 @@ Implicit Types N : namespace.
Implicit Types P Q R : iProp Σ.
Global Instance inv_contractive N : Contractive (inv N).
Proof.
rewrite inv_eq=> n ???. apply exist_ne=>i. by apply and_ne, ownI_contractive.
Qed.
Proof. rewrite inv_eq. solve_contractive. Qed.
Global Instance inv_ne N : NonExpansive (inv N).
Proof. apply contractive_ne, _. Qed.
Global Instance inv_Proper N : Proper ((⊣⊢) ==> (⊣⊢)) (inv N).
Global Instance inv_proper N : Proper ((⊣⊢) ==> (⊣⊢)) (inv N).
Proof. apply ne_proper, _. Qed.
Global Instance inv_persistent N P : Persistent (inv N P).
Proof. rewrite inv_eq /inv; apply _. Qed.
Lemma inv_iff N P Q : (P Q) - inv N P - inv N Q.
Proof.
iIntros "#HPQ". rewrite inv_eq. iDestruct 1 as (i P') "(?&#HP&?)".
iExists i, P'. iFrame. iNext; iAlways; iSplit.
- iIntros "HP'". iApply "HPQ". by iApply "HP".
- iIntros "HQ". iApply "HP". by iApply "HPQ".
Qed.
Lemma fresh_inv_name (E : gset positive) N : i, i E i (N:coPset).
Proof.
exists (coPpick ( N coPset.of_gset E)).
......@@ -48,6 +54,7 @@ Proof.
rewrite inv_eq /inv_def fupd_eq /fupd_def. iIntros "HP [Hw $]".
iMod (ownI_alloc ( (N : coPset)) P with "[$HP $Hw]")
as (i ?) "[$ ?]"; auto using fresh_inv_name.
do 2 iModIntro. iExists i, P. rewrite -(iff_refl True). auto.
Qed.
Lemma inv_alloc_open N E P :
......@@ -61,7 +68,9 @@ Proof.
{ rewrite -?ownE_op; [|set_solver..].
rewrite assoc_L -!union_difference_L //. set_solver. }
do 2 iModIntro. iFrame "HE\N". iSplitL "Hw HEi"; first by iApply "Hw".
iSplitL "Hi"; first by eauto. iIntros "HP [Hw HE\N]".
iSplitL "Hi".
{ iExists i, P. rewrite -(iff_refl True). auto. }
iIntros "HP [Hw HE\N]".
iDestruct (ownI_close with "[$Hw $Hi $HP $HD]") as "[$ HEi]".
do 2 iModIntro. iSplitL; [|done].
iCombine "HEi" "HEN\i" as "HEN"; iCombine "HEN" "HE\N" as "HE".
......@@ -72,13 +81,16 @@ Qed.
Lemma inv_open E N P :
N E inv N P ={E,E∖↑N}= P ( P ={E∖↑N,E}= True).
Proof.
rewrite inv_eq /inv_def fupd_eq /fupd_def; iDestruct 1 as (i) "[Hi #HiP]".
rewrite inv_eq /inv_def fupd_eq /fupd_def.
iDestruct 1 as (i P') "(Hi & #HP' & #HiP)".
iDestruct "Hi" as % ?%elem_of_subseteq_singleton.
rewrite {1 4}(union_difference_L ( N) E) // ownE_op; last set_solver.
rewrite {1 5}(union_difference_L {[ i ]} ( N)) // ownE_op; last set_solver.
iIntros "(Hw & [HE $] & $) !> !>".
iDestruct (ownI_open i P with "[$Hw $HE $HiP]") as "($ & $ & HD)".
iIntros "HP [Hw $] !> !>". iApply ownI_close; by iFrame.
iDestruct (ownI_open i with "[$Hw $HE $HiP]") as "($ & HP & HD)".
iDestruct ("HP'" with "HP") as "$".
iIntros "HP [Hw $] !> !>". iApply (ownI_close _ P'). iFrame "HD Hw HiP".
iApply "HP'". iFrame.
Qed.
Lemma inv_open_timeless E N P `{!Timeless P} :
......
......@@ -43,6 +43,14 @@ Section proofs.
Global Instance na_inv_persistent p N P : Persistent (na_inv p N P).
Proof. rewrite /na_inv; apply _. Qed.
Lemma na_inv_iff p N P Q : (P Q) - na_inv p N P - na_inv p N Q.
Proof.
iIntros "#HPQ". rewrite /na_inv. iDestruct 1 as (i ?) "#Hinv".
iExists i. iSplit; first done. iApply (inv_iff with "[] Hinv").
iNext. iAlways. iSplit; (iIntros "[[? Ho]|?]";
[iLeft; iFrame "Ho"; by iApply "HPQ"|by iRight]).
Qed.
Lemma na_alloc : (|==> p, na_own p )%I.
Proof. by apply own_alloc. Qed.
......
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