Commit 7ccbb8cd authored by Joseph Tassarotti's avatar Joseph Tassarotti

Use explicit names in some scripts, re-organize fupd plainly derived laws,...

Use explicit names in some scripts, re-organize fupd plainly derived laws, adjust wsat import/export.
parent 334b689e
......@@ -50,7 +50,7 @@ Proof.
iNext. by iMod ("HP" with "[$]") as "(_ & _ & HP)".
Qed.
Lemma fupd_plain_soundness `{invPreG Σ} E (P: iPropSI Σ) `{!Plain P}:
Lemma fupd_plain_soundness `{invPreG Σ} E (P: iProp Σ) `{!Plain P}:
( `{Hinv: invG Σ}, (|={, E}=> P)%I) ( P)%I.
Proof.
iIntros (Hfupd). iMod wsat_alloc as (Hinv) "[Hw HE]".
......@@ -68,7 +68,7 @@ Proof.
eapply (fupd_plain_soundness ); first by apply _.
intros Hinv. rewrite -/sbi_laterN.
iPoseProof (Hiter Hinv) as "H".
destruct n.
destruct n as [|n].
- rewrite //=. iPoseProof (fupd_plain_strong with "H") as "H'".
do 2 iMod "H'"; iModIntro; auto.
- iPoseProof (step_fupdN_mono _ _ _ _ (|={}=> ⌜φ⌝)%I with "H") as "H'".
......
......@@ -13,23 +13,24 @@ Module invG.
enabled_name : gname;
disabled_name : gname;
}.
End invG.
Import invG.
Definition invΣ : gFunctors :=
#[GFunctor (authRF (gmapURF positive (agreeRF (laterCF idCF))));
GFunctor coPset_disjUR;
GFunctor (gset_disjUR positive)].
Definition invΣ : gFunctors :=
#[GFunctor (authRF (gmapURF positive (agreeRF (laterCF idCF))));
GFunctor coPset_disjUR;
GFunctor (gset_disjUR positive)].
Class invPreG (Σ : gFunctors) : Set := WsatPreG {
inv_inPreG :> inG Σ (authR (gmapUR positive (agreeR (laterC (iPreProp Σ)))));
enabled_inPreG :> inG Σ coPset_disjR;
disabled_inPreG :> inG Σ (gset_disjR positive);
}.
Class invPreG (Σ : gFunctors) : Set := WsatPreG {
inv_inPreG :> inG Σ (authR (gmapUR positive (agreeR (laterC (iPreProp Σ)))));
enabled_inPreG :> inG Σ coPset_disjR;
disabled_inPreG :> inG Σ (gset_disjR positive);
}.
Instance subG_invΣ {Σ} : subG invΣ Σ invPreG Σ.
Proof. solve_inG. Qed.
End invG.
Import invG.
Definition invariant_unfold {Σ} (P : iProp Σ) : agree (later (iPreProp Σ)) :=
to_agree (Next (iProp_unfold P)).
Definition ownI `{invG Σ} (i : positive) (P : iProp Σ) : iProp Σ :=
......
......@@ -272,38 +272,6 @@ Section fupd_derived.
intros P1 P2 HP Q1 Q2 HQ. by rewrite HP HQ -fupd_sep.
Qed.
Lemma fupd_plain_weak `{BiPlainly PROP, !BiFUpdPlainly PROP} E P Q `{!Plain P}:
(Q ={E}= P) - Q ={E}= Q P.
Proof. by rewrite {1}(plain P) fupd_plainly_weak. Qed.
Lemma later_fupd_plain `{BiPlainly PROP, !BiFUpdPlainly PROP} p E1 E2 P `{!Plain P} :
(?p |={E1, E2}=> P) ={E1}= ?p P.
Proof. by rewrite {1}(plain P) later_fupd_plainly. Qed.
Lemma fupd_plain_strong `{BiPlainly PROP, !BiFUpdPlainly PROP} E1 E2 P `{!Plain P} :
(|={E1, E2}=> P) ={E1}= P.
Proof. by apply (later_fupd_plain false). Qed.
Lemma fupd_plain' `{BiPlainly PROP, !BiFUpdPlainly PROP} E1 E2 E2' P Q `{!Plain P} :
E1 E2
(Q ={E1, E2'}= P) - (|={E1, E2}=> Q) ={E1}= (|={E1, E2}=> Q) P.
Proof.
intros (E3&->&HE)%subseteq_disjoint_union_L.
apply wand_intro_l. rewrite fupd_frame_r.
rewrite fupd_plain_strong fupd_except_0 fupd_plain_weak wand_elim_r.
rewrite (fupd_mask_mono E1 (E1 E3)); last by set_solver+.
rewrite fupd_trans -(fupd_trans E1 (E1 E3) E1).
apply fupd_mono. rewrite -fupd_frame_r.
apply sep_mono; auto. apply fupd_intro_mask; set_solver+.
Qed.
Lemma fupd_plain `{BiPlainly PROP, !BiFUpdPlainly PROP} E1 E2 P Q `{!Plain P} :
E1 E2 (Q - P) - (|={E1, E2}=> Q) ={E1}= (|={E1, E2}=> Q) P.
Proof.
intros HE. rewrite -(fupd_plain' _ _ E1) //. apply wand_intro_l.
by rewrite wand_elim_r -fupd_intro.
Qed.
(** Fancy updates that take a step derived rules. *)
Lemma step_fupd_wand E1 E2 E3 P Q : (|={E1,E2,E3}=> P) - (P - Q) - |={E1,E2,E3}=> Q.
Proof.
......@@ -345,13 +313,6 @@ Section fupd_derived.
by apply later_mono, fupd_mono.
Qed.
Lemma step_fupd_plain `{BiPlainly PROP, !BiFUpdPlainly PROP} E P `{!Plain P} :
(|={E, }=> P) ={E}= P.
Proof.
specialize (later_fupd_plain true E P) => //= ->.
rewrite fupd_trans fupd_plain_strong. apply fupd_mono, except_0_later.
Qed.
Lemma step_fupd_fupd E P:
(|={E, }=> P) (|={E, }=> |={E}=> P).
Proof.
......@@ -380,15 +341,58 @@ Section fupd_derived.
rewrite step_fupd_frame_l IH //=.
Qed.
Lemma step_fupdN_plain `{BiPlainly PROP, !BiFUpdPlainly PROP} E n P `{!Plain P}:
(|={E, }=>^n P) ={E}= ^n P.
Proof.
induction n as [| n].
- rewrite -fupd_intro. apply except_0_intro.
- rewrite Nat_iter_S step_fupd_fupd IHn ?fupd_trans step_fupd_plain.
apply fupd_mono. destruct n; simpl.
* by rewrite except_0_idemp.
* by rewrite except_0_later.
Qed.
Section fupd_plainly_derived.
Context `{BiPlainly PROP, !BiFUpdPlainly PROP}.
Lemma fupd_plain_weak E P Q `{!Plain P}:
(Q ={E}= P) - Q ={E}= Q P.
Proof. by rewrite {1}(plain P) fupd_plainly_weak. Qed.
Lemma later_fupd_plain p E1 E2 P `{!Plain P} :
(?p |={E1, E2}=> P) ={E1}= ?p P.
Proof. by rewrite {1}(plain P) later_fupd_plainly. Qed.
Lemma fupd_plain_strong E1 E2 P `{!Plain P} :
(|={E1, E2}=> P) ={E1}= P.
Proof. by apply (later_fupd_plain false). Qed.
Lemma fupd_plain' E1 E2 E2' P Q `{!Plain P} :
E1 E2
(Q ={E1, E2'}= P) - (|={E1, E2}=> Q) ={E1}= (|={E1, E2}=> Q) P.
Proof.
intros (E3&->&HE)%subseteq_disjoint_union_L.
apply wand_intro_l. rewrite fupd_frame_r.
rewrite fupd_plain_strong fupd_except_0 fupd_plain_weak wand_elim_r.
rewrite (fupd_mask_mono E1 (E1 E3)); last by set_solver+.
rewrite fupd_trans -(fupd_trans E1 (E1 E3) E1).
apply fupd_mono. rewrite -fupd_frame_r.
apply sep_mono; auto. apply fupd_intro_mask; set_solver+.
Qed.
Lemma fupd_plain E1 E2 P Q `{!Plain P} :
E1 E2 (Q - P) - (|={E1, E2}=> Q) ={E1}= (|={E1, E2}=> Q) P.
Proof.
intros HE. rewrite -(fupd_plain' _ _ E1) //. apply wand_intro_l.
by rewrite wand_elim_r -fupd_intro.
Qed.
Lemma step_fupd_plain E P `{!Plain P} :
(|={E, }=> P) ={E}= P.
Proof.
specialize (later_fupd_plain true E P) => //= ->.
rewrite fupd_trans fupd_plain_strong. apply fupd_mono, except_0_later.
Qed.
Lemma step_fupdN_plain E n P `{!Plain P}:
(|={E, }=>^n P) ={E}= ^n P.
Proof.
induction n as [|n IH].
- rewrite -fupd_intro. apply except_0_intro.
- rewrite Nat_iter_S step_fupd_fupd IH ?fupd_trans step_fupd_plain.
apply fupd_mono. destruct n; simpl.
* by rewrite except_0_idemp.
* by rewrite except_0_later.
Qed.
End fupd_plainly_derived.
End fupd_derived.
From stdpp Require Import namespaces.
From iris.program_logic Require Export weakestpre.
From iris.algebra Require Import gmap auth agree gset coPset.
From iris.base_logic.lib Require Export wsat.
From iris.base_logic.lib Require Import wsat.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
......
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