Commit 52c3006d authored by Robbert Krebbers's avatar Robbert Krebbers Committed by Jacques-Henri Jourdan

Generalize proofmode.

parent 65bde879
......@@ -24,17 +24,21 @@ theories/algebra/local_updates.v
theories/algebra/gset.v
theories/algebra/coPset.v
theories/algebra/deprecated.v
theories/bi/interface.v
theories/bi/derived.v
theories/bi/big_op.v
theories/bi/bi.v
theories/bi/tactics.v
theories/bi/fractional.v
theories/base_logic/upred.v
theories/base_logic/primitive.v
theories/base_logic/derived.v
theories/base_logic/base_logic.v
theories/base_logic/tactics.v
theories/base_logic/big_op.v
theories/base_logic/hlist.v
theories/base_logic/soundness.v
theories/base_logic/double_negation.v
theories/base_logic/deprecated.v
theories/base_logic/fixpoint.v
theories/base_logic/proofmode.v
theories/base_logic/proofmode_classes.v
theories/base_logic/lib/iprop.v
theories/base_logic/lib/own.v
theories/base_logic/lib/saved_prop.v
......@@ -49,7 +53,6 @@ theories/base_logic/lib/boxes.v
theories/base_logic/lib/na_invariants.v
theories/base_logic/lib/cancelable_invariants.v
theories/base_logic/lib/counter_examples.v
theories/base_logic/lib/fractional.v
theories/base_logic/lib/gen_heap.v
theories/base_logic/lib/core.v
theories/base_logic/lib/fancy_updates_from_vs.v
......@@ -89,6 +92,7 @@ theories/proofmode/class_instances.v
theories/tests/heap_lang.v
theories/tests/one_shot.v
theories/tests/proofmode.v
theories/tests/proofmode_iris.v
theories/tests/list_reverse.v
theories/tests/tree_sum.v
theories/tests/ipm_paper.v
......
From iris.algebra Require Export excl local_updates.
From iris.base_logic Require Import base_logic.
From iris.proofmode Require Import classes.
From iris.base_logic Require Import base_logic proofmode_classes.
Set Default Proof Using "Type".
Record auth (A : Type) := Auth { authoritative : excl' A; auth_own : A }.
......
From Coq.QArith Require Import Qcanon.
From iris.algebra Require Export cmra.
From iris.proofmode Require Import classes.
From iris.base_logic Require Import proofmode_classes.
Set Default Proof Using "Type".
Notation frac := Qp (only parsing).
......
From iris.algebra Require Export frac auth.
From iris.algebra Require Export updates local_updates.
From iris.proofmode Require Import classes.
From iris.base_logic Require Import proofmode_classes.
Definition frac_authR (A : cmraT) : cmraT :=
authR (optionUR (prodR fracR A)).
......
From iris.base_logic Require Export derived.
From iris.bi Require Export bi.
Set Default Proof Using "Type".
Module Import uPred.
Export upred.uPred.
Export primitive.uPred.
Export derived.uPred.
Export bi.
End uPred.
(* Hint DB for the logic *)
......@@ -12,6 +13,6 @@ Hint Resolve pure_intro.
Hint Resolve or_elim or_intro_l' or_intro_r' : I.
Hint Resolve and_intro and_elim_l' and_elim_r' : I.
Hint Resolve persistently_mono : I.
Hint Resolve sep_elim_l' sep_elim_r' sep_mono : I.
Hint Resolve sep_mono : I. (* sep_elim_l' sep_elim_r' *)
Hint Immediate True_intro False_elim : I.
Hint Immediate iff_refl internal_eq_refl' : I.
Hint Immediate iff_refl internal_eq_refl : I.
(*
FIXME
From iris.base_logic Require Import primitive.
Set Default Proof Using "Type".
......@@ -10,3 +13,4 @@ Notation "x = y" := (uPred_pure (x%C%type = y%C%type)) (only parsing) : uPred_sc
(* Deprecated 2016-11-22. Use ⌜x ⊥ y ⌝ instead. *)
Notation "x ⊥ y" := (uPred_pure (x%C%type ⊥ y%C%type)) (only parsing) : uPred_scope.
*)
This diff is collapsed.
......@@ -7,11 +7,11 @@ Definition uPred_nnupd {M} (P: uPred M) : uPred M :=
n, (P - ^n False) - ^n False.
Notation "|=n=> Q" := (uPred_nnupd Q)
(at level 99, Q at level 200, format "|=n=> Q") : uPred_scope.
(at level 99, Q at level 200, format "|=n=> Q") : bi_scope.
Notation "P =n=> Q" := (P |=n=> Q)
(at level 99, Q at level 200, only parsing) : C_scope.
Notation "P =n=∗ Q" := (P - |=n=> Q)%I
(at level 99, Q at level 200, format "P =n=∗ Q") : uPred_scope.
(at level 99, Q at level 200, format "P =n=∗ Q") : bi_scope.
(* Our goal is to prove that:
(1) |=n=> has (nearly) all the properties of the |==> modality that are used in Iris
......@@ -27,7 +27,7 @@ Implicit Types x : M.
Import uPred.
(* Helper lemmas about iterated later modalities *)
Lemma laterN_big n a x φ: {n} x a n (^a ⌜φ⌝)%I n x φ.
Lemma laterN_big n a x φ: {n} x a n (^a ⌜φ⌝ : uPred M)%I n x φ.
Proof.
induction 2 as [| ?? IHle].
- induction a; repeat (rewrite //= || uPred.unseal).
......@@ -37,7 +37,7 @@ Proof.
eapply uPred_closed; eauto using cmra_validN_S.
Qed.
Lemma laterN_small n a x φ: {n} x n < a (^a ⌜φ⌝)%I n x.
Lemma laterN_small n a x φ: {n} x n < a (^a ⌜φ⌝ : uPred M)%I n x.
Proof.
induction 2.
- induction n as [| n IHn]; [| move: IHn];
......@@ -132,7 +132,7 @@ Fixpoint uPred_nnupd_k {M} k (P: uPred M) : uPred M :=
end.
Notation "|=n=>_ k Q" := (uPred_nnupd_k k Q)
(at level 99, k at level 9, Q at level 200, format "|=n=>_ k Q") : uPred_scope.
(at level 99, k at level 9, Q at level 200, format "|=n=>_ k Q") : bi_scope.
(* One direction of the limiting process is easy -- nnupd implies nnupd_k for each k *)
......@@ -183,13 +183,14 @@ Lemma nnupd_nnupd_k_dist k P: (|=n=> P)%I ≡{k}≡ (|=n=>_k P)%I.
specialize (HPF n'' x''). exfalso.
eapply laterN_big; last (unseal; eauto).
eauto. omega.
* inversion Hle; subst.
* inversion Hle; simpl; subst.
** unseal. intros (HnnP&HnnP_IH) n k' x' ?? HPF.
case (decide (k' < n)).
*** move: laterN_small; uPred.unseal; naive_solver.
*** intros. exfalso. assert (n k'). omega.
assert (n = S k n < S k) as [->|] by omega.
**** eapply laterN_big; eauto; unseal. eapply HnnP; eauto.
**** eapply laterN_big; eauto; unseal.
eapply HnnP; eauto. move: HPF; by unseal.
**** move:nnupd_k_elim. unseal. intros Hnnupdk.
eapply laterN_big; eauto. unseal.
eapply (Hnnupdk n k); first omega; eauto.
......@@ -326,7 +327,6 @@ Proof.
specialize (Hf3 (S k) (S k) ε). rewrite right_id in Hf3 *. unseal.
intros Hf3. eapply Hf3; eauto.
intros ??? Hx'. rewrite left_id in Hx' *=> Hx'.
unseal.
assert (n' < S k n' = S k) as [|] by omega.
* intros. move:(laterN_small n' (S k) x' False). rewrite //=. unseal. intros Hsmall.
eapply Hsmall; eauto.
......@@ -353,7 +353,7 @@ Lemma adequacy φ n : Nat.iter n (λ P, |=n=> ▷ P)%I ⌜φ⌝%I → ¬¬ φ.
Proof.
cut ( x, {S n} x Nat.iter n (λ P, |=n=> P)%I ⌜φ⌝%I (S n) x ¬¬φ).
{ intros help H. eapply (help ); eauto using ucmra_unit_validN.
eapply H; try unseal; eauto using ucmra_unit_validN. red; rewrite //=. }
eapply H; eauto using ucmra_unit_validN. by unseal. }
destruct n.
- rewrite //=; unseal; auto.
- intros ??? Hfal.
......
From stdpp Require Export hlist.
From iris.base_logic Require Export base_logic.
Set Default Proof Using "Type".
Import uPred.
Fixpoint uPred_hexist {M As} : himpl As (uPred M) uPred M :=
match As return himpl As (uPred M) uPred M with
| tnil => id
| tcons A As => λ Φ, x, uPred_hexist (Φ x)
end%I.
Fixpoint uPred_hforall {M As} : himpl As (uPred M) uPred M :=
match As return himpl As (uPred M) uPred M with
| tnil => id
| tcons A As => λ Φ, x, uPred_hforall (Φ x)
end%I.
Section hlist.
Context {M : ucmraT}.
Lemma hexist_exist {As B} (f : himpl As B) (Φ : B uPred M) :
uPred_hexist (hcompose Φ f) xs : hlist As, Φ (f xs).
Proof.
apply (anti_symm _).
- induction As as [|A As IH]; simpl.
+ by rewrite -(exist_intro hnil) .
+ apply exist_elim=> x; rewrite IH; apply exist_elim=> xs.
by rewrite -(exist_intro (hcons x xs)).
- apply exist_elim=> xs; induction xs as [|A As x xs IH]; simpl; auto.
by rewrite -(exist_intro x) IH.
Qed.
Lemma hforall_forall {As B} (f : himpl As B) (Φ : B uPred M) :
uPred_hforall (hcompose Φ f) xs : hlist As, Φ (f xs).
Proof.
apply (anti_symm _).
- apply forall_intro=> xs; induction xs as [|A As x xs IH]; simpl; auto.
by rewrite (forall_elim x) IH.
- induction As as [|A As IH]; simpl.
+ by rewrite (forall_elim hnil) .
+ apply forall_intro=> x; rewrite -IH; apply forall_intro=> xs.
by rewrite (forall_elim (hcons x xs)).
Qed.
End hlist.
From iris.base_logic.lib Require Export invariants.
From iris.algebra Require Export auth.
From iris.algebra Require Import gmap.
From iris.base_logic Require Import big_op.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
......@@ -73,6 +72,7 @@ Section auth.
Lemma auth_own_op γ a b : auth_own γ (a b) auth_own γ a auth_own γ b.
Proof. by rewrite /auth_own -own_op auth_frag_op. Qed.
(*
Global Instance from_and_auth_own γ a b1 b2 :
IsOp a b1 b2 →
FromAnd false (auth_own γ a) (auth_own γ b1) (auth_own γ b2) | 90.
......@@ -89,6 +89,7 @@ Section auth.
IsOp a b1 b2 →
IntoAnd p (auth_own γ a) (auth_own γ b1) (auth_own γ b2) | 90.
Proof. intros. apply mk_into_and_sep. by rewrite (is_op a) auth_own_op. Qed.
*)
Lemma auth_own_mono γ a b : a b auth_own γ b auth_own γ a.
Proof. intros [? ->]. by rewrite auth_own_op sep_elim_l. Qed.
......
From iris.base_logic.lib Require Export invariants.
From iris.algebra Require Import auth gmap agree.
From iris.base_logic Require Import big_op.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
......@@ -101,7 +100,7 @@ Qed.
Lemma box_alloc : box N True%I.
Proof.
iIntros; iExists (λ _, True)%I; iSplit; last done.
iIntros; iExists (λ _, True)%I; iSplit; last by auto.
iNext. by rewrite big_opM_empty.
Qed.
......@@ -209,11 +208,11 @@ Lemma box_fill E f P :
Proof.
iIntros (?) "H HP"; iDestruct "H" as (Φ) "[#HeqP Hf]".
iExists Φ; iSplitR; first by rewrite big_opM_fmap.
rewrite internal_eq_iff later_iff big_opM_commute.
rewrite internal_eq_iff later_iff big_sepM_later.
iDestruct ("HeqP" with "HP") as "HP".
iCombine "Hf" "HP" as "Hf".
rewrite -big_opM_opM big_opM_fmap; iApply (fupd_big_sepM _ _ f).
iApply (@big_sepM_impl with "[$Hf]").
iApply (@big_sepM_impl with "Hf").
iIntros "!#" (γ b' ?) "[(Hγ' & #$ & #$) HΦ]".
iInv N as (b) "[>Hγ _]" "Hclose".
iMod (box_own_auth_update γ with "[Hγ Hγ']") as "[Hγ $]"; first by iFrame.
......@@ -238,7 +237,7 @@ Proof.
iMod ("Hclose" with "[Hγ]"); first (iNext; iExists false; iFrame; eauto).
iFrame "HγΦ Hinv". by iApply "HΦ". }
iModIntro; iSplitL "HΦ".
- rewrite internal_eq_iff later_iff big_opM_commute. by iApply "HeqP".
- rewrite internal_eq_iff later_iff big_sepM_later. by iApply "HeqP".
- iExists Φ; iSplit; by rewrite big_opM_fmap.
Qed.
......@@ -273,7 +272,7 @@ Proof.
iExists γ1, γ2. iIntros "{$% $#} !>". iSplit; last iSplit; try iPureIntro.
{ by eapply lookup_insert_None. }
{ by apply (lookup_insert_None (delete γ f) γ1 γ2 true). }
iNext. eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. eapply internal_eq_rewrite_contractive'; [by apply _| |by eauto].
iNext. iRewrite "Heq". iPureIntro. by rewrite assoc (comm _ Q2).
- iMod (slice_delete_empty with "Hslice Hbox") as (P') "[Heq Hbox]"; try done.
iMod (slice_insert_empty with "Hbox") as (γ1 ?) "[#Hslice1 Hbox]".
......@@ -281,7 +280,7 @@ Proof.
iExists γ1, γ2. iIntros "{$% $#} !>". iSplit; last iSplit; try iPureIntro.
{ by eapply lookup_insert_None. }
{ by apply (lookup_insert_None (delete γ f) γ1 γ2 false). }
iNext. eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. eapply internal_eq_rewrite_contractive'; [by apply _| |by eauto].
iNext. iRewrite "Heq". iPureIntro. by rewrite assoc (comm _ Q2).
Qed.
......@@ -298,14 +297,14 @@ Proof.
iMod (slice_insert_full _ _ _ _ (Q1 Q2)%I with "[$HQ1 $HQ2] Hbox")
as (γ ?) "[#Hslice Hbox]"; first done.
iExists γ. iIntros "{$% $#} !>". iNext.
eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
eapply internal_eq_rewrite_contractive'; [by apply _| |by eauto].
iNext. iRewrite "Heq1". iRewrite "Heq2". by rewrite assoc.
- iMod (slice_delete_empty with "Hslice1 Hbox") as (P1) "(Heq1 & Hbox)"; try done.
iMod (slice_delete_empty with "Hslice2 Hbox") as (P2) "(Heq2 & Hbox)"; first done.
{ by simplify_map_eq. }
iMod (slice_insert_empty with "Hbox") as (γ ?) "[#Hslice Hbox]".
iExists γ. iIntros "{$% $#} !>". iNext.
eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
eapply internal_eq_rewrite_contractive'; [by apply _| |by eauto].
iNext. iRewrite "Heq1". iRewrite "Heq2". by rewrite assoc.
Qed.
End box.
......
From iris.base_logic.lib Require Export invariants fractional.
From iris.base_logic.lib Require Export invariants.
From iris.bi Require Import fractional.
From iris.algebra Require Export frac.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
......
From iris.base_logic Require Import base_logic soundness.
From iris.base_logic Require Import base_logic soundness proofmode.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type*".
......@@ -7,7 +7,7 @@ name-dependent allocation. *)
Module savedprop. Section savedprop.
Context (M : ucmraT).
Notation iProp := (uPred M).
Notation "¬ P" := ( (P False))%I : uPred_scope.
Notation "¬ P" := ( (P False))%I : bi_scope.
Implicit Types P : iProp.
(** Saved Propositions and the update modality *)
......@@ -41,7 +41,7 @@ Module savedprop. Section savedprop.
Lemma contradiction : False.
Proof using All.
apply (@soundness M False 1); simpl.
iIntros "". iMod A_alloc as (i) "#H".
iMod A_alloc as (i) "#H".
iPoseProof (saved_NA with "H") as "HN".
iModIntro. iNext.
iApply "HN". iApply saved_A. done.
......@@ -108,25 +108,25 @@ Module inv. Section inv.
Proof. intros P Q ?. by apply fupd_mono. Qed.
Instance fupd_proper E : Proper (() ==> ()) (fupd E).
Proof.
intros P Q; rewrite !uPred.equiv_spec=> -[??]; split; by apply fupd_mono.
intros P Q; rewrite !bi.equiv_spec=> -[??]; split; by apply fupd_mono.
Qed.
Lemma fupd_frame_r E P Q : fupd E P Q fupd E (P Q).
Proof. by rewrite comm fupd_frame_l comm. Qed.
Global Instance elim_fupd_fupd E P Q : ElimModal (fupd E P) P (fupd E Q) (fupd E Q).
Proof. by rewrite /ElimModal fupd_frame_r uPred.wand_elim_r fupd_fupd. Qed.
Proof. by rewrite /ElimModal fupd_frame_r bi.wand_elim_r fupd_fupd. Qed.
Global Instance elim_fupd0_fupd1 P Q : ElimModal (fupd M0 P) P (fupd M1 Q) (fupd M1 Q).
Proof.
by rewrite /ElimModal fupd_frame_r uPred.wand_elim_r fupd_mask_mono fupd_fupd.
by rewrite /ElimModal fupd_frame_r bi.wand_elim_r fupd_mask_mono fupd_fupd.
Qed.
Global Instance exists_split_fupd0 {A} E P (Φ : A iProp) :
FromExist P Φ FromExist (fupd E P) (λ a, fupd E (Φ a)).
Proof.
rewrite /FromExist=>HP. apply uPred.exist_elim=> a.
apply fupd_mono. by rewrite -HP -(uPred.exist_intro a).
rewrite /FromExist=>HP. apply bi.exist_elim=> a.
apply fupd_mono. by rewrite -HP -(bi.exist_intro a).
Qed.
(** Now to the actual counterexample. We start with a weird form of saved propositions. *)
......@@ -163,7 +163,7 @@ Module inv. Section inv.
Qed.
(** And now we tie a bad knot. *)
Notation "¬ P" := ( (P - fupd M1 False))%I : uPred_scope.
Notation "¬ P" := ( (P - fupd M1 False))%I : bi_scope.
Definition A i : iProp := P, ¬P saved i P.
Global Instance A_persistent i : Persistent (A i) := _.
......
......@@ -2,7 +2,6 @@ From iris.base_logic.lib Require Export own.
From stdpp Require Export coPset.
From iris.base_logic.lib Require Import wsat.
From iris.algebra Require Import gmap.
From iris.base_logic Require Import big_op.
From iris.proofmode Require Import tactics classes.
Set Default Proof Using "Type".
Export invG.
......@@ -19,19 +18,19 @@ Instance: Params (@fupd) 4.
Notation "|={ E1 , E2 }=> Q" := (fupd E1 E2 Q)
(at level 99, E1, E2 at level 50, Q at level 200,
format "|={ E1 , E2 }=> Q") : uPred_scope.
format "|={ E1 , E2 }=> Q") : bi_scope.
Notation "P ={ E1 , E2 }=∗ Q" := (P - |={E1,E2}=> Q)%I
(at level 99, E1,E2 at level 50, Q at level 200,
format "P ={ E1 , E2 }=∗ Q") : uPred_scope.
format "P ={ E1 , E2 }=∗ Q") : bi_scope.
Notation "P ={ E1 , E2 }=∗ Q" := (P - |={E1,E2}=> Q)
(at level 99, E1, E2 at level 50, Q at level 200, only parsing) : C_scope.
Notation "|={ E }=> Q" := (fupd E E Q)
(at level 99, E at level 50, Q at level 200,
format "|={ E }=> Q") : uPred_scope.
format "|={ E }=> Q") : bi_scope.
Notation "P ={ E }=∗ Q" := (P - |={E}=> Q)%I
(at level 99, E at level 50, Q at level 200,
format "P ={ E }=∗ Q") : uPred_scope.
format "P ={ E }=∗ Q") : bi_scope.
Notation "P ={ E }=∗ Q" := (P - |={E}=> Q)
(at level 99, E at level 50, Q at level 200, only parsing) : C_scope.
......@@ -154,22 +153,37 @@ Section proofmode_classes.
FromAssumption p P (|==> Q) FromAssumption p P (|={E}=> Q)%I.
Proof. rewrite /FromAssumption=>->. apply bupd_fupd. Qed.
Global Instance wand_weaken_fupd E1 E2 P Q P' Q' :
WandWeaken false P Q P' Q'
WandWeaken' false P Q (|={E1,E2}=> P') (|={E1,E2}=> Q').
Global Instance into_wand_fupd E p q R P Q :
IntoWand false false R P Q
IntoWand p q (|={E}=> R) (|={E}=> P) (|={E}=> Q).
Proof.
rewrite /WandWeaken' /WandWeaken=>->. apply wand_intro_l. by rewrite fupd_wand_r.
rewrite /IntoWand /= => HR. rewrite !bare_persistently_if_elim HR.
apply wand_intro_l. by rewrite fupd_sep wand_elim_r.
Qed.
Global Instance from_and_fupd E P Q1 Q2 :
FromAnd false P Q1 Q2 FromAnd false (|={E}=> P) (|={E}=> Q1) (|={E}=> Q2).
Proof. rewrite /FromAnd=><-. apply fupd_sep. Qed.
Global Instance into_wand_fupd_persistent E1 E2 p q R P Q :
IntoWand false q R P Q IntoWand p q (|={E1,E2}=> R) P (|={E1,E2}=> Q).
Proof.
rewrite /IntoWand /= => HR. rewrite bare_persistently_if_elim HR.
apply wand_intro_l. by rewrite fupd_frame_l wand_elim_r.
Qed.
Global Instance into_wand_fupd_args E1 E2 p q R P Q :
IntoWand p false R P Q IntoWand' p q R (|={E1,E2}=> P) (|={E1,E2}=> Q).
Proof.
rewrite /IntoWand' /IntoWand /= => ->.
apply wand_intro_l. by rewrite bare_persistently_if_elim fupd_wand_r.
Qed.
Global Instance from_sep_fupd E P Q1 Q2 :
FromSep P Q1 Q2 FromSep (|={E}=> P) (|={E}=> Q1) (|={E}=> Q2).
Proof. rewrite /FromSep =><-. apply fupd_sep. Qed.
Global Instance or_split_fupd E1 E2 P Q1 Q2 :
Global Instance from_or_fupd E1 E2 P Q1 Q2 :
FromOr P Q1 Q2 FromOr (|={E1,E2}=> P) (|={E1,E2}=> Q1) (|={E1,E2}=> Q2).
Proof. rewrite /FromOr=><-. apply or_elim; apply fupd_mono; auto with I. Qed.
Global Instance exists_split_fupd {A} E1 E2 P (Φ : A iProp Σ) :
Global Instance from_exist_fupd {A} E1 E2 P (Φ : A iProp Σ) :
FromExist P Φ FromExist (|={E1,E2}=> P) (λ a, |={E1,E2}=> Φ a)%I.
Proof.
rewrite /FromExist=><-. apply exist_elim=> a. by rewrite -(exist_intro a).
......@@ -204,16 +218,16 @@ Hint Extern 2 (coq_tactics.of_envs _ ⊢ |={_}=> _) => iModIntro.
Notation "|={ E1 , E2 }▷=> Q" := (|={E1,E2}=> ( |={E2,E1}=> Q))%I
(at level 99, E1, E2 at level 50, Q at level 200,
format "|={ E1 , E2 }▷=> Q") : uPred_scope.
format "|={ E1 , E2 }▷=> Q") : bi_scope.
Notation "P ={ E1 , E2 }▷=∗ Q" := (P - |={ E1 , E2 }=> Q)%I
(at level 99, E1, E2 at level 50, Q at level 200,
format "P ={ E1 , E2 }▷=∗ Q") : uPred_scope.
format "P ={ E1 , E2 }▷=∗ Q") : bi_scope.
Notation "|={ E }▷=> Q" := (|={E,E}=> Q)%I
(at level 99, E at level 50, Q at level 200,
format "|={ E }▷=> Q") : uPred_scope.
format "|={ E }▷=> Q") : bi_scope.
Notation "P ={ E }▷=∗ Q" := (P ={E,E}= Q)%I
(at level 99, E at level 50, Q at level 200,
format "P ={ E }▷=∗ Q") : uPred_scope.
format "P ={ E }▷=∗ Q") : bi_scope.
Section step_fupd.
Context `{invG Σ}.
......
(* This file shows that the fancy update can be encoded in terms of the
view shift, and that the laws of the fancy update can be derived from the
laws of the view shift. *)
From iris.base_logic Require Import proofmode.
From iris.proofmode Require Import tactics.
From stdpp Require Export coPset.
Set Default Proof Using "Type*".
......@@ -10,7 +11,7 @@ Context {M} (vs : coPset → coPset → uPred M → uPred M → uPred M).
Notation "P ={ E1 , E2 }=> Q" := (vs E1 E2 P Q)
(at level 99, E1,E2 at level 50, Q at level 200,
format "P ={ E1 , E2 }=> Q") : uPred_scope.
format "P ={ E1 , E2 }=> Q") : bi_scope.
Context (vs_ne : E1 E2, NonExpansive2 (vs E1 E2)).
Context (vs_persistent : E1 E2 P Q, Persistent (P ={E1,E2}=> Q)).
......@@ -32,7 +33,7 @@ Definition fupd (E1 E2 : coPset) (P : uPred M) : uPred M :=
Notation "|={ E1 , E2 }=> Q" := (fupd E1 E2 Q)
(at level 99, E1, E2 at level 50, Q at level 200,
format "|={ E1 , E2 }=> Q") : uPred_scope.
format "|={ E1 , E2 }=> Q") : bi_scope.
Global Instance fupd_ne E1 E2 : NonExpansive (@fupd E1 E2).
Proof. solve_proper. Qed.
......
From iris.algebra Require Import auth gmap frac agree.
From iris.base_logic Require Import proofmode.
From iris.base_logic.lib Require Export own.
From iris.base_logic.lib Require Import fractional.
From iris.bi Require Import fractional.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
......@@ -41,12 +42,12 @@ Section definitions.
End definitions.
Local Notation "l ↦{ q } v" := (mapsto l q v)
(at level 20, q at level 50, format "l ↦{ q } v") : uPred_scope.
Local Notation "l ↦ v" := (mapsto l 1 v) (at level 20) : uPred_scope.
(at level 20, q at level 50, format "l ↦{ q } v") : bi_scope.
Local Notation "l ↦ v" := (mapsto l 1 v) (at level 20) : bi_scope.
Local Notation "l ↦{ q } -" := ( v, l {q} v)%I
(at level 20, q at level 50, format "l ↦{ q } -") : uPred_scope.
Local Notation "l ↦ -" := (l {1} -)%I (at level 20) : uPred_scope.
(at level 20, q at level 50, format "l ↦{ q } -") : bi_scope.
Local Notation "l ↦ -" := (l {1} -)%I (at level 20) : bi_scope.
Section to_gen_heap.
Context (L V : Type) `{Countable L}.
......
......@@ -64,9 +64,9 @@ Proof.
iSplitL "Hi"; first by eauto. 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".
iCombine "HEi HEN\i HE\N" as "HEN".
rewrite -?ownE_op; [|set_solver..].
rewrite -!union_difference_L //; set_solver.
rewrite assoc_L -!union_difference_L //; set_solver.
Qed.
Lemma inv_open E N P :
......
......@@ -152,6 +152,5 @@ Lemma iProp_unfold_equivI {Σ} (P Q : iProp Σ) :
iProp_unfold P iProp_unfold Q (P Q : iProp Σ).
Proof.
rewrite -{2}(iProp_fold_unfold P) -{2}(iProp_fold_unfold Q).
eapply (uPred.internal_eq_rewrite _ _ (λ z,
iProp_fold (iProp_unfold P) iProp_fold z))%I; auto with I; solve_proper.
apply: bi.f_equiv.
Qed.
From iris.algebra Require Import iprod gmap.
From iris.base_logic Require Import big_op.
From iris.base_logic Require Export iprop.
From iris.proofmode Require Import classes.
From iris.base_logic.lib Require Export iprop.
From iris.base_logic Require Import proofmode_classes.
Set Default Proof Using "Type".
Import uPred.
......@@ -84,7 +83,7 @@ Global Instance own_proper γ :
Lemma own_op γ a1 a2 : own γ (a1 a2) own γ a1 own γ a2.
Proof. by rewrite !own_eq /own_def -ownM_op iRes_singleton_op. Qed.
Lemma own_mono γ a1 a2 : a2 a1 own γ a1 own γ a2.
Proof. move=> [c ->]. rewrite own_op. eauto with I. Qed.
Proof. move=> [c ->]. by rewrite own_op sep_elim_l. Qed.
Global Instance own_mono' γ : Proper (flip () ==> ()) (@own Σ A _ γ).
Proof. intros a1 a2. apply own_mono. Qed.
......@@ -102,7 +101,7 @@ Proof. apply wand_intro_r. by rewrite -own_op own_valid. Qed.
Lemma own_valid_3 γ a1 a2 a3 : own γ a1 - own γ a2 - own γ a3 - (a1 a2 a3).
Proof. do 2 apply wand_intro_r. by rewrite -!own_op own_valid. Qed.
Lemma own_valid_r γ a : own γ a own γ a a.
Proof. apply: uPred.sep_entails_r. apply own_valid. Qed.
Proof. apply: bi.persistent_entails_r. apply own_valid. Qed.
Lemma own_valid_l γ a : own γ a a own γ a.
Proof. by rewrite comm -own_valid_r. Qed.
......@@ -119,7 +118,7 @@ Lemma own_alloc_strong a (G : gset gname) :
Proof.
intros Ha.
rewrite -(bupd_mono </