Merge branch 'gen_big_op' into 'master'

Generic big operators that are computational for lists

Closes #38

See merge request !54

_CoqProject

 -Q theories iris
 -arg -w -arg -notation-overridden,-redundant-canonical-projection,-several-object-files
+theories/algebra/monoid.v
 theories/algebra/cmra.v
+theories/algebra/big_op.v
 theories/algebra/cmra_big_op.v
-theories/algebra/cmra_tactics.v
 theories/algebra/sts.v
 theories/algebra/auth.v
 theories/algebra/gmap.v

opam.pins

-coq-stdpp https://gitlab.mpi-sws.org/robbertkrebbers/coq-stdpp 0ac2b4db07bdc471421c5a4c47789087b3df074c
+coq-stdpp https://gitlab.mpi-sws.org/robbertkrebbers/coq-stdpp a0ce0937cfabe16a184af2d92c0466ebacecbca2

theories/algebra/auth.v

@@ -203,7 +203,8 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) = ◯ a ⋅ ◯ b.
 Proof. done. Qed.
 Lemma auth_frag_mono a b : a ≼ b → ◯ a ≼ ◯ b.
 Proof. intros [c ->]. rewrite auth_frag_op. apply cmra_included_l. Qed.
-Global Instance auth_frag_cmra_homomorphism : UCMRAHomomorphism (Auth None).
+
+Global Instance auth_frag_sep_homomorphism : MonoidHomomorphism op op (Auth None).
 Proof. done. Qed.
 
 Lemma auth_both_op a b : Auth (Excl' a) b ≡ ● a ⋅ ◯ b.

theories/algebra/cmra.v

-From iris.algebra Require Export ofe.
+From iris.algebra Require Export ofe monoid.
 Set Default Proof Using "Type".
 
 Class PCore (A : Type) := pcore : A → option A.
@@ -243,20 +243,6 @@ Class CMRAMonotone {A B : cmraT} (f : A → B) := {
 Arguments cmra_monotone_validN {_ _} _ {_} _ _ _.
 Arguments cmra_monotone {_ _} _ {_} _ _ _.
 
-(* Not all intended homomorphisms preserve validity, in particular it does not
-hold for the [ownM] and [own] connectives. *)
-Class CMRAHomomorphism {A B : cmraT} (f : A → B) := {
-  cmra_homomorphism_ne :> NonExpansive f;
-  cmra_homomorphism x y : f (x ⋅ y) ≡ f x ⋅ f y
-}.
-Arguments cmra_homomorphism {_ _} _ _ _ _.
-
-Class UCMRAHomomorphism {A B : ucmraT} (f : A → B) := {
-  ucmra_homomorphism :> CMRAHomomorphism f;
-  ucmra_homomorphism_unit : f ∅ ≡ ∅
-}.
-Arguments ucmra_homomorphism_unit {_ _} _ _.
-
 (** * Properties **)
 Section cmra.
 Context {A : cmraT}.
@@ -633,9 +619,12 @@ Section ucmra.
   Qed.
   Global Instance empty_cancelable : Cancelable (∅:A).
   Proof. intros ???. by rewrite !left_id. Qed.
+
+  (* For big ops *)
+  Global Instance cmra_monoid : Monoid (@op A _) := {| monoid_unit := ∅ |}.
 End ucmra.
-Hint Immediate cmra_unit_total.
 
+Hint Immediate cmra_unit_total.
 
 (** * Properties about CMRAs with Leibniz equality *)
 Section cmra_leibniz.
@@ -752,26 +741,6 @@ Section cmra_monotone.
   Proof. rewrite !cmra_valid_validN; eauto using cmra_monotone_validN. Qed.
 End cmra_monotone.
 
-Instance cmra_homomorphism_id {A : cmraT} : CMRAHomomorphism (@id A).
-Proof. repeat split; by try apply _. Qed.
-Instance cmra_homomorphism_compose {A B C : cmraT} (f : A → B) (g : B → C) :
-  CMRAHomomorphism f → CMRAHomomorphism g → CMRAHomomorphism (g ∘ f).
-Proof.
-  split.
-  - apply _.
-  - move=> x y /=. rewrite -(cmra_homomorphism g).
-    by apply (ne_proper _), cmra_homomorphism.
-Qed.
-
-Instance cmra_homomorphism_proper {A B : cmraT} (f : A → B) :
-  CMRAHomomorphism f → Proper ((≡) ==> (≡)) f := λ _, ne_proper _.
-
-Instance ucmra_homomorphism_id {A : ucmraT} : UCMRAHomomorphism (@id A).
-Proof. repeat split; by try apply _. Qed.
-Instance ucmra_homomorphism_compose {A B C : ucmraT} (f : A → B) (g : B → C) :
-  UCMRAHomomorphism f → UCMRAHomomorphism g → UCMRAHomomorphism (g ∘ f).
-Proof. split. apply _. by rewrite /= !ucmra_homomorphism_unit. Qed.
-
 (** Functors *)
 Structure rFunctor := RFunctor {
   rFunctor_car : ofeT → ofeT → cmraT;
@@ -1316,8 +1285,6 @@ Section option.
   (** Misc *)
   Global Instance Some_cmra_monotone : CMRAMonotone Some.
   Proof. split; [apply _|done|intros x y [z ->]; by exists (Some z)]. Qed.
-  Global Instance Some_cmra_homomorphism : CMRAHomomorphism Some.
-  Proof. split. apply _. done. Qed.
 
   Lemma op_None mx my : mx ⋅ my = None ↔ mx = None ∧ my = None.
   Proof. destruct mx, my; naive_solver. Qed.

theories/algebra/cmra_tactics.v

-From iris.algebra Require Export cmra.
-From iris.algebra Require Import cmra_big_op.
-Set Default Proof Using "Type".
-
-(** * Simple solver for validity and inclusion by reflection *)
-Module ra_reflection. Section ra_reflection.
-  Context  {A : ucmraT}.
-
-  Inductive expr :=
-    | EVar : nat → expr
-    | EEmpty : expr
-    | EOp : expr → expr → expr.
-  Fixpoint eval (Σ : list A) (e : expr) : A :=
-    match e with
-    | EVar n => from_option id ∅ (Σ !! n)
-    | EEmpty => ∅
-    | EOp e1 e2 => eval Σ e1 ⋅ eval Σ e2
-    end.
-  Fixpoint flatten (e : expr) : list nat :=
-    match e with
-    | EVar n => [n]
-    | EEmpty => []
-    | EOp e1 e2 => flatten e1 ++ flatten e2
-    end.
-  Lemma eval_flatten Σ e :
-    eval Σ e ≡ big_op ((λ n, from_option id ∅ (Σ !! n)) <$> flatten e).
-  Proof.
-    induction e as [| |e1 IH1 e2 IH2]; rewrite /= ?right_id //.
-    by rewrite fmap_app IH1 IH2 big_op_app.
-  Qed.
-  Lemma flatten_correct Σ e1 e2 :
-    flatten e1 ⊆+ flatten e2 → eval Σ e1 ≼ eval Σ e2.
-  Proof.
-    by intros He; rewrite !eval_flatten; apply big_op_submseteq; rewrite ->He.
-  Qed.
-
-  Class Quote (Σ1 Σ2 : list A) (l : A) (e : expr) := {}.
-  Global Instance quote_empty: Quote E1 E1 ∅ EEmpty.
-  Global Instance quote_var Σ1 Σ2 e i:
-    rlist.QuoteLookup Σ1 Σ2 e i → Quote Σ1 Σ2 e (EVar i) | 1000.
-  Global Instance quote_app Σ1 Σ2 Σ3 x1 x2 e1 e2 :
-    Quote Σ1 Σ2 x1 e1 → Quote Σ2 Σ3 x2 e2 → Quote Σ1 Σ3 (x1 ⋅ x2) (EOp e1 e2).
-  End ra_reflection.
-
-  Ltac quote :=
-    match goal with
-    | |- @included _ _ _ ?x ?y =>
-      lazymatch type of (_ : Quote [] _ x _) with Quote _ ?Σ2 _ ?e1 =>
-      lazymatch type of (_ : Quote Σ2 _ y _) with Quote _ ?Σ3 _ ?e2 =>
-        change (eval Σ3 e1 ≼ eval Σ3 e2)
-      end end
-    end.
-End ra_reflection.
-
-Ltac solve_included :=
-  ra_reflection.quote;
-  apply ra_reflection.flatten_correct, (bool_decide_unpack _);
-  vm_compute; apply I.
-
-Ltac solve_validN :=
-  match goal with
-  | H : ✓{?n} ?y |- ✓{?n'} ?x =>
-     let Hn := fresh in let Hx := fresh in
-     assert (n' ≤ n) as Hn by omega;
-     assert (x ≼ y) as Hx by solve_included;
-     eapply cmra_validN_le, Hn; eapply cmra_validN_included, Hx; apply H
-  end.

theories/algebra/csum.v

@@ -281,11 +281,6 @@ Proof. intros ? [] ? EQ; inversion_clear EQ. by eapply id_free0_r. Qed.
 Global Instance Cinr_id_free b : IdFree b → IdFree (Cinr b).
 Proof. intros ? [] ? EQ; inversion_clear EQ. by eapply id_free0_r. Qed.
 
-Global Instance Cinl_cmra_homomorphism : CMRAHomomorphism Cinl.
-Proof. split. apply _. done. Qed.
-Global Instance Cinr_cmra_homomorphism : CMRAHomomorphism Cinr.
-Proof. split. apply _. done. Qed.
-
 (** Internalized properties *)
 Lemma csum_equivI {M} (x y : csum A B) :
   x ≡ y ⊣⊢ (match x, y with

theories/algebra/gmap.v

@@ -200,9 +200,9 @@ Implicit Types m : gmap K A.
 Implicit Types i : K.
 Implicit Types x y : A.
 
-Global Instance lookup_cmra_homomorphism :
-  UCMRAHomomorphism (lookup i : gmap K A → option A).
-Proof. split. split. apply _. intros m1 m2; by rewrite lookup_op. done. Qed.
+Global Instance lookup_op_homomorphism :
+  MonoidHomomorphism op op (lookup i : gmap K A → option A).
+Proof. split; [split|]. apply _. intros m1 m2; by rewrite lookup_op. done. Qed.
 
 Lemma lookup_opM m1 mm2 i : (m1 ⋅? mm2) !! i = m1 !! i ⋅ (mm2 ≫= (!! i)).
 Proof. destruct mm2; by rewrite /= ?lookup_op ?right_id_L. Qed.
@@ -247,9 +247,6 @@ Qed.
 Lemma op_singleton (i : K) (x y : A) :
   {[ i := x ]} ⋅ {[ i := y ]} = ({[ i := x ⋅ y ]} : gmap K A).
 Proof. by apply (merge_singleton _ _ _ x y). Qed.
-Global Instance singleton_cmra_homomorphism :
-  CMRAHomomorphism (singletonM i : A → gmap K A).
-Proof. split. apply _. intros. by rewrite op_singleton. Qed.
 
 Global Instance gmap_persistent m : (∀ x : A, Persistent x) → Persistent m.
 Proof.

theories/algebra/list.v

@@ -464,3 +464,63 @@ Instance listURF_contractive F :
 Proof.
   by intros ? A1 A2 B1 B2 n f g Hfg; apply listC_map_ne, urFunctor_contractive.
 Qed.
+
+(** * Persistence and timelessness of lists of uPreds *)
+Class PersistentL {M} (Ps : list (uPred M)) :=
+  persistentL : Forall PersistentP Ps.
+Arguments persistentL {_} _ {_}.
+Hint Mode PersistentL + ! : typeclass_instances.
+
+Class TimelessL {M} (Ps : list (uPred M)) :=
+  timelessL : Forall TimelessP Ps.
+Arguments timelessL {_} _ {_}.
+Hint Mode TimelessP + ! : typeclass_instances.
+
+Section persistent_timeless.
+  Context {M : ucmraT}.
+  Implicit Types Ps Qs : list (uPred M).
+  Implicit Types A : Type.
+
+  Global Instance nil_persistentL : PersistentL (@nil (uPred M)).
+  Proof. constructor. Qed.
+  Global Instance cons_persistentL P Ps :
+    PersistentP P → PersistentL Ps → PersistentL (P :: Ps).
+  Proof. by constructor. Qed.
+  Global Instance app_persistentL Ps Ps' :
+    PersistentL Ps → PersistentL Ps' → PersistentL (Ps ++ Ps').
+  Proof. apply Forall_app_2. Qed.
+
+  Global Instance fmap_persistentL {A} (f : A → uPred M) xs :
+    (∀ x, PersistentP (f x)) → PersistentL (f <$> xs).
+  Proof. intros. apply Forall_fmap, Forall_forall; auto. Qed.
+  Global Instance zip_with_persistentL {A B} (f : A → B → uPred M) xs ys :
+    (∀ x y, PersistentP (f x y)) → PersistentL (zip_with f xs ys).
+  Proof.
+    unfold PersistentL=> ?; revert ys; induction xs=> -[|??]; constructor; auto.
+  Qed.
+  Global Instance imap_persistentL {A} (f : nat → A → uPred M) xs :
+    (∀ i x, PersistentP (f i x)) → PersistentL (imap f xs).
+  Proof. revert f. induction xs; simpl; constructor; naive_solver. Qed.
+
+  (** ** Timelessness *)
+  Global Instance nil_timelessL : TimelessL (@nil (uPred M)).
+  Proof. constructor. Qed.
+  Global Instance cons_timelessL P Ps :
+    TimelessP P → TimelessL Ps → TimelessL (P :: Ps).
+  Proof. by constructor. Qed.
+  Global Instance app_timelessL Ps Ps' :
+    TimelessL Ps → TimelessL Ps' → TimelessL (Ps ++ Ps').
+  Proof. apply Forall_app_2. Qed.
+
+  Global Instance fmap_timelessL {A} (f : A → uPred M) xs :
+    (∀ x, TimelessP (f x)) → TimelessL (f <$> xs).
+  Proof. intros. apply Forall_fmap, Forall_forall; auto. Qed.
+  Global Instance zip_with_timelessL {A B} (f : A → B → uPred M) xs ys :
+    (∀ x y, TimelessP (f x y)) → TimelessL (zip_with f xs ys).
+  Proof.
+    unfold TimelessL=> ?; revert ys; induction xs=> -[|??]; constructor; auto.
+  Qed.
+  Global Instance imap_timelessL {A} (f : nat → A → uPred M) xs :
+    (∀ i x, TimelessP (f i x)) → TimelessL (imap f xs).
+  Proof. revert f. induction xs; simpl; constructor; naive_solver. Qed.
+End persistent_timeless.

theories/algebra/monoid.v

+From iris.algebra Require Export ofe.
+Set Default Proof Using "Type".
+
+(** The Monoid class that is used for generic big operators in the file
+[algebra/big_op]. The operation is an argument because we want to have multiple
+monoids over the same type (for example, on [uPred]s we have monoids for [∗],
+[∧], and [∨]). However, we do bundle the unit because:
+
+- If we would not, it would appear explicitly in an argument of the big
+  operators, which confuses rewrite. Now it is hidden in the class, and hence
+  rewrite won't even see it.
+- The unit is unique.
+
+We could in principle have big ops over setoids instead of OFEs. However, since
+we do not have a canonical structure for setoids, we do not go that way.
+
+Note that we do not declare any of the projections as type class instances. That
+is because we only need them in the [big_op] file, and nowhere else. Hence, we
+declare these instances locally there to avoid them being used elsewhere. *)
+Class Monoid {M : ofeT} (o : M → M → M) := {
+  monoid_unit : M;
+  monoid_ne : NonExpansive2 o;
+  monoid_assoc : Assoc (≡) o;
+  monoid_comm : Comm (≡) o;
+  monoid_left_id : LeftId (≡) monoid_unit o;
+}.
+Lemma monoid_proper `{Monoid M o} : Proper ((≡) ==> (≡) ==> (≡)) o.
+Proof. apply ne_proper_2, monoid_ne. Qed.
+Lemma monoid_right_id `{Monoid M o} : RightId (≡) monoid_unit o.
+Proof. intros x. etrans; [apply monoid_comm|apply monoid_left_id]. Qed.
+
+(** The [Homomorphism] classes give rise to generic lemmas about big operators
+commuting with each other. We also consider a [WeakMonoidHomomorphism] which
+does not necesarrily commute with unit; an example is the [own] connective: we
+only have `True ==∗ own γ ∅`, not `True ↔ own γ ∅`. *)
+Class WeakMonoidHomomorphism {M1 M2 : ofeT} (o1 : M1 → M1 → M1) (o2 : M2 → M2 → M2)
+    `{Monoid M1 o1, Monoid M2 o2} (f : M1 → M2) := {
+  monoid_homomorphism_ne : NonExpansive f;
+  monoid_homomorphism x y : f (o1 x y) ≡ o2 (f x) (f y)
+}.
+
+Class MonoidHomomorphism {M1 M2 : ofeT} (o1 : M1 → M1 → M1) (o2 : M2 → M2 → M2)
+    `{Monoid M1 o1, Monoid M2 o2} (f : M1 → M2) := {
+  monoid_homomorphism_weak :> WeakMonoidHomomorphism o1 o2 f;
+  monoid_homomorphism_unit : f monoid_unit ≡ monoid_unit
+}.
+
+Lemma weak_monoid_homomorphism_proper
+  `{WeakMonoidHomomorphism M1 M2 o1 o2 f} : Proper ((≡) ==> (≡)) f.
+Proof. apply ne_proper, monoid_homomorphism_ne. Qed.

theories/base_logic/derived.v

@@ -889,5 +889,64 @@ Proof. intros. by rewrite /PersistentP always_ownM. Qed.
 Global Instance from_option_persistent {A} P (Ψ : A → uPred M) (mx : option A) :
   (∀ x, PersistentP (Ψ x)) → PersistentP P → PersistentP (from_option Ψ P mx).
 Proof. destruct mx; apply _. Qed.
+
+(* For big ops *)
+Global Instance uPred_and_monoid : Monoid (@uPred_and M) :=
+  {| monoid_unit := True%I |}.
+Global Instance uPred_or_monoid : Monoid (@uPred_or M) :=
+  {| monoid_unit := False%I |}.
+Global Instance uPred_sep_monoid : Monoid (@uPred_sep M) :=
+  {| monoid_unit := True%I |}.
+
+Global Instance uPred_always_and_homomorphism :
+  MonoidHomomorphism uPred_and uPred_and (@uPred_always M).
+Proof. split; [split|]. apply _. apply always_and. apply always_pure. Qed.
+Global Instance uPred_always_if_and_homomorphism b :
+  MonoidHomomorphism uPred_and uPred_and (@uPred_always_if M b).
+Proof. split; [split|]. apply _. apply always_if_and. apply always_if_pure. Qed.
+Global Instance uPred_later_monoid_and_homomorphism :
+  MonoidHomomorphism uPred_and uPred_and (@uPred_later M).
+Proof. split; [split|]. apply _. apply later_and. apply later_True. Qed.
+Global Instance uPred_laterN_and_homomorphism n :
+  MonoidHomomorphism uPred_and uPred_and (@uPred_laterN M n).
+Proof. split; [split|]. apply _. apply laterN_and. apply laterN_True. Qed.
+Global Instance uPred_except_0_and_homomorphism :
+  MonoidHomomorphism uPred_and uPred_and (@uPred_except_0 M).
+Proof. split; [split|]. apply _. apply except_0_and. apply except_0_True. Qed.
+
+Global Instance uPred_always_or_homomorphism :
+  MonoidHomomorphism uPred_or uPred_or (@uPred_always M).
+Proof. split; [split|]. apply _. apply always_or. apply always_pure. Qed.
+Global Instance uPred_always_if_or_homomorphism b :
+  MonoidHomomorphism uPred_or uPred_or (@uPred_always_if M b).
+Proof. split; [split|]. apply _. apply always_if_or. apply always_if_pure. Qed.
+Global Instance uPred_later_monoid_or_homomorphism :
+  WeakMonoidHomomorphism uPred_or uPred_or (@uPred_later M).
+Proof. split. apply _. apply later_or. Qed.
+Global Instance uPred_laterN_or_homomorphism n :
+  WeakMonoidHomomorphism uPred_or uPred_or (@uPred_laterN M n).
+Proof. split. apply _. apply laterN_or. Qed.
+Global Instance uPred_except_0_or_homomorphism :
+  WeakMonoidHomomorphism uPred_or uPred_or (@uPred_except_0 M).
+Proof. split. apply _. apply except_0_or. Qed. 
+
+Global Instance uPred_always_sep_homomorphism :
+  MonoidHomomorphism uPred_sep uPred_sep (@uPred_always M).
+Proof. split; [split|]. apply _. apply always_sep. apply always_pure. Qed.
+Global Instance uPred_always_if_sep_homomorphism b :
+  MonoidHomomorphism uPred_sep uPred_sep (@uPred_always_if M b).
+Proof. split; [split|]. apply _. apply always_if_sep. apply always_if_pure. Qed.
+Global Instance uPred_later_monoid_sep_homomorphism :
+  MonoidHomomorphism uPred_sep uPred_sep (@uPred_later M).
+Proof. split; [split|]. apply _. apply later_sep. apply later_True. Qed.
+Global Instance uPred_laterN_sep_homomorphism n :
+  MonoidHomomorphism uPred_sep uPred_sep (@uPred_laterN M n).
+Proof. split; [split|]. apply _. apply laterN_sep. apply laterN_True. Qed.
+Global Instance uPred_except_0_sep_homomorphism :
+  MonoidHomomorphism uPred_sep uPred_sep (@uPred_except_0 M).
+Proof. split; [split|]. apply _. apply except_0_sep. apply except_0_True. Qed.
+Global Instance uPred_ownM_sep_homomorphism :
+  MonoidHomomorphism op uPred_sep (@uPred_ownM M).
+Proof. split; [split|]. apply _. apply ownM_op. apply ownM_empty'. Qed.
 End derived.
 End uPred.

theories/base_logic/lib/auth.v

@@ -94,9 +94,10 @@ Section auth.
   Proof. intros [? ->]. by rewrite auth_own_op sep_elim_l. Qed.
   Lemma auth_own_valid γ a : auth_own γ a ⊢ ✓ a.
   Proof. by rewrite /auth_own own_valid auth_validI. Qed.
-
-  Global Instance auth_own_cmra_homomorphism : CMRAHomomorphism (auth_own γ).
+  Global Instance auth_own_sep_homomorphism γ :
+    WeakMonoidHomomorphism op uPred_sep (auth_own γ).
   Proof. split. apply _. apply auth_own_op. Qed.
+
   Global Instance own_mono' γ : Proper (flip (≼) ==> (⊢)) (auth_own γ).
   Proof. intros a1 a2. apply auth_own_mono. Qed.
 

theories/base_logic/lib/boxes.v

@@ -97,9 +97,8 @@ Qed.
 
 Lemma box_alloc : box N ∅ True%I.
 Proof.
-  iIntros; iExists (λ _, True)%I; iSplit.
-  - iNext. by rewrite big_sepM_empty.
-  - by rewrite big_sepM_empty.
+  iIntros; iExists (λ _, True)%I; iSplit; last done.
+  iNext. by rewrite big_opM_empty.
 Qed.
 
 Lemma slice_insert_empty E q f Q P :
@@ -116,8 +115,8 @@ Proof.
   { iNext. iExists false; eauto. }
   iModIntro; iExists γ; repeat iSplit; auto.
   iNext. iExists (<[γ:=Q]> Φ); iSplit.
-  - iNext. iRewrite "HeqP". by rewrite big_sepM_fn_insert'.
-  - rewrite (big_sepM_fn_insert (λ _ _ P',  _ ∗ _ _ P' ∗ _ _ (_ _ P')))%I //.
+  - iNext. iRewrite "HeqP". by rewrite big_opM_fn_insert'.
+  - rewrite (big_opM_fn_insert (λ _ _ P',  _ ∗ _ _ P' ∗ _ _ (_ _ P')))%I //.
     iFrame; eauto.
 Qed.
 
@@ -130,13 +129,13 @@ Proof.
   iIntros (??) "[#HγQ Hinv] H". iDestruct "H" as (Φ) "[#HeqP Hf]".
   iExists ([∗ map] γ'↦_ ∈ delete γ f, Φ γ')%I.
   iInv N as (b) "[>Hγ _]" "Hclose".
-  iDestruct (big_sepM_delete _ f _ false with "Hf")
+  iDestruct (big_opM_delete _ f _ false with "Hf")
     as "[[>Hγ' #[HγΦ ?]] ?]"; first done.
   iDestruct (box_own_auth_agree γ b false with "[-]") as %->; first by iFrame.
   iMod ("Hclose" with "[Hγ]"); first iExists false; eauto.
   iModIntro. iNext. iSplit.
   - iDestruct (box_own_agree γ Q (Φ γ) with "[#]") as "HeqQ"; first by eauto.
-    iNext. iRewrite "HeqP". iRewrite "HeqQ". by rewrite -big_sepM_delete.
+    iNext. iRewrite "HeqP". iRewrite "HeqQ". by rewrite -big_opM_delete.
   - iExists Φ; eauto.
 Qed.
 
@@ -147,13 +146,13 @@ Lemma slice_fill E q f γ P Q :
 Proof.
   iIntros (??) "#[HγQ Hinv] HQ H"; iDestruct "H" as (Φ) "[#HeqP Hf]".
   iInv N as (b') "[>Hγ _]" "Hclose".
-  iDestruct (big_sepM_delete _ f _ false with "Hf")
+  iDestruct (big_opM_delete _ f _ false with "Hf")
     as "[[>Hγ' #[HγΦ Hinv']] ?]"; first done.
   iMod (box_own_auth_update γ b' false true with "[$Hγ $Hγ']") as "[Hγ Hγ']".
   iMod ("Hclose" with "[Hγ HQ]"); first (iNext; iExists true; by iFrame).
   iModIntro; iNext; iExists Φ; iSplit.
-  - by rewrite big_sepM_insert_override.
-  - rewrite -insert_delete big_sepM_insert ?lookup_delete //.
+  - by rewrite big_opM_insert_override.
+  - rewrite -insert_delete big_opM_insert ?lookup_delete //.
     iFrame; eauto.
 Qed.
 
@@ -164,15 +163,15 @@ Lemma slice_empty E q f P Q γ :
 Proof.
   iIntros (??) "#[HγQ Hinv] H"; iDestruct "H" as (Φ) "[#HeqP Hf]".
   iInv N as (b) "[>Hγ HQ]" "Hclose".
-  iDestruct (big_sepM_delete _ f with "Hf")
+  iDestruct (big_opM_delete _ f with "Hf")
     as "[[>Hγ' #[HγΦ Hinv']] ?]"; first done.
   iDestruct (box_own_auth_agree γ b true with "[-]") as %->; first by iFrame.
   iFrame "HQ".
   iMod (box_own_auth_update γ with "[$Hγ $Hγ']") as "[Hγ Hγ']".
   iMod ("Hclose" with "[Hγ]"); first (iNext; iExists false; by repeat iSplit).
   iModIntro; iNext; iExists Φ; iSplit.
-  - by rewrite big_sepM_insert_override.
-  - rewrite -insert_delete big_sepM_insert ?lookup_delete //.
+  - by rewrite big_opM_insert_override.
+  - rewrite -insert_delete big_opM_insert ?lookup_delete //.
     iFrame; eauto.
 Qed.
 
@@ -205,11 +204,11 @@ Lemma box_fill E f P :
   box N f P -∗ ▷ P ={E}=∗ box N (const true <$> f) P.
 Proof.
   iIntros (?) "H HP"; iDestruct "H" as (Φ) "[#HeqP Hf]".
-  iExists Φ; iSplitR; first by rewrite big_sepM_fmap.
-  rewrite internal_eq_iff later_iff big_sepM_later.
+  iExists Φ; iSplitR; first by rewrite big_opM_fmap.
+  rewrite internal_eq_iff later_iff big_opM_commute.
   iDestruct ("HeqP" with "HP") as "HP".
   iCombine "Hf" "HP" as "Hf".
-  rewrite -big_sepM_sepM big_sepM_fmap; iApply (fupd_big_sepM _ _ f).
+  rewrite -big_opM_opM big_opM_fmap; iApply (fupd_big_sepM _ _ f).
   iApply (@big_sepM_impl with "[$Hf]").
   iAlways; iIntros (γ b' ?) "[(Hγ' & #$ & #$) HΦ]".
   iInv N as (b) "[>Hγ _]" "Hclose".
@@ -226,7 +225,7 @@ Proof.
   iAssert (([∗ map] γ↦b ∈ f, ▷ Φ γ) ∗
     [∗ map] γ↦b ∈ f, box_own_auth γ (◯ Excl' false) ∗  box_own_prop γ (Φ γ) ∗
       inv N (slice_inv γ (Φ γ)))%I with "[> Hf]" as "[HΦ ?]".
-  { rewrite -big_sepM_sepM -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
+  { rewrite -big_opM_opM -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
     iAlways; iIntros (γ b ?) "(Hγ' & #HγΦ & #Hinv)".
     assert (true = b) as <- by eauto.
     iInv N as (b) "[>Hγ HΦ]" "Hclose".
@@ -235,8 +234,8 @@ 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_sepM_later. by iApply "HeqP".
-  - iExists Φ; iSplit; by rewrite big_sepM_fmap.
+  - rewrite internal_eq_iff later_iff big_opM_commute. by iApply "HeqP".
+  - iExists Φ; iSplit; by rewrite big_opM_fmap.
 Qed.
 
 Lemma slice_iff E q f P Q Q' γ b :

theories/base_logic/lib/fractional.v

@@ -63,30 +63,22 @@ Section fractional.
   Global Instance fractional_big_sepL {A} l Ψ :
     (∀ k (x : A), Fractional (Ψ k x)) →
     Fractional (M:=M) (λ q, [∗ list] k↦x ∈ l, Ψ k x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepL_sepL. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opL_opL. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepM `{Countable K} {A} (m : gmap K A) Ψ :
     (∀ k (x : A), Fractional (Ψ k x)) →
     Fractional (M:=M) (λ q, [∗ map] k↦x ∈ m, Ψ k x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepM_sepM. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opM_opM. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepS `{Countable A} (X : gset A) Ψ :
     (∀ x, Fractional (Ψ x)) →
     Fractional (M:=M) (λ q, [∗ set] x ∈ X, Ψ x q)%I.