Add monadic ;; and change level of do-notation to 100.

This way, we will be compabile with Iris's heap_lang, which puts ;;
at level 100.

theories/base.v

@@ -865,23 +865,26 @@ Notation "(≫= f )" := (mbind f) (only parsing) : C_scope.
 Notation "(≫=)" := (λ m f, mbind f m) (only parsing) : C_scope.
 
 Notation "x ← y ; z" := (y ≫= (λ x : _, z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, only parsing, right associativity) : C_scope.
+
 Infix "<$>" := fmap (at level 60, right associativity) : C_scope.
 Notation "' ( x1 , x2 ) ← y ; z" :=
   (y ≫= (λ x : _, let ' (x1, x2) := x in z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
 Notation "' ( x1 , x2 , x3 ) ← y ; z" :=
   (y ≫= (λ x : _, let ' (x1,x2,x3) := x in z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
 Notation "' ( x1 , x2 , x3  , x4 ) ← y ; z" :=
   (y ≫= (λ x : _, let ' (x1,x2,x3,x4) := x in z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
 Notation "' ( x1 , x2 , x3  , x4 , x5 ) ← y ; z" :=
   (y ≫= (λ x : _, let ' (x1,x2,x3,x4,x5) := x in z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
 Notation "' ( x1 , x2 , x3  , x4 , x5 , x6 ) ← y ; z" :=
   (y ≫= (λ x : _, let ' (x1,x2,x3,x4,x5,x6) := x in z))
-  (at level 65, only parsing, right associativity) : C_scope.
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
+Notation "x ;; z" := (x ≫= λ _, z)
+  (at level 100, z at level 200, only parsing, right associativity): C_scope.
 
 Notation "ps .*1" := (fmap (M:=list) fst ps)
   (at level 10, format "ps .*1").
@@ -891,11 +894,10 @@ Notation "ps .*2" := (fmap (M:=list) snd ps)
 Class MGuard (M : Type → Type) :=
   mguard: ∀ P {dec : Decision P} {A}, (P → M A) → M A.
 Arguments mguard _ _ _ !_ _ _ / : assert.
-Notation "'guard' P ; o" := (mguard P (λ _, o))
-  (at level 65, only parsing, right associativity) : C_scope.
-Notation "'guard' P 'as' H ; o" := (mguard P (λ H, o))
-  (at level 65, only parsing, right associativity) : C_scope.
-
+Notation "'guard' P ; z" := (mguard P (λ _, z))
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
+Notation "'guard' P 'as' H ; z" := (mguard P (λ H, z))
+  (at level 100, z at level 200, only parsing, right associativity) : C_scope.
 
 (** * Operations on maps *)
 (** In this section we define operational type classes for the operations

theories/collections.v

@@ -797,7 +797,7 @@ Global Instance collection_guard `{CollectionMonad M} : MGuard M :=
 Section collection_monad_base.
   Context `{CollectionMonad M}.
   Lemma elem_of_guard `{Decision P} {A} (x : A) (X : M A) :
-    x ∈ guard P; X ↔ P ∧ x ∈ X.
+    (x ∈ guard P; X) ↔ P ∧ x ∈ X.
   Proof.
     unfold mguard, collection_guard; simpl; case_match;
       rewrite ?elem_of_empty; naive_solver.
@@ -805,7 +805,7 @@ Section collection_monad_base.
   Lemma elem_of_guard_2 `{Decision P} {A} (x : A) (X : M A) :
     P → x ∈ X → x ∈ guard P; X.
   Proof. by rewrite elem_of_guard. Qed.
-  Lemma guard_empty `{Decision P} {A} (X : M A) : guard P; X ≡ ∅ ↔ ¬P ∨ X ≡ ∅.
+  Lemma guard_empty `{Decision P} {A} (X : M A) : (guard P; X) ≡ ∅ ↔ ¬P ∨ X ≡ ∅.
   Proof.
     rewrite !elem_of_equiv_empty; setoid_rewrite elem_of_guard.
     destruct (decide P); naive_solver.
@@ -945,7 +945,7 @@ Section collection_monad.
 
   Lemma collection_bind_singleton {A B} (f : A → M B) x : {[ x ]} ≫= f ≡ f x.
   Proof. set_solver. Qed.
-  Lemma collection_guard_True {A} `{Decision P} (X : M A) : P → guard P; X ≡ X.
+  Lemma collection_guard_True {A} `{Decision P} (X : M A) : P → (guard P; X) ≡ X.
   Proof. set_solver. Qed.
   Lemma collection_fmap_compose {A B C} (f : A → B) (g : B → C) (X : M A) :
     g ∘ f <$> X ≡ g <$> (f <$> X).

theories/fin_maps.v

@@ -1212,7 +1212,7 @@ End more_merge.
 
 (** Properties of the zip_with function *)
 Lemma map_lookup_zip_with {A B C} (f : A → B → C) (m1 : M A) (m2 : M B) i :
-  map_zip_with f m1 m2 !! i = x ← m1 !! i; y ← m2 !! i; Some (f x y).
+  map_zip_with f m1 m2 !! i = (x ← m1 !! i; y ← m2 !! i; Some (f x y)).
 Proof.
   unfold map_zip_with. rewrite lookup_merge by done.
   by destruct (m1 !! i), (m2 !! i).

theories/list.v

@@ -3394,7 +3394,7 @@ Section zip_with.
     Forall2 P l k → length (zip_with f l k) = length k.
   Proof. induction 1; simpl; auto. Qed.
   Lemma lookup_zip_with l k i :
-    zip_with f l k !! i = x ← l !! i; y ← k !! i; Some (f x y).
+    zip_with f l k !! i = (x ← l !! i; y ← k !! i; Some (f x y)).
   Proof.
     revert k i. induction l; intros [|??] [|?]; f_equal/=; auto.
     by destruct (_ !! _).

theories/option.v

@@ -336,13 +336,13 @@ Tactic Notation "case_option_guard" :=
   let H := fresh in case_option_guard as H.
 
 Lemma option_guard_True {A} P `{Decision P} (mx : option A) :
-  P → guard P; mx = mx.
+  P → (guard P; mx) = mx.
 Proof. intros. by case_option_guard. Qed.
 Lemma option_guard_False {A} P `{Decision P} (mx : option A) :
-  ¬P → guard P; mx = None.
+  ¬P → (guard P; mx) = None.
 Proof. intros. by case_option_guard. Qed.
 Lemma option_guard_iff {A} P Q `{Decision P, Decision Q} (mx : option A) :
-  (P ↔ Q) → guard P; mx = guard Q; mx.
+  (P ↔ Q) → (guard P; mx) = guard Q; mx.
 Proof. intros [??]. repeat case_option_guard; intuition. Qed.
 
 Tactic Notation "simpl_option" "by" tactic3(tac) :=