add some notation for writing cFunctors

algebra/cofe.v

@@ -347,6 +347,9 @@ Structure cFunctor := CFunctor {
 Existing Instance cFunctor_ne.
 Instance: Params (@cFunctor_map) 5.
 
+Delimit Scope cFunctor_scope with CF.
+Bind Scope cFunctor_scope with cFunctor.
+
 Class cFunctorContractive (F : cFunctor) :=
   cFunctor_contractive A1 A2 B1 B2 :> Contractive (@cFunctor_map F A1 A2 B1 B2).
 
@@ -412,6 +415,7 @@ Proof.
   apply cofe_morC_map_ne; apply cFunctor_contractive=>i ?; split; by apply Hfg.
 Qed.
 
+
 (** Discrete cofe *)
 Section discrete_cofe.
   Context `{Equiv A, @Equivalence A (≡)}.
@@ -518,3 +522,10 @@ Proof.
   intros A1 A2 B1 B2 n fg fg' Hfg.
   apply laterC_map_contractive => i ?. by apply cFunctor_ne, Hfg.
 Qed.
+
+(** Notation for writing functors *)
+Notation "∙" := idCF : cFunctor_scope.
+Notation "F1 -n> F2" := (cofe_morCF F1%CF F2%CF) : cFunctor_scope.
+Notation "( F1 , F2 , .. , Fn )" := (prodCF .. (prodCF F1%CF F2%CF) .. Fn%CF) : cFunctor_scope.
+Notation "▶ F"  := (laterCF F%CF) (at level 20, right associativity) : cFunctor_scope.
+Coercion constCF : cofeT >-> cFunctor.

heap_lang/lang.v

@@ -20,7 +20,7 @@ Inductive binder := BAnon | BNamed : string → binder.
 Definition cons_binder (mx : binder) (X : list string) : list string :=
   match mx with BAnon => X | BNamed x => x :: X end.
 Infix ":b:" := cons_binder (at level 60, right associativity).
-Delimit Scope binder_scope with binder.
+Delimit Scope binder_scope with bind.
 Bind Scope binder_scope with binder.
 Instance binder_dec_eq (x1 x2 : binder) : Decision (x1 = x2).
 Proof. solve_decision. Defined.

program_logic/model.v

@@ -34,7 +34,7 @@ End iProp_solution_sig.
 
 Module Export iProp_solution : iProp_solution_sig.
 Definition iProp_result (Λ : language) (Σ : iFunctor) :
-  solution (uPredCF (resRF Λ (laterCF idCF) Σ)) := solver.result _.
+  solution (uPredCF (resRF Λ (▶ ∙) Σ)) := solver.result _.
 
 Definition iPreProp (Λ : language) (Σ : iFunctor) : cofeT := iProp_result Λ Σ.
 Definition iGst (Λ : language) (Σ : iFunctor) : cmraT := Σ (iPreProp Λ Σ).

program_logic/saved_prop.v

@@ -5,7 +5,7 @@ Import uPred.
 Class savedPropG (Λ : language) (Σ : gFunctors) (F : cFunctor) :=
   saved_prop_inG :> inG Λ Σ (agreeR (laterC (F (iPreProp Λ (globalF Σ))))).
 Definition savedPropGF (F : cFunctor) : gFunctor :=
-  GFunctor (agreeRF (laterCF F)).
+  GFunctor (agreeRF (▶ F)).
 Instance inGF_savedPropG  `{inGF Λ Σ (savedPropGF F)} : savedPropG Λ Σ F.
 Proof. apply: inGF_inG. Qed.
 

program_logic/tests.v

@@ -9,7 +9,7 @@ End ModelTest.
 Module SavedPropTest.
   (* Test if we can really go "crazy higher order" *)
   Section sec.
-    Definition F := (cofe_morCF idCF idCF).
+    Definition F : cFunctor := ( ∙ -n> ∙ ).
     Definition Σ : gFunctors := #[ savedPropGF F ].
     Context {Λ : language}.
     Notation iProp := (iPropG Λ Σ).