Improve notations for heap_lang.

heap_lang/sugar.v

 Require Export heap_lang.heap_lang heap_lang.lifting.
-Import uPred.
-Import heap_lang.
+Import uPred heap_lang.
 
 (** Define some syntactic sugar. LitTrue and LitFalse are defined in heap_lang.v. *)
 Definition Lam (e : {bind expr}) := Rec e.[ren(+1)].
@@ -17,42 +16,38 @@ Definition LamV (e : {bind expr}) := RecV e.[ren(+1)].
 Definition LetCtx (e2 : {bind expr}) := AppRCtx (LamV e2).
 Definition SeqCtx (e2 : expr) := LetCtx (e2.[ren(+1)]).
 
-Delimit Scope lang_scope with L.
-Bind Scope lang_scope with expr.
-Arguments wp {_ _} _ _%L _.
-(* TODO: The levels are all random. Also maybe we should not
-   make 'new' a keyword. What about Arguments for hoare triples?. *)
-(* The colons indicate binders. "let" is not consistent here though,
-   thing are only bound in the "in". *)
-Notation "'rec::' e" := (Rec e) (at level 100) : lang_scope.
-Notation "'λ:' e" := (Lam e) (at level 100) : lang_scope.
-Notation "'let:' e1 'in' e2" := (Let e1 e2) (at level 70) : lang_scope.
-Notation "e1 ';' e2" := (Seq e1 e2) (at level 70) : lang_scope.
-Notation "'if' e1 'then' e2 'else' e3" := (If e1 e2 e3) : lang_scope.
+Module notations.
+  Delimit Scope lang_scope with L.
+  Bind Scope lang_scope with expr.
+  Arguments wp {_ _} _ _%L _.
 
-Notation "#0" := (Var 0) (at level 0) : lang_scope.
-Notation "#1" := (Var 1) (at level 0) : lang_scope.
-Notation "#2" := (Var 2) (at level 0) : lang_scope.
-Notation "#3" := (Var 3) (at level 0) : lang_scope.
-Notation "#4" := (Var 4) (at level 0) : lang_scope.
-Notation "#5" := (Var 5) (at level 0) : lang_scope.
-Notation "#6" := (Var 6) (at level 0) : lang_scope.
-Notation "#7" := (Var 7) (at level 0) : lang_scope.
-Notation "#8" := (Var 8) (at level 0) : lang_scope.
-Notation "#9" := (Var 9) (at level 0) : lang_scope.
+  Coercion LitNat : nat >-> expr.
+  Coercion LitNatV : nat >-> val.
+  Coercion Loc : loc >-> expr.
+  Coercion LocV : loc >-> val.
+  Coercion App : expr >-> Funclass.
 
-Notation "'★' e" := (Load e) (at level 30) : lang_scope.
-Notation "e1 '<-' e2" := (Store e1 e2) (at level 60) : lang_scope.
-Notation "'new' e" := (Alloc e) (at level 60) : lang_scope.
-Notation "e1 '+' e2" := (Plus e1 e2) : lang_scope.
-Notation "e1 '≤' e2" := (Le e1 e2) : lang_scope.
-Notation "e1 '<' e2" := (Lt e1 e2) : lang_scope.
-
-Coercion LitNat : nat >-> expr.
-Coercion LitNatV : nat >-> val.
-Coercion Loc : loc >-> expr.
-Coercion LocV : loc >-> val.
-Coercion App : expr >-> Funclass.
+  (** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
+  first. *)
+  (* What about Arguments for hoare triples?. *)
+  (* The colons indicate binders. "let" is not consistent here though,
+     thing are only bound in the "in". *)
+  Notation "# n" := (Var n) (at level 1, format "# n") : lang_scope.
+  Notation "! e" := (Load e%L) (at level 10, format "! e") : lang_scope.
+  Notation "'ref' e" := (Alloc e%L) (at level 30) : lang_scope.
+  Notation "e1 + e2" := (Plus e1%L e2%L)
+    (at level 50, left associativity) : lang_scope.
+  Notation "e1 ≤ e2" := (Le e1%L e2%L) (at level 70) : lang_scope.
+  Notation "e1 < e2" := (Lt e1%L e2%L) (at level 70) : lang_scope.
+  (* The unicode ← is already part of the notation "_ ← _; _" for bind. *)
+  Notation "e1 <- e2" := (Store e1%L e2%L) (at level 80) : lang_scope.
+  Notation "e1 ; e2" := (Seq e1%L e2%L) (at level 100) : lang_scope.
+  Notation "'let:' e1 'in' e2" := (Let e1%L e2%L) (at level 102) : lang_scope.
+  Notation "'λ:' e" := (Lam e%L) (at level 102) : lang_scope.
+  Notation "'rec::' e" := (Rec e%L) (at level 102) : lang_scope.
+  Notation "'if' e1 'then' e2 'else' e3" := (If e1%L e2%L e3%L)
+    (at level 200, e1, e2, e3 at level 200, only parsing) : lang_scope.
+End notations.
 
 Section suger.
 Context {Σ : iFunctor}.

heap_lang/tests.v

 (** This file is essentially a bunch of testcases. *)
 Require Import program_logic.upred.
 Require Import heap_lang.lifting heap_lang.sugar.
-Import heap_lang.
-Import uPred.
+Import heap_lang uPred notations.
 
 Module LangTests.
   Definition add := (21 + 21)%L.
@@ -24,7 +23,7 @@ Module LiftingTests.
   Implicit Types Q : val → iProp heap_lang Σ.
 
   (* FIXME: Fix levels so that we do not need the parenthesis here. *)
-  Definition e  : expr := let: new 1 in (#0 <- ★#0 + 1 ; ★#0)%L.
+  Definition e  : expr := (let: ref 1 in #0 <- !#0 + 1; !#0)%L.
   Goal ∀ σ E, (ownP σ : iProp heap_lang Σ) ⊑ (wp E e (λ v, ■(v = 2))).
   Proof.
     move=> σ E. rewrite /e.
@@ -56,15 +55,12 @@ Module LiftingTests.
   (* TODO: once asimpl preserves notation, we don't need
      FindPred' anymore. *)
   (* FIXME: fix notation so that we do not need parenthesis or %L *)
-  Definition FindPred' n1 Sn1 n2 f : expr := if Sn1 < n2
-                                             then f Sn1
-                                             else n1.
-  Definition FindPred n2 : expr := rec:: (let: (#1 + 1) in
-                                     FindPred' #2 #0 n2.[ren(+3)] #1)%L.
-  Definition Pred : expr := λ: (if #0 ≤ 0
-                                then 0
-                                else FindPred (#0) 0
-                               )%L.
+  Definition FindPred' n1 Sn1 n2 f : expr :=
+    if Sn1 < n2 then f Sn1 else n1.
+  Definition FindPred n2 : expr :=
+    rec:: (let: #1 + 1 in FindPred' #2 #0 n2.[ren(+3)] #1)%L.
+  Definition Pred : expr :=
+    λ: (if #0 ≤ 0 then 0 else FindPred #0 0)%L.
 
   Lemma FindPred_spec n1 n2 E Q :
     (■(n1 < n2) ∧ Q (pred n2)) ⊑
@@ -112,9 +108,7 @@ Module LiftingTests.
   Qed.
 
   Goal ∀ E,
-    True ⊑ wp (Σ:=Σ) E
-         (* FIXME why do we need %L here? *)
-      (let: Pred 42 in Pred #0)%L (λ v, ■(v = 40)).
+    True ⊑ wp (Σ:=Σ) E (let: Pred 42 in Pred #0) (λ v, ■(v = 40)).
   Proof.
     intros E. rewrite -wp_let. rewrite -Pred_spec -!later_intro.
     asimpl. (* TODO RJ: Can we somehow make it so that Pred gets folded again? *)