centralize all heap_lang notation in one file

theories/heap_lang/lang.v

@@ -735,19 +735,3 @@ Proof.
     apply (H κs (fill_item K (foldl (flip fill_item) e2' Ks)) σ' efs).
     econstructor 1 with (K := Ks ++ [K]); last done; simpl; by rewrite fill_app.
 Qed.
-
-(** Define some derived forms. *)
-Notation Lam x e := (Rec BAnon x e) (only parsing).
-Notation Let x e1 e2 := (App (Lam x e2) e1) (only parsing).
-Notation Seq e1 e2 := (Let BAnon e1 e2) (only parsing).
-Notation LamV x e := (RecV BAnon x e) (only parsing).
-Notation LetCtx x e2 := (AppRCtx (LamV x e2)) (only parsing).
-Notation SeqCtx e2 := (LetCtx BAnon e2) (only parsing).
-Notation Match e0 x1 e1 x2 e2 := (Case e0 (Lam x1 e1) (Lam x2 e2)) (only parsing).
-Notation Alloc e := (AllocN (Val $ LitV $ LitInt 1) e) (only parsing).
-
-(* Skip should be atomic, we sometimes open invariants around
-   it. Hence, we need to explicitly use LamV instead of e.g., Seq. *)
-Notation Skip := (App (Val $ LamV BAnon (Val $ LitV LitUnit)) (Val $ LitV LitUnit)).
-
-Notation ResolveProph e1 e2 := (Resolve Skip e1 e2) (only parsing).

theories/heap_lang/lifting.v

@@ -4,7 +4,7 @@ From iris.base_logic.lib Require Export proph_map.
 From iris.program_logic Require Export weakestpre.
 From iris.program_logic Require Import ectx_lifting total_ectx_lifting.
 From iris.heap_lang Require Export lang.
-From iris.heap_lang Require Import tactics.
+From iris.heap_lang Require Import tactics notation.
 From iris.proofmode Require Import tactics.
 From stdpp Require Import fin_maps.
 Set Default Proof Using "Type".

theories/heap_lang/notation.v

 From iris.program_logic Require Import language.
-From iris.heap_lang Require Export lang tactics.
+From iris.heap_lang Require Export lang.
 Set Default Proof Using "Type".
 
 Delimit Scope expr_scope with E.
 Delimit Scope val_scope with V.
 
+(** Coercions to make programs easier to type. *)
 Coercion LitInt : Z >-> base_lit.
 Coercion LitBool : bool >-> base_lit.
 Coercion LitLoc : loc >-> base_lit.
 Coercion LitProphecy : proph_id >-> base_lit.
 
 Coercion App : expr >-> Funclass.
-Coercion Val : val >-> expr.
 
+Coercion Val : val >-> expr.
 Coercion Var : string >-> expr.
 
+(** Define some derived forms. *)
+Notation Lam x e := (Rec BAnon x e) (only parsing).
+Notation Let x e1 e2 := (App (Lam x e2) e1) (only parsing).
+Notation Seq e1 e2 := (Let BAnon e1 e2) (only parsing).
+Notation LamV x e := (RecV BAnon x e) (only parsing).
+Notation LetCtx x e2 := (AppRCtx (LamV x e2)) (only parsing).
+Notation SeqCtx e2 := (LetCtx BAnon e2) (only parsing).
+Notation Match e0 x1 e1 x2 e2 := (Case e0 (Lam x1 e1) (Lam x2 e2)) (only parsing).
+Notation Alloc e := (AllocN (Val $ LitV $ LitInt 1) e) (only parsing).
+
+(* Skip should be atomic, we sometimes open invariants around
+   it. Hence, we need to explicitly use LamV instead of e.g., Seq. *)
+Notation Skip := (App (Val $ LamV BAnon (Val $ LitV LitUnit)) (Val $ LitV LitUnit)).
+
 (* No scope for the values, does not conflict and scope is often not inferred
 properly. *)
 Notation "# l" := (LitV l%Z%V) (at level 8, format "# l").
@@ -141,4 +156,5 @@ Notation "'match:' e0 'with' 'SOME' x => e2 | 'NONE' => e1 'end'" :=
   (Match e0 BAnon e1 x%binder e2)
   (e0, e1, x, e2 at level 200, only parsing) : expr_scope.
 
+Notation ResolveProph e1 e2 := (Resolve Skip e1 e2) (only parsing).
 Notation "'resolve_proph:' p 'to:' v" := (ResolveProph p v) (at level 100) : expr_scope.