From semantics.ts.stlc_extended Require Export lang.
Set Default Proof Using "Type".


(** Coercions to make programs easier to type. *)
Coercion of_val : val >-> expr.
Coercion App : expr >-> Funclass.
Coercion Var : string >-> expr.

(** Define some derived forms. *)
Notation Let x e1 e2 := (App (Lam x e2) e1) (only parsing).
Notation Seq e1 e2 := (Let BAnon e1 e2) (only parsing).
Notation Match e0 x1 e1 x2 e2 := (Case e0 (Lam x1 e1) (Lam x2 e2)) (only parsing).

(* No scope for the values, does not conflict and scope is often not inferred
properly. *)
Notation "# l" := (LitIntV l%Z%V%stdpp) (at level 8, format "# l").
Notation "# l" := (LitInt l%Z%E%stdpp) (at level 8, format "# l") : expr_scope.

(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
    first. *)
Notation "( e1 , e2 , .. , en )" := (Pair .. (Pair e1 e2) .. en) : expr_scope.
Notation "( e1 , e2 , .. , en )" := (PairV .. (PairV e1 e2) .. en) : val_scope.

Notation "'match:' e0 'with' 'InjL' x1 => e1 | 'InjR' x2 => e2 'end'" :=
  (Match e0 x1%binder e1 x2%binder e2)
  (e0, x1, e1, x2, e2 at level 200,
   format "'[hv' 'match:'  e0  'with'  '/  ' '[' 'InjL'  x1  =>  '/  ' e1 ']'  '/' '[' |  'InjR'  x2  =>  '/  ' e2 ']'  '/' 'end' ']'") : expr_scope.
Notation "'match:' e0 'with' 'InjR' x1 => e1 | 'InjL' x2 => e2 'end'" :=
  (Match e0 x2%binder e2 x1%binder e1)
  (e0, x1, e1, x2, e2 at level 200, only parsing) : expr_scope.

Notation "e1 + e2" := (Plus e1%E e2%E) : expr_scope.

(*Notation "~ e" := (UnOp NegOp e%E) (at level 75, right associativity) : expr_scope.*)

Notation "λ: x , e" := (Lam x%binder e%E)
  (at level 200, x at level 1, e at level 200,
   format "'[' 'λ:'  x ,  '/  ' e ']'") : expr_scope.
Notation "λ: x y .. z , e" := (Lam x%binder (Lam y%binder .. (Lam z%binder e%E) ..))
  (at level 200, x, y, z at level 1, e at level 200,
   format "'[' 'λ:'  x  y  ..  z ,  '/  ' e ']'") : expr_scope.

Notation "λ: x , e" := (LamV x%binder e%E)
  (at level 200, x at level 1, e at level 200,
   format "'[' 'λ:'  x ,  '/  ' e ']'") : val_scope.
Notation "λ: x y .. z , e" := (LamV x%binder (Lam y%binder .. (Lam z%binder e%E) .. ))
  (at level 200, x, y, z at level 1, e at level 200,
   format "'[' 'λ:'  x  y  ..  z ,  '/  ' e ']'") : val_scope.

Notation "'let:' x := e1 'in' e2" := (Lam x%binder e2%E e1%E)
  (at level 200, x at level 1, e1, e2 at level 200,
   format "'[' 'let:'  x  :=  '[' e1 ']'  'in'  '/' e2 ']'") : expr_scope.
Notation "e1 ;; e2" := (Lam BAnon e2%E e1%E)
  (at level 100, e2 at level 200,
   format "'[' '[hv' '[' e1 ']' ;;  ']' '/' e2 ']'") : expr_scope.