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-Require Import Coq.Lists.List.
-Require Import Crypto.Compilers.Syntax.
-Require Import Crypto.Util.Notations.
-
-Create HintDb wf discriminated.
-
-Ltac solve_wf_side_condition := solve [ eassumption | eauto 250 with wf ].
-
-Section language.
- Context {base_type_code : Type}
- {op : flat_type base_type_code -> flat_type base_type_code -> Type}.
- Local Notation exprf := (@exprf base_type_code op).
- Local Notation expr := (@expr base_type_code op).
- Local Notation Expr := (@Expr base_type_code op).
-
- Section with_var.
- Context {var1 var2 : base_type_code -> Type}.
-
- Local Notation eP2 := (fun t1t2 => var1 (fst t1t2) * var2 (snd t1t2))%type (only parsing).
- Local Notation eP := (fun t => var1 t * var2 t)%type (only parsing).
- Local Notation "x == y" := (existT eP _ (x, y)%core).
- Fixpoint flatten_binding_list2 {t1 t2} (x : interp_flat_type var1 t1) (y : interp_flat_type var2 t2) : list (sigT eP2)
- := (match t1, t2 return interp_flat_type var1 t1 -> interp_flat_type var2 t2 -> list _ with
- | Tbase t1, Tbase t2 => fun x y => existT eP2 (t1, t2)%core (x, y)%core :: nil
- | Unit, Unit => fun x y => nil
- | Prod t0 t1, Prod t0' t1'
- => fun x y => @flatten_binding_list2 _ _ (snd x) (snd y) ++ @flatten_binding_list2 _ _ (fst x) (fst y)
- | Tbase _, _
- | Unit, _
- | Prod _ _, _
- => fun _ _ => nil
- end x y)%list.
- Fixpoint flatten_binding_list {t} (x : interp_flat_type var1 t) (y : interp_flat_type var2 t) : list (sigT eP)
- := (match t return interp_flat_type var1 t -> interp_flat_type var2 t -> list _ with
- | Tbase _ => fun x y => (x == y) :: nil
- | Unit => fun x y => nil
- | Prod t0 t1 => fun x y => @flatten_binding_list _ (snd x) (snd y) ++ @flatten_binding_list _ (fst x) (fst y)
- end x y)%list.
-
- Inductive wff : list (sigT eP) -> forall {t}, @exprf var1 t -> @exprf var2 t -> Prop :=
- | WfTT : forall G, @wff G _ TT TT
- | WfVar : forall G (t : base_type_code) x x', List.In (x == x') G -> @wff G (Tbase t) (Var x) (Var x')
- | WfOp : forall G {t} {tR} (e : @exprf var1 t) (e' : @exprf var2 t) op,
- wff G e e'
- -> wff G (Op (tR := tR) op e) (Op (tR := tR) op e')
- | WfLetIn : forall G t1 t2 e1 e1' (e2 : interp_flat_type var1 t1 -> @exprf var1 t2) e2',
- wff G e1 e1'
- -> (forall x1 x2, wff (flatten_binding_list x1 x2 ++ G) (e2 x1) (e2' x2))
- -> wff G (LetIn e1 e2) (LetIn e1' e2')
- | WfPair : forall G {t1} {t2} (e1: @exprf var1 t1) (e2: @exprf var1 t2)
- (e1': @exprf var2 t1) (e2': @exprf var2 t2),
- wff G e1 e1'
- -> wff G e2 e2'
- -> wff G (Pair e1 e2) (Pair e1' e2').
- Inductive wf : forall {t}, @expr var1 t -> @expr var2 t -> Prop :=
- | WfAbs : forall A B e e',
- (forall x x', @wff (flatten_binding_list x x') B (e x) (e' x'))
- -> @wf (Arrow A B) (Abs e) (Abs e').
- End with_var.
-
- Definition Wf {t} (E : @Expr t) := forall var1 var2, wf (E var1) (E var2).
-End language.
-
-Global Arguments wff {_ _ _ _} G {t} _ _.
-Global Arguments wf {_ _ _ _ t} _ _.
-Global Arguments Wf {_ _ t} _.
-
-Hint Constructors wf wff : wf.