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Require Import Crypto.Reflection.Syntax.
Require Import Crypto.Reflection.Application.
Section language.
Context {base_type1 base_type2 : Type}
{interp_base_type1 : base_type1 -> Type}
{interp_base_type2 : base_type2 -> Type}
{op1 : flat_type base_type1 -> flat_type base_type1 -> Type}
{op2 : flat_type base_type2 -> flat_type base_type2 -> Type}
{interp_op1 : forall src dst, op1 src dst -> interp_flat_type interp_base_type1 src -> interp_flat_type interp_base_type1 dst}
{interp_op2 : forall src dst, op2 src dst -> interp_flat_type interp_base_type2 src -> interp_flat_type interp_base_type2 dst}
(R : forall t1 t2, interp_base_type1 t1 -> interp_base_type2 t2 -> Prop).
Fixpoint rel_interp_all_binders_for' {t1 : type base_type1} {t2 : type base_type2}
: interp_all_binders_for' t1 interp_base_type1 -> interp_all_binders_for' t2 interp_base_type2 -> Prop
:= match t1, t2 return interp_all_binders_for' t1 _ -> interp_all_binders_for' t2 _ -> Prop with
| Tflat T1, Tflat T2 => fun _ _ => True
| Arrow A1 B1, Arrow A2 B2
=> fun x y => R _ _ (fst x) (fst y) /\ @rel_interp_all_binders_for' _ _ (snd x) (snd y)
| Tflat _, _
| Arrow _ _, _
=> fun _ _ => False
end.
Definition rel_interp_all_binders_for {t1 : type base_type1} {t2 : type base_type2}
(x : interp_all_binders_for t1 interp_base_type1) (y : interp_all_binders_for t2 interp_base_type2)
: Prop
:= rel_interp_all_binders_for' (interp_all_binders_for_to' x) (interp_all_binders_for_to' y).
End language.
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