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Require Import Crypto.Reflection.Syntax.
Section language.
Context {base_type : Type}
{interp_base_type : base_type -> Type}
{op : flat_type base_type -> flat_type base_type -> Type}
{interp_op : forall src dst, op src dst -> interp_flat_type interp_base_type src -> interp_flat_type interp_base_type dst}.
Fixpoint count_binders (t : type base_type) : nat
:= match t with
| Arrow A B => S (count_binders B)
| Tflat _ => 0
end.
Fixpoint remove_binders' (n : nat) (t : type base_type) {struct t} : type base_type
:= match t, n with
| Tflat _, _ => t
| Arrow _ B, 0 => B
| Arrow A B, S n'
=> remove_binders' n' B
end.
Definition remove_binders (n : nat) (t : type base_type) : type base_type
:= match n with
| 0 => t
| S n' => remove_binders' n' t
end.
Fixpoint remove_all_binders (t : type base_type) : flat_type base_type
:= match t with
| Tflat T => T
| Arrow A B => remove_all_binders B
end.
Fixpoint binders_for' (n : nat) (t : type base_type) (var : base_type -> Type) {struct t}
:= match n, t return Type with
| 0, Arrow A B => var A
| S n', Arrow A B => var A * binders_for' n' B var
| _, _ => unit
end%type.
Definition binders_for (n : nat) (t : type base_type) (var : base_type -> Type)
:= match n return Type with
| 0 => unit
| S n' => binders_for' n' t var
end.
Fixpoint all_binders_for (t : type base_type)
:= match t return match t with
| Tflat _ => unit
| _ => flat_type base_type
end with
| Tflat T => tt
| Arrow A B
=> match B return match B with Tflat _ => _ | _ => _ end -> _ with
| Tflat T => fun _ => Tbase A
| Arrow _ _ => fun T => Tbase A * T
end%ctype (all_binders_for B)
end.
Definition interp_all_binders_for T var
:= match T return Type with
| Tflat _ => unit
| Arrow A B => interp_flat_type var (all_binders_for (Arrow A B))
end.
Definition fst_binder {A B var} (args : interp_flat_type var (all_binders_for (Arrow A B))) : var A
:= match B return interp_flat_type var (all_binders_for (Arrow A B)) -> var A with
| Tflat _ => fun x => x
| Arrow _ _ => fun x => fst x
end args.
Definition snd_binder {A B var} (args : interp_flat_type var (all_binders_for (Arrow A B)))
: interp_all_binders_for B var
:= match B return interp_flat_type var (all_binders_for (Arrow A B))
-> interp_all_binders_for B var
with
| Tflat _ => fun _ => tt
| Arrow _ _ => fun x => snd x
end args.
Fixpoint Apply' n {var t} (x : @expr base_type interp_base_type op var t)
: forall (args : binders_for' n t var),
@expr base_type interp_base_type op var (remove_binders' n t)
:= match x in (@expr _ _ _ _ t), n return (binders_for' n t var -> @expr _ _ _ _ (remove_binders' n t)) with
| Return _ _ as y, _ => fun _ => y
| Abs _ _ f, 0 => f
| Abs src dst f, S n' => fun args => @Apply' n' var dst (f (fst args)) (snd args)
end.
Definition Apply n {var t} (x : @expr base_type interp_base_type op var t)
: forall (args : binders_for n t var),
@expr base_type interp_base_type op var (remove_binders n t)
:= match n return binders_for n t var -> @expr _ _ _ _ (remove_binders n t) with
| 0 => fun _ => x
| S n' => @Apply' n' var t x
end.
Fixpoint ApplyAll {var t} (x : @expr base_type interp_base_type op var t)
: forall (args : interp_all_binders_for t var),
@exprf base_type interp_base_type op var (remove_all_binders t)
:= match x in @expr _ _ _ _ t
return (forall (args : interp_all_binders_for t var),
@exprf base_type interp_base_type op var (remove_all_binders t))
with
| Return _ x => fun _ => x
| Abs src dst f => fun args => @ApplyAll var dst (f (fst_binder args)) (snd_binder args)
end.
Fixpoint ApplyInterped' n {t} {struct t}
: forall (x : interp_type interp_base_type t)
(args : binders_for' n t interp_base_type),
interp_type interp_base_type (remove_binders' n t)
:= match t, n return (forall (x : interp_type interp_base_type t)
(args : binders_for' n t interp_base_type),
interp_type interp_base_type (remove_binders' n t)) with
| Tflat _, _ => fun x _ => x
| Arrow s d, 0 => fun x => x
| Arrow s d, S n' => fun f args => @ApplyInterped' n' d (f (fst args)) (snd args)
end.
Definition ApplyInterped (n : nat) {t} (x : interp_type interp_base_type t)
: forall (args : binders_for n t interp_base_type),
interp_type interp_base_type (remove_binders n t)
:= match n return (binders_for n t interp_base_type -> interp_type interp_base_type (remove_binders n t)) with
| 0 => fun _ => x
| S n' => @ApplyInterped' n' t x
end.
Fixpoint ApplyInterpedAll {t}
: forall (x : interp_type interp_base_type t)
(args : interp_all_binders_for t interp_base_type),
interp_flat_type interp_base_type (remove_all_binders t)
:= match t return (forall (x : interp_type _ t)
(args : interp_all_binders_for t _),
interp_flat_type _ (remove_all_binders t))
with
| Tflat _ => fun x _ => x
| Arrow A B => fun f x => @ApplyInterpedAll B (f (fst_binder x)) (snd_binder x)
end.
End language.
Arguments all_binders_for {_} !_ / .
Arguments interp_all_binders_for {_} !_ _ / .
Arguments count_binders {_} !_ / .
Arguments binders_for {_} !_ !_ _ / .
Arguments remove_binders {_} !_ !_ / .
(* Work around bug #5175 *)
Arguments Apply {_ _ _ _ _ _} _ _ , {_ _ _} _ {_ _} _ _.
Arguments Apply _ _ _ !_ _ _ !_ !_ / .
Arguments ApplyInterped {_ _ !_ !_} _ _ / .
Arguments ApplyAll {_ _ _ _ !_} !_ _ / .
Arguments ApplyInterpedAll {_ _ !_} _ _ / .
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