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Require Import Crypto.Util.Tuple.
Require Import Crypto.Reflection.Syntax.
Local Open Scope ctype_scope.
Section language.
Context {base_type_code : Type}.
Local Notation flat_type := (flat_type base_type_code).
Section interp.
Section flat_type.
Context {interp_base_type : base_type_code -> Type}.
Local Notation interp_flat_type := (interp_flat_type interp_base_type).
Fixpoint flat_interp_tuple' {T n} : interp_flat_type (tuple' T n) -> Tuple.tuple' (interp_flat_type T) n
:= match n return interp_flat_type (tuple' T n) -> Tuple.tuple' (interp_flat_type T) n with
| O => fun x => x
| S n' => fun xy => (@flat_interp_tuple' _ n' (fst xy), snd xy)
end.
Definition flat_interp_tuple {T n} : interp_flat_type (tuple T n) -> Tuple.tuple (interp_flat_type T) n
:= match n return interp_flat_type (tuple T n) -> Tuple.tuple (interp_flat_type T) n with
| O => fun x => x
| S n' => @flat_interp_tuple' T n'
end.
Fixpoint flat_interp_untuple' {T n} : Tuple.tuple' (interp_flat_type T) n -> interp_flat_type (tuple' T n)
:= match n return Tuple.tuple' (interp_flat_type T) n -> interp_flat_type (tuple' T n) with
| O => fun x => x
| S n' => fun xy => (@flat_interp_untuple' _ n' (fst xy), snd xy)
end.
Definition flat_interp_untuple {T n} : Tuple.tuple (interp_flat_type T) n -> interp_flat_type (tuple T n)
:= match n return Tuple.tuple (interp_flat_type T) n -> interp_flat_type (tuple T n) with
| O => fun x => x
| S n' => @flat_interp_untuple' T n'
end.
Lemma flat_interp_untuple'_tuple' {T n v}
: @flat_interp_untuple' T n (flat_interp_tuple' v) = v.
Proof. induction n; [ reflexivity | simpl; rewrite IHn; destruct v; reflexivity ]. Qed.
Lemma flat_interp_untuple_tuple {T n v}
: flat_interp_untuple (@flat_interp_tuple T n v) = v.
Proof. destruct n; [ reflexivity | apply flat_interp_untuple'_tuple' ]. Qed.
Lemma flat_interp_tuple'_untuple' {T n v}
: @flat_interp_tuple' T n (flat_interp_untuple' v) = v.
Proof. induction n; [ reflexivity | simpl; rewrite IHn; destruct v; reflexivity ]. Qed.
Lemma flat_interp_tuple_untuple {T n v}
: @flat_interp_tuple T n (flat_interp_untuple v) = v.
Proof. destruct n; [ reflexivity | apply flat_interp_tuple'_untuple' ]. Qed.
Definition tuple_map {A B n} (f : interp_flat_type A -> interp_flat_type B) (v : interp_flat_type (tuple A n))
: interp_flat_type (tuple B n)
:= let fv := Tuple.map f (flat_interp_tuple v) in
match n return interp_flat_type (tuple A n) -> Tuple.tuple (interp_flat_type B) n -> interp_flat_type (tuple B n) with
| 0 => fun v x => x
| S _ => fun v fv => flat_interp_untuple' fv
end v fv.
End flat_type.
End interp.
End language.
Global Arguments flat_interp_tuple' {_ _ _ _} _.
Global Arguments flat_interp_tuple {_ _ _ _} _.
Global Arguments flat_interp_untuple' {_ _ _ _} _.
Global Arguments flat_interp_untuple {_ _ _ _} _.
Global Arguments tuple_map {_ _ _ _ n} _ _.
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