(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Jacques-Henri Jourdan, INRIA Paris-Rocquencourt            *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the GNU General Public License as published by  *)
(*  the Free Software Foundation, either version 2 of the License, or  *)
(*  (at your option) any later version.  This file is also distributed *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
(** A curryfied function with multiple parameters **)
Definition arrows_left: list Type -> Type -> Type :=
fold_left (fun A B => B -> A).
(** A curryfied function with multiple parameters **)
Definition arrows_right: Type -> list Type -> Type :=
fold_right (fun A B => A -> B).
(** A tuple is a heterogeneous list. For convenience, we use pairs. **)
Fixpoint tuple (types : list Type) : Type :=
match types with
| nil => unit
| t::q => prod t (tuple q)
end.
Fixpoint uncurry {args:list Type} {res:Type}:
arrows_left args res -> tuple args -> res :=
match args return forall res, arrows_left args res -> tuple args -> res with
| [] => fun _ f _ => f
| t::q => fun res f p => let (d, t) := p in
(@uncurry q _ f t) d
end res.

Lemma JMeq_eqrect:
forall (U:Type) (a b:U) (P:U -> Type) (x:P a) (e:a=b),
eq_rect a P x b e ~= x.