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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* Definition mutuellement inductive et dependante *)
Require Export PolyList.
Record signature : Type := {
sort : Set;
sort_beq : sort->sort->bool;
sort_beq_refl : (f:sort)true=(sort_beq f f);
sort_beq_eq : (f1,f2:sort)true=(sort_beq f1 f2)->f1=f2;
fsym :> Set;
fsym_type : fsym->(list sort)*sort;
fsym_beq : fsym->fsym->bool;
fsym_beq_refl : (f:fsym)true=(fsym_beq f f);
fsym_beq_eq : (f1,f2:fsym)true=(fsym_beq f1 f2)->f1=f2
}.
Variable F : signature.
Definition vsym := (sort F)*nat.
Definition vsym_sort := (fst (sort F) nat).
Definition vsym_nat := (snd (sort F) nat).
Mutual Inductive term : (sort F)->Set :=
| term_var : (v:vsym)(term (vsym_sort v))
| term_app : (f:F)(list_term (Fst (fsym_type F f)))
->(term (Snd (fsym_type F f)))
with list_term : (list (sort F)) -> Set :=
| term_nil : (list_term (nil (sort F)))
| term_cons : (s:(sort F);l:(list (sort F)))
(term s)->(list_term l)->(list_term (cons s l)).
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