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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \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 List.
Record signature : Type :=
{sort : Set;
sort_beq : sort -> sort -> bool;
sort_beq_refl : forall f : sort, true = sort_beq f f;
sort_beq_eq : forall 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 : forall f : fsym, true = fsym_beq f f;
fsym_beq_eq : forall f1 f2 : fsym, true = fsym_beq f1 f2 -> f1 = f2}.
Variable F : signature.
Definition vsym := (sort F * nat)%type.
Definition vsym_sort := fst (A:=sort F) (B:=nat).
Definition vsym_nat := snd (A:=sort F) (B:=nat).
Inductive term : sort F -> Set :=
| term_var : forall v : vsym, term (vsym_sort v)
| term_app :
forall 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
| term_cons :
forall (s : sort F) (l : list (sort F)),
term s -> list_term l -> list_term (s :: l).
|
