blob: 2c76a135975e551214129a77f0a2508535e841f3 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* 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).
|
