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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 *)
(************************************************************************)
(* $Id: Field_Compl.v,v 1.8.2.1 2004/07/16 19:30:09 herbelin Exp $ *)
Inductive listT (A:Type) : Type :=
| nilT : listT A
| consT : A -> listT A -> listT A.
Fixpoint appT (A:Type) (l m:listT A) {struct l} : listT A :=
match l with
| nilT => m
| consT a l1 => consT A a (appT A l1 m)
end.
Inductive prodT (A B:Type) : Type :=
pairT : A -> B -> prodT A B.
Definition assoc_2nd :=
(fix assoc_2nd_rec (A:Type) (B:Set)
(eq_dec:forall e1 e2:B, {e1 = e2} + {e1 <> e2})
(lst:listT (prodT A B)) {struct lst} :
B -> A -> A :=
fun (key:B) (default:A) =>
match lst with
| nilT => default
| consT (pairT v e) l =>
match eq_dec e key with
| left _ => v
| right _ => assoc_2nd_rec A B eq_dec l key default
end
end).
Definition fstT (A B:Type) (c:prodT A B) := match c with
| pairT a _ => a
end.
Definition sndT (A B:Type) (c:prodT A B) := match c with
| pairT _ a => a
end.
Definition mem :=
(fix mem (A:Set) (eq_dec:forall e1 e2:A, {e1 = e2} + {e1 <> e2})
(a:A) (l:listT A) {struct l} : bool :=
match l with
| nilT => false
| consT a1 l1 =>
match eq_dec a a1 with
| left _ => true
| right _ => mem A eq_dec a l1
end
end).
Inductive field_rel_option (A:Type) : Type :=
| Field_None : field_rel_option A
| Field_Some : (A -> A -> A) -> field_rel_option A.
|
