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+(***********************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
+(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
+(*   \VV/  *************************************************************)
+(*    //   *      This file is distributed under the terms of the      *)
+(*         *       GNU Lesser General Public License Version 2.1       *)
+(***********************************************************************)
+
+(* $Id: DecidableTypeEx.v 8933 2006-06-09 14:08:38Z herbelin $ *)
+
+Require Import DecidableType OrderedType OrderedTypeEx.
+Set Implicit Arguments.
+Unset Strict Implicit.
+
+(** * Examples of Decidable Type structures. *)
+
+(** A particular case of [DecidableType] where 
+    the equality is the usual one of Coq. *)
+
+Module Type UsualDecidableType.
+ Parameter t : Set.
+ Definition eq := @eq t.
+ Definition eq_refl := @refl_equal t.
+ Definition eq_sym := @sym_eq t.
+ Definition eq_trans := @trans_eq t.
+ Parameter eq_dec : forall x y, { eq x y }+{~eq x y }.
+End UsualDecidableType.
+
+(** a [UsualDecidableType] is in particular an [DecidableType]. *)
+
+Module UDT_to_DT (U:UsualDecidableType) <: DecidableType := U.
+
+(** An OrderedType can be seen as a DecidableType *)
+
+Module OT_as_DT (O:OrderedType) <: DecidableType. 
+ Module OF := OrderedTypeFacts O.
+ Definition t := O.t.
+ Definition eq := O.eq. 
+ Definition eq_refl := O.eq_refl. 
+ Definition eq_sym := O.eq_sym. 
+ Definition eq_trans := O.eq_trans. 
+ Definition eq_dec := OF.eq_dec. 
+End OT_as_DT.
+
+(** (Usual) Decidable Type for [nat], [positive], [N], [Z] *)
+
+Module Nat_as_DT <: UsualDecidableType := OT_as_DT (Nat_as_OT).
+Module Positive_as_DT <: UsualDecidableType := OT_as_DT (Positive_as_OT).
+Module N_as_DT <: UsualDecidableType := OT_as_DT (N_as_OT).
+Module Z_as_DT <: UsualDecidableType := OT_as_DT (Z_as_OT).