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(*                                                                    *)
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(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
(*****************************************************************************)
(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
(*****************************************************************************)
(*									     *)
(*	            Functor Free Monoid : SET -> MON                         *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export FreeMonoid.
Require Export Functor.
Require Export MON.
Set Implicit Arguments.
Unset Strict Implicit.
(* SET -> MON *)
Section funfreemon_map_def.
Variable A B : Setoid.
Section funfreemon_mor_def.
Variable f : Map A B.
Fixpoint Dist_fun (l : Tlist A) : Tlist B :=
match l with
| Empty => Empty B
| Concat1 a l1 => Concat1 (f a) (Dist_fun l1)
end.

(* Specifications: *)
Lemma Dist_map_law : Map_law Dist_fun.
Canonical Structure Dist_map := Build_Map Dist_map_law.
Lemma Dist_map_unit_law : MonUnit_law Dist_map.
Lemma Dist_map_op_law : MonOp_law Dist_map.
Canonical Structure FunFreeMon_mor :=
Build_MonMor Dist_map_unit_law Dist_map_op_law.