ajout d'exemples de decidable types

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8819 85f007b7-540e-0410-9357-904b9bb8a0f7

5 files changed, 65 insertions, 7 deletions

diff --git a/.depend.coq b/.depend.coq
index a00983c4ba..35fbcaa2d2 100644
--- a/.depend.coq
+++ b/.depend.coq
@@ -13,13 +13,13 @@ theories/FSets/FSetWeakProperties.vo: theories/FSets/FSetWeakProperties.v theori
 theories/FSets/FSetWeakInterface.vo: theories/FSets/FSetWeakInterface.v theories/Bool/Bool.vo theories/FSets/DecidableType.vo
 theories/FSets/FSetWeakList.vo: theories/FSets/FSetWeakList.v theories/FSets/FSetWeakInterface.vo
 theories/FSets/FSetWeakFacts.vo: theories/FSets/FSetWeakFacts.v theories/FSets/FSetWeakInterface.vo
-theories/FSets/FSetWeak.vo: theories/FSets/FSetWeak.v theories/FSets/DecidableType.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FSetFacts.vo theories/FSets/FSetProperties.vo theories/FSets/FSetWeakList.vo
+theories/FSets/FSetWeak.vo: theories/FSets/FSetWeak.v theories/FSets/DecidableType.vo theories/FSets/DecidableTypeEx.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FSetFacts.vo theories/FSets/FSetProperties.vo theories/FSets/FSetWeakList.vo
 theories/FSets/FMapInterface.vo: theories/FSets/FMapInterface.v theories/FSets/FSetInterface.vo
 theories/FSets/FMapList.vo: theories/FSets/FMapList.v theories/FSets/FSetInterface.vo theories/FSets/FMapInterface.vo
 theories/FSets/FMaps.vo: theories/FSets/FMaps.v theories/FSets/OrderedType.vo theories/FSets/OrderedTypeEx.vo theories/FSets/OrderedTypeAlt.vo theories/FSets/FMapInterface.vo theories/FSets/FMapList.vo theories/FSets/FMapPositive.vo theories/FSets/FMapIntMap.vo
 theories/FSets/FMapWeakInterface.vo: theories/FSets/FMapWeakInterface.v theories/FSets/FSetInterface.vo theories/FSets/FSetWeakInterface.vo
 theories/FSets/FMapWeakList.vo: theories/FSets/FMapWeakList.v theories/FSets/FSetInterface.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FMapWeakInterface.vo
-theories/FSets/FMapWeak.vo: theories/FSets/FMapWeak.v theories/FSets/FMapWeakInterface.vo theories/FSets/FMapWeakList.vo
+theories/FSets/FMapWeak.vo: theories/FSets/FMapWeak.v theories/FSets/DecidableType.vo theories/FSets/DecidableTypeEx.vo theories/FSets/FMapWeakInterface.vo theories/FSets/FMapWeakList.vo
 theories/FSets/FMapPositive.vo: theories/FSets/FMapPositive.v theories/ZArith/ZArith.vo theories/FSets/OrderedType.vo theories/FSets/FMapInterface.vo
 theories/FSets/FMapIntMap.vo: theories/FSets/FMapIntMap.v theories/Bool/Bool.vo theories/NArith/NArith.vo theories/NArith/Ndigits.vo theories/NArith/Ndec.vo theories/NArith/Nnat.vo theories/IntMap/Allmaps.vo theories/FSets/OrderedType.vo theories/FSets/OrderedTypeEx.vo theories/FSets/FMapInterface.vo theories/FSets/FMapList.vo
 theories/FSets/FSetToFiniteSet.vo: theories/FSets/FSetToFiniteSet.v theories/Sets/Ensembles.vo theories/Sets/Finite_sets.vo theories/FSets/FSetInterface.vo theories/FSets/FSetProperties.vo theories/FSets/OrderedTypeEx.vo
@@ -181,7 +181,7 @@ theories/Lists/MonoList.vo: theories/Lists/MonoList.v theories/Arith/Le.vo
 theories/Lists/ListSet.vo: theories/Lists/ListSet.v theories/Lists/List.vo
 theories/Lists/Streams.vo: theories/Lists/Streams.v
 theories/Lists/TheoryList.vo: theories/Lists/TheoryList.v theories/Lists/List.vo theories/Arith/Le.vo theories/Arith/Lt.vo theories/Arith/Minus.vo theories/Bool/DecBool.vo
-theories/Lists/List.vo: theories/Lists/List.v theories/Arith/Le.vo theories/Arith/Minus.vo theories/Arith/Min.vo theories/Bool/Bool.vo
+theories/Lists/List.vo: theories/Lists/List.v theories/Arith/Le.vo theories/Arith/Gt.vo theories/Arith/Minus.vo theories/Arith/Min.vo theories/Bool/Bool.vo
 theories/Lists/SetoidList.vo: theories/Lists/SetoidList.v theories/Lists/List.vo theories/Sorting/Sorting.vo theories/Setoids/Setoid.vo
 theories/Strings/Ascii.vo: theories/Strings/Ascii.v theories/Bool/Bool.vo theories/NArith/BinPos.vo
 theories/Strings/String.vo: theories/Strings/String.v theories/Arith/Arith.vo theories/Strings/Ascii.vo
@@ -222,13 +222,13 @@ theories/FSets/FSetWeakProperties.vo: theories/FSets/FSetWeakProperties.v theori
 theories/FSets/FSetWeakInterface.vo: theories/FSets/FSetWeakInterface.v theories/Bool/Bool.vo theories/FSets/DecidableType.vo
 theories/FSets/FSetWeakList.vo: theories/FSets/FSetWeakList.v theories/FSets/FSetWeakInterface.vo
 theories/FSets/FSetWeakFacts.vo: theories/FSets/FSetWeakFacts.v theories/FSets/FSetWeakInterface.vo
-theories/FSets/FSetWeak.vo: theories/FSets/FSetWeak.v theories/FSets/DecidableType.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FSetFacts.vo theories/FSets/FSetProperties.vo theories/FSets/FSetWeakList.vo
+theories/FSets/FSetWeak.vo: theories/FSets/FSetWeak.v theories/FSets/DecidableType.vo theories/FSets/DecidableTypeEx.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FSetFacts.vo theories/FSets/FSetProperties.vo theories/FSets/FSetWeakList.vo
 theories/FSets/FMapInterface.vo: theories/FSets/FMapInterface.v theories/FSets/FSetInterface.vo
 theories/FSets/FMapList.vo: theories/FSets/FMapList.v theories/FSets/FSetInterface.vo theories/FSets/FMapInterface.vo
 theories/FSets/FMaps.vo: theories/FSets/FMaps.v theories/FSets/OrderedType.vo theories/FSets/OrderedTypeEx.vo theories/FSets/OrderedTypeAlt.vo theories/FSets/FMapInterface.vo theories/FSets/FMapList.vo theories/FSets/FMapPositive.vo theories/FSets/FMapIntMap.vo
 theories/FSets/FMapWeakInterface.vo: theories/FSets/FMapWeakInterface.v theories/FSets/FSetInterface.vo theories/FSets/FSetWeakInterface.vo
 theories/FSets/FMapWeakList.vo: theories/FSets/FMapWeakList.v theories/FSets/FSetInterface.vo theories/FSets/FSetWeakInterface.vo theories/FSets/FMapWeakInterface.vo
-theories/FSets/FMapWeak.vo: theories/FSets/FMapWeak.v theories/FSets/FMapWeakInterface.vo theories/FSets/FMapWeakList.vo
+theories/FSets/FMapWeak.vo: theories/FSets/FMapWeak.v theories/FSets/DecidableType.vo theories/FSets/DecidableTypeEx.vo theories/FSets/FMapWeakInterface.vo theories/FSets/FMapWeakList.vo
 theories/FSets/FMapPositive.vo: theories/FSets/FMapPositive.v theories/ZArith/ZArith.vo theories/FSets/OrderedType.vo theories/FSets/FMapInterface.vo
 theories/FSets/FMapIntMap.vo: theories/FSets/FMapIntMap.v theories/Bool/Bool.vo theories/NArith/NArith.vo theories/NArith/Ndigits.vo theories/NArith/Ndec.vo theories/NArith/Nnat.vo theories/IntMap/Allmaps.vo theories/FSets/OrderedType.vo theories/FSets/OrderedTypeEx.vo theories/FSets/FMapInterface.vo theories/FSets/FMapList.vo
 theories/FSets/FSetToFiniteSet.vo: theories/FSets/FSetToFiniteSet.v theories/Sets/Ensembles.vo theories/Sets/Finite_sets.vo theories/FSets/FSetInterface.vo theories/FSets/FSetProperties.vo theories/FSets/OrderedTypeEx.vo
@@ -270,7 +270,7 @@ theories/Reals/DiscrR.vo: theories/Reals/DiscrR.v theories/Reals/RIneq.vo contri
 theories/Reals/Rbase.vo: theories/Reals/Rbase.v theories/Reals/Rdefinitions.vo theories/Reals/Raxioms.vo theories/Reals/RIneq.vo theories/Reals/DiscrR.vo
 theories/Setoids/Setoid.vo: theories/Setoids/Setoid.v theories/Relations/Relation_Definitions.vo
 theories/Sorting/Heap.vo: theories/Sorting/Heap.v theories/Lists/List.vo theories/Sets/Multiset.vo theories/Sorting/Permutation.vo theories/Relations/Relations.vo theories/Sorting/Sorting.vo
-theories/Sorting/Permutation.vo: theories/Sorting/Permutation.v theories/Relations/Relations.vo theories/Lists/List.vo theories/Sets/Multiset.vo
+theories/Sorting/Permutation.vo: theories/Sorting/Permutation.v theories/Relations/Relations.vo theories/Lists/List.vo theories/Sets/Multiset.vo theories/Arith/Arith.vo
 theories/Sorting/Sorting.vo: theories/Sorting/Sorting.v theories/Lists/List.vo theories/Sets/Multiset.vo theories/Sorting/Permutation.vo theories/Relations/Relations.vo
 contrib/omega/OmegaLemmas.vo: contrib/omega/OmegaLemmas.v theories/ZArith/ZArith_base.vo
 contrib/omega/Omega.vo: contrib/omega/Omega.v theories/ZArith/ZArith_base.vo contrib/omega/OmegaLemmas.vo theories/ZArith/Zhints.vo
diff --git a/theories/FSets/DecidableType.v b/theories/FSets/DecidableType.v
index 4e34bbc0d1..a4de6ca7fe 100644
--- a/theories/FSets/DecidableType.v
+++ b/theories/FSets/DecidableType.v
@@ -31,6 +31,7 @@ Module Type DecidableType.
 
 End DecidableType. 
 
+(** * Additional notions about keys and datas used in FMap *)
 
 Module KeyDecidableType(D:DecidableType).
  Import D.
@@ -147,5 +148,9 @@ Module KeyDecidableType(D:DecidableType).
  Hint Unfold MapsTo In.
  Hint Resolve In_inv_2 In_inv_3.
 
-
 End KeyDecidableType.
+
+
+
+
+
diff --git a/theories/FSets/DecidableTypeEx.v b/theories/FSets/DecidableTypeEx.v
new file mode 100644
index 0000000000..dcca370953
--- /dev/null
+++ b/theories/FSets/DecidableTypeEx.v
@@ -0,0 +1,50 @@
+(***********************************************************************)
+(*  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       *)
+(***********************************************************************)
+
+(* $Id$ *)
+
+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).
diff --git a/theories/FSets/FMapWeak.v b/theories/FSets/FMapWeak.v
index 7baeb2970d..7bdee004e3 100644
--- a/theories/FSets/FMapWeak.v
+++ b/theories/FSets/FMapWeak.v
@@ -8,5 +8,7 @@
 
 (* $Id$ *)
 
+Require Export DecidableType.
+Require Export DecidableTypeEx.
 Require Export FMapWeakInterface.
 Require Export FMapWeakList.
diff --git a/theories/FSets/FSetWeak.v b/theories/FSets/FSetWeak.v
index ccf590ca3d..8631841fb1 100644
--- a/theories/FSets/FSetWeak.v
+++ b/theories/FSets/FSetWeak.v
@@ -9,6 +9,7 @@
 (* $Id$ *)
 
 Require Export DecidableType.
+Require Export DecidableTypeEx.
 Require Export FSetWeakInterface.
 Require Export FSetFacts.
 Require Export FSetProperties.