FSet/OrderedType now includes an eq_dec, and hence become an extension of DecidableType

 After lots of hesitations, OrderedType now requires this "eq_dec" field, which
 is redundant (can be deduced from "compare"), but allows the subtyping relation
 DecidableType <= OrderedType, and hence WS <= S : ordered sets are now truly
 extensions of weak sets. Of course this change introduces a last-minute
 incompatibility, but:

  - There is a clear gain in term of functionnality / simplicity.
  - FSets 8.2 already needs some adaptations when compared with 8.1, so it's
    the right time to push such incompatible changes.
  - Transition shouldn't be too hard: the old OrderedType still exists under
    the name MiniOrderedType, and functor MOT_to_OT allows to convert from
    one to the other.

 Beware, for a FSetInterface.WS (resp. S) to be coercible to a DecidableType
 (resp. OrderedType), an eq_dec on sets is now required in these interfaces
 and in the implementations. In pratice, it is really easy to build from
 equal and equal_1 and equal_2.

 Some name changes : in FSetFacts, old WFacts now correspond to WFacts_fun,
 while WFacts now expects only one argument (WFacts M := WFacts_fun M.E M).
 Idem with WDecide, WProperties and WEqProperties.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11693 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 8 insertions, 1 deletions

diff --git a/theories/FSets/OrderedTypeAlt.v b/theories/FSets/OrderedTypeAlt.v
index 9f8412a60..95c9c31a9 100644
--- a/theories/FSets/OrderedTypeAlt.v
+++ b/theories/FSets/OrderedTypeAlt.v
@@ -15,7 +15,8 @@
 
 Require Import OrderedType.
 
-(** * An alternative (but equivalent) presentation for an Ordered Type inferface. *)
+(** * An alternative (but equivalent) presentation for an Ordered Type
+   inferface. *)
 
 (** NB: [comparison], defined in [Datatypes.v] is [Eq|Lt|Gt]
 whereas [compare], defined in [OrderedType.v] is [EQ _ | LT _ | GT _ ] 
@@ -81,6 +82,12 @@ Module OrderedType_from_Alt (O:OrderedTypeAlt) <: OrderedType.
  rewrite compare_sym; rewrite H; auto.
  Defined.
 
+ Definition eq_dec : forall x y, { eq x y } + { ~ eq x y }.
+ Proof.
+ intros; unfold eq.
+ case (x ?= y); [ left | right | right ]; auto; discriminate.
+ Defined.
+
 End OrderedType_from_Alt. 
 
 (** From the original presentation to this alternative one. *)