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, 0 deletions

diff --git a/theories/FSets/FSetAVL.v b/theories/FSets/FSetAVL.v
index 6a1e07185..10e06711f 100644
--- a/theories/FSets/FSetAVL.v
+++ b/theories/FSets/FSetAVL.v
@@ -1881,6 +1881,14 @@ Module IntMake (I:Int)(X: OrderedType) <: S with Module E := X.
   destruct Raw.compare; intros; [apply EQ|apply LT|apply GT]; red; auto.
  Defined.
 
+ Definition eq_dec (s s':t) : { eq s s' } + { ~ eq s s' }.
+ Proof.
+  intros (s,b) (s',b'); unfold eq; simpl.
+  case_eq (Raw.equal s s'); intro H; [left|right].
+  apply equal_2; auto.
+  intro H'; rewrite equal_1 in H; auto; discriminate.
+ Defined.
+
  (* specs *)
  Section Specs. 
  Variable s s' s'': t.