Revision of the FSetWeak Interface, so that it becomes a precise

subtype of the FSet Interface (and idem for FMapWeak / FMap). 

1) No eq_dec is officially required in FSetWeakInterface.S.E
(EqualityType instead of DecidableType). But of course,
implementations still needs this eq_dec. 

2) elements_3 differs in FSet and FSetWeak (sort vs. nodup). In
FSetWeak we rename it into elements_3w, whereas in FSet we
artificially add elements_3w along to the original elements_3.

Initial steps toward factorization of FSetFacts and FSetWeakFacts, 
and so on...

Even if it's not required, FSetWeakList provides a eq_dec on sets, 
allowing weak sets of weak sets. 





git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10271 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 3 insertions, 0 deletions

diff --git a/theories/FSets/FSetInterface.v b/theories/FSets/FSetInterface.v
index ded81426d..f701dcf12 100644
--- a/theories/FSets/FSetInterface.v
+++ b/theories/FSets/FSetInterface.v
@@ -247,6 +247,9 @@ Module Type S.
   Parameter elements_1 : In x s -> InA E.eq x (elements s).
   Parameter elements_2 : InA E.eq x (elements s) -> In x s.
   Parameter elements_3 : sort E.lt (elements s).  
+  (* We add artificially elements_3w, a weaker version of 
+     elements_3, for allowing FSetWeak < FSet subtyping. *)
+  Parameter elements_3w : NoDupA E.eq (elements s).
 
   (** Specification of [min_elt] *)
   Parameter min_elt_1 : min_elt s = Some x -> In x s.