Numbers: new functions pow, even, odd + many reorganisations

 - Simplification of functor names, e.g. ZFooProp instead of ZFooPropFunct
 - The axiomatisations of the different fonctions are now in {N,Z}Axioms.v
   apart for Z division (three separate flavours in there own files).
   Content of {N,Z}AxiomsSig is extended, old version is {N,Z}AxiomsMiniSig.
 - In NAxioms, the recursion field isn't that useful, since we axiomatize
   other functions and not define them (apart in the toy NDefOps.v).
   We leave recursion there, but in a separate NAxiomsFullSig.
 - On Z, the pow function is specified to behave as Zpower : a^(-1)=0
 - In BigN/BigZ, (power:t->N->t) is now pow_N, while pow is t->t->t
   These pow could be more clever (we convert 2nd arg to N and use pow_N).
   Default "^" is now (pow:t->t->t). BigN/BigZ ring is adapted accordingly
 - In BigN, is_even is now even, its spec is changed to use Zeven_bool.
   We add an odd. In BigZ, we add even and odd.
 - In ZBinary (implem of ZAxioms by ZArith), we create an efficient Zpow
   to implement pow. This Zpow should replace the current linear Zpower
   someday.
 - In NPeano (implem of NAxioms by Arith), we create pow, even, odd functions,
   and we modify the div and mod functions for them to be linear, structural,
   tail-recursive.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13546 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 5 insertions, 10 deletions

diff --git a/theories/Numbers/Natural/Abstract/NProperties.v b/theories/Numbers/Natural/Abstract/NProperties.v
index 46117b25b..c1977f353 100644
--- a/theories/Numbers/Natural/Abstract/NProperties.v
+++ b/theories/Numbers/Natural/Abstract/NProperties.v
@@ -6,15 +6,10 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-Require Export NAxioms NMaxMin.
+Require Export NAxioms.
+Require Import NMaxMin NParity NPow NDiv.
 
-(** This functor summarizes all known facts about N.
-    For the moment it is only an alias to the last functor which
-    subsumes all others.
-*)
+(** This functor summarizes all known facts about N. *)
 
-Module Type NPropSig := NMaxMinProp.
-
-Module NPropFunct (N:NAxiomsSig) <: NPropSig N.
- Include NPropSig N.
-End NPropFunct.
+Module Type NProp (N:NAxiomsSig) :=
+ NMaxMinProp N <+ NParityProp N <+ NPowProp N <+ NDivProp N.