Fixing an incompleteness of the ring/field tactics

The problem occurs when a customized ring/field structure       
declared with a so-called "morphism" (see 24.5 in the manual) tactic
allowing to reify (numerical) constants efficiently.

When declaring a ring/field structure, the user can provide a cast 
function phi in order to express numerical constants in another type than 
the carrier of the ring. This is useful for instance when the ring is
abstract (like the type R of reals) and one needs to express constants
to large to be parsed in unary representation (for instance using a
phi : Z -> R).

Formerly, the completeness of the tactic required (phi 1) (resp. (phi 0))
to be convertible to 1 (resp. 0), which is not the case when phi is
opaque. This was not documented untill recently
but I moreover think this is also not desirable
since the user can have good reasons to work with such an opaque case phi.

Hence this commit:
- adds two constructors to PExpr and FExpr for a correct reification
- unplugs the optimizations in reification: optimizing reification 
  is much less efficient than using a cast known to the tactic.

TODO : It would probably be worth declaring IZR as a cast in the ring/field
tactics provided for Reals in the std lib.

The completeness of the tactic formerly relied on the fact that 


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@16730 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 3 insertions, 1 deletions

diff --git a/plugins/nsatz/Nsatz.v b/plugins/nsatz/Nsatz.v
index 21a94afca..2a287556b 100644
--- a/plugins/nsatz/Nsatz.v
+++ b/plugins/nsatz/Nsatz.v
@@ -98,7 +98,7 @@ Definition PhiR : list R -> PolZ -> R :=
     (InitialRing.gen_phiZ ring0 ring1 add mul opp)).
 
 Definition PEevalR : list R -> PEZ -> R :=
-   PEeval ring0 add mul sub opp
+   PEeval ring0 ring1 add mul sub opp
     (gen_phiZ ring0 ring1 add mul opp)
          N.to_nat pow.
 
@@ -241,6 +241,8 @@ Fixpoint interpret3 t fv {struct t}: R :=
   | (PEpow t1 t2) =>
        let v1  := interpret3 t1 fv in pow v1 (N.to_nat t2)
   | (PEc t1) => (IZR1 t1)
+  | PEO => 0
+  | PEI => 1
   | (PEX _ n) => List.nth (pred (Pos.to_nat n)) fv 0
   end.