coq/theories/Numbers/Integer/TreeMod, branch master

ZTreeMod was meant to prove that BigZ correspond to the Integer Axioms.

2008-05-16T01:15:08+00:00

In fact, for the moment, it was only containing a proof that Z/nZ
implements the NatInt NZAxiomsSig. We move it to a more meaningful 
place and name.



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10937 85f007b7-540e-0410-9357-904b9bb8a0f7

More BigNum cleanup:

2008-05-16T00:53:17+00:00

 * View of Int31 as a Z/nZ moved to file Z31Z.v (TO FINISH: specs are still admitted!)
 * Modular specification of Z/nZ moved to ZnZ and renamed CyclicType
 * More isolation between Cyclic/Abstract and Cyclic/DoubleCyclic
 * A few comments



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10936 85f007b7-540e-0410-9357-904b9bb8a0f7

Integration of theories/Ints into theories/Numbers, part 1: moving files

2008-05-07T18:04:23+00:00

For the moment, the Ints files are simply moved into directories in
theories/Numbers with meaningful names. No filenames changed, apart
from: 
 Zaux.v -> theories/Numbers/BigNumPrelude.v 
 MemoFn.v -> theories/Lists/StreamMemo.v

More to come...



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10899 85f007b7-540e-0410-9357-904b9bb8a0f7

Suite r10857

2008-04-27T16:27:38+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10858 85f007b7-540e-0410-9357-904b9bb8a0f7

Plug the new setoid implemtation in, leaving the original one commented

2008-03-06T18:17:24+00:00

out. The semantics of the old setoid are faithfully simulated by the new
tactic, hence no scripts involving rewrite are modified. However,
parametric morphism declarations need to be changed, but there are only a
few in the standard library, notably in FSets. The declaration and the
introduction of variables in the script need to be tweaked a bit,
otherwise the proofs remain unchanged. 
Some fragile scripts not introducting their variable names explicitely
were broken. Requiring Setoid requires Program.Basics which sets stronger
implicit arguments on some constants, a few scripts benefit from that.
Ring/field have been ported but do not really use the new typeclass
architecture as well as they could. Performance should be mostly
unchanged, but will certainly improve in the near future. Size of the
vo's seems not to have changed at all.
It will certainly break some contribs using Setoid.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10631 85f007b7-540e-0410-9357-904b9bb8a0f7

Update on Numbers; renamed ZOrder.v to ZLt to remove clash with ZArith/Zorder on MacOS.

2007-11-14T19:47:46+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10323 85f007b7-540e-0410-9357-904b9bb8a0f7

Replaced BinNat with a new version that is based on theories/Numbers/Natural/Binary/NBinDefs. Most of the entities in the new BinNat are notations for the development in Numbers. Also added min and max to the new natural numbers and integers.

2007-11-07T18:39:28+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10298 85f007b7-540e-0410-9357-904b9bb8a0f7

Integration of theories/Ints/Z/* in ZArith and large cleanup and extension of Zdiv

2007-11-06T02:18:53+00:00

Some details:

- ZAux.v is the only file left in Ints/Z. The few elements that remain in it
are rather specific or compatibility oriented. Others parts and files have
been either deleted when unused or pushed into some place of ZArith.
- Ints/List/ is removed since it was not needed anymore
- Ints/Tactic.v disappear: some of its tactic were unused, some already in
Tactics.v (case_eq, f_equal instead of eq_tac), and the nice contradict
has been added to Tactics.v
- Znumtheory inherits lots of results about Zdivide, rel_prime, prime, Zgcd, ...
- A new file Zpow_facts inherits lots of results about Zpower. Placing them
into Zpower would have been difficult with respect to compatibility
(import of ring)
- A few things added to Zmax, Zabs, Znat, Zsqrt, Zeven, Zorder
- Adequate adaptations to Ints/num/* (mainly renaming of lemmas)

Now, concerning Zdiv, the behavior when dividing by a negative number is now
fully proved. When this was possible, existing lemmas has been extended,
either from strictly positive to non-zero divisor, or even to arbitrary
divisor (especially when playing with Zmod). These extended lemmas are named
with the suffix _full, whereas the original restrictive lemmas are retained
for compatibility. Several lemmas now have shorter proofs (based on unicity
lemmas). Lemmas are now more or less organized by themes (division and order,
division and usual operations, etc). Three possible choices of spec for
divisions on negative numbers are presented: this Zdiv, the ocaml approach
and the remainder-always-positive approach. The ugly behavior of Zopp
with the current choice of Zdiv/Zmod is now fully covered. A embryo of
division "a la Ocaml" is given: Odiv and Omod.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10291 85f007b7-540e-0410-9357-904b9bb8a0f7

Added Numbers/Natural/Abstract/NIso.v that proves that any two models of natural numbers are isomorphic. Added NatScope and IntScope for abstract developments.

2007-10-23T11:09:40+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10247 85f007b7-540e-0410-9357-904b9bb8a0f7

Added the proof (in Numbers/Integers/TreeMod) that tree-like representation of integers due to Gregoire and Théry satisfies the axioms of integers without order. This refers to integers modulo n, i.e., those that fit trees of certain size, not to BigZ.

2007-10-04T17:24:56+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10178 85f007b7-540e-0410-9357-904b9bb8a0f7