| Commit message (Collapse) | Author | Age |
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A file ZOdiv is added which contains results about this euclidean division.
Interest compared with Zdiv: ZOdiv implements others (better?) conventions
concerning negative numbers, in particular it is compatible with Caml
div and mod.
ZOdiv is only partially finished...
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10302 85f007b7-540e-0410-9357-904b9bb8a0f7
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of Zdiv
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
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------------------------------------------------
See file PreOmega for more details and/or test-suite/succes/*Omega*.v
The zify tactic performs a Z-ification of your current goal,
transforming parts of type nat, N, positive, taking advantage of many
equivalences of operations, and of the positivity implied by these
types.
Integration with omega and romega:
(r)omega : the earlier tactics, 100% compatible
(r)omega with * : full zify applied before the (r)omega run
(r)omega with <types>, where <types> is a sub-list of {nat,N,positive,Z},
applies only specific parts of zify (btw "with Z" means take advantage
of Zmax, Zmin, Zabs and Zsgn).
As a particular consequence, "romega with nat" should now be a
close-to-perfect replacement for omega. Slightly more powerful, since
(forall x:nat, x*x>=0) is provable and also slightly less powerful: if
False is somewhere in the hypothesis, it doesn't use it.
For the moment zify is done in a direct way in Ltac, using rewrite
when necessary, but crucial chains of rewrite may be made reflexive
some day.
Even though zify is designed to help (r)omega, I think it might be
of interest for other tactics (micromega ?). Feel free to complete
zify if your favorite operation / type isn't handled yet.
Side-effects:
- additional results for ZArith, NArith, etc...
- definition of Ple, Plt, Pgt, Pge and notations for them in positive_scope
- romega now start by doing "intros". Since the conclusion will be negated,
and this operation will be justified by means of decidability, it helps
to have as little as possible in the conclusion.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10028 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9302 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9245 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5920 85f007b7-540e-0410-9357-904b9bb8a0f7
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par les fichiers nouvelle syntaxe
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5027 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5018 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@4871 85f007b7-540e-0410-9357-904b9bb8a0f7
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de la partie Omega dans contrib/omega
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@4801 85f007b7-540e-0410-9357-904b9bb8a0f7
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