coq/theories/ZArith/vo.itarget, branch master

drop vo.itarget files and compute the corresponding the corresponding values automatically instead

2017-06-01T15:33:19+00:00

Cleanup of files related with power over Z.

2011-07-01T17:38:17+00:00

 - Zpow_def, Zpower, Zpow_facts shortened thanks to stuff in BinInt.Z

 - The alternative Zpower_alt is now in a separate file Zpow_alt.v,
   not loaded by default.

 - Some more injection lemmas in Znat (pow, div, mod, quot, rem)

 - Btw, added a "square" function in Z, N, Pos, ... (instead of
   Zpow_facts.Zsquare).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14253 85f007b7-540e-0410-9357-904b9bb8a0f7

Deletion of useless Zdigits_def

2011-06-28T23:30:32+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14247 85f007b7-540e-0410-9357-904b9bb8a0f7

Deletion of useless Zlog_def

2011-06-28T23:30:21+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14246 85f007b7-540e-0410-9357-904b9bb8a0f7

Deletion of useless Zsqrt_def

2011-06-28T23:30:10+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14245 85f007b7-540e-0410-9357-904b9bb8a0f7

Some cleanup of Zdiv and Zquot, deletion of useless Zdiv_def

2011-06-28T23:29:59+00:00

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14244 85f007b7-540e-0410-9357-904b9bb8a0f7

Clean-up of Znumtheory, deletion of Zgcd_def

2011-06-24T15:50:17+00:00

 In particular, we merge the old Zdivide (used to be an ad-hoc
 inductive predicate) and the new Z.divide (based on exists).
 Notations allow to do that (almost) transparently, the only
 impact is that the name picked by the system will not be "q"
 anymore when destructing a Z.divide. Some fragile scripts
 may have to be fixed.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14239 85f007b7-540e-0410-9357-904b9bb8a0f7

Modularization of BinInt, related fixes in the stdlib

2011-05-05T15:12:59+00:00

 All the functions about Z is now in a separated file BinIntDef,
 which is Included in BinInt.Z. This BinInt.Z directly
 implements ZAxiomsSig, and instantiates derived properties ZProp.

 Note that we refer to Z instead of t inside BinInt.Z,
 otherwise ring breaks later on @eq Z.t

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14106 85f007b7-540e-0410-9357-904b9bb8a0f7

Numbers and bitwise functions.

2010-12-06T15:47:32+00:00

 See NatInt/NZBits.v for the common axiomatization of bitwise functions
 over naturals / integers. Some specs aren't pretty, but easier to
 prove, see alternate statements in property functors {N,Z}Bits.
 Negative numbers are considered via the two's complement convention.

 We provide implementations for N (in Ndigits.v), for nat (quite dummy,
 just for completeness), for Z (new file Zdigits_def), for BigN
 (for the moment partly by converting to N, to be improved soon)
 and for BigZ.

 NOTA: For BigN.shiftl and BigN.shiftr, the two arguments are now in
 the reversed order (for consistency with the rest of the world):
 for instance BigN.shiftl 1 10 is 2^10.

 NOTA2: Zeven.Zdiv2 is _not_ doing (Zdiv _ 2), but rather (Zquot _ 2)
 on negative numbers. For the moment I've kept it intact, and have
 just added a Zdiv2' which is truly equivalent to (Zdiv _ 2).
 To reorganize someday ?

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13689 85f007b7-540e-0410-9357-904b9bb8a0f7

Integer division: quot and rem (trunc convention) in addition to div and mod

2010-11-10T12:58:38+00:00

(floor convention).

We follow Haskell naming convention: quot and rem are for
Round-Toward-Zero (a.k.a Trunc, what Ocaml, C, Asm do by default, cf.
the ex-ZOdiv file), while div and mod are for Round-Toward-Bottom
(a.k.a Floor, what Coq does historically in Zdiv). We use unicode ÷
for quot, and infix rem for rem (which is actually remainder in
full). This way, both conventions can be used at the same time.

Definitions (and proofs of specifications) for div mod quot rem are
migrated in a new file Zdiv_def. Ex-ZOdiv file is now Zquot. With
this new organisation, no need for functor application in Zdiv and
Zquot.

On the abstract side, ZAxiomsSig now provides div mod quot rem.
Zproperties now contains properties of them. In NZDiv, we stop
splitting specifications in Common vs. Specific parts. Instead,
the NZ specification is be extended later, even if this leads to
a useless mod_bound_pos, subsumed by more precise axioms.

A few results in ZDivTrunc and ZDivFloor are improved (sgn stuff).

A few proofs in Nnat, Znat, Zabs are reworked (no more dependency
to Zmin, Zmax).

A lcm (least common multiple) is derived abstractly from gcd and
division (and hence available for nat N BigN Z BigZ :-).
In these new files NLcm and ZLcm, we also provide some combined
properties of div mod quot rem gcd.

We also provide a new file Zeuclid implementing a third division
convention, where the remainder is always positive. This file
instanciate the abstract one ZDivEucl. Operation names are
ZEuclid.div and ZEuclid.modulo.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13633 85f007b7-540e-0410-9357-904b9bb8a0f7