aboutsummaryrefslogtreecommitdiffhomepage
path: root/theories/ZArith/Zeuclid.v
Commit message (Collapse)AuthorAge
* Update copyright headers.Gravatar Maxime Dénès2016-01-20
|
* Update headers.Gravatar Maxime Dénès2015-01-12
|
* Updating headers.Gravatar herbelin2012-08-08
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15715 85f007b7-540e-0410-9357-904b9bb8a0f7
* Some cleanup of Zdiv and Zquot, deletion of useless Zdiv_defGravatar letouzey2011-06-28
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14244 85f007b7-540e-0410-9357-904b9bb8a0f7
* Modularization of BinInt, related fixes in the stdlibGravatar letouzey2011-05-05
| | | | | | | | | | | 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
* Integer division: quot and rem (trunc convention) in addition to div and modGravatar letouzey2010-11-10
(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