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2009-12-17Division in Numbers : more properties, new filenames based on a paper by R. ↵letouzey
Boute Following R. Boute (paper "the Euclidean Definition of the Functions div and mod"): - ZDivFloor.v for Coq historical division (former ZDivCoq.v) - ZDivTrunc.v for Ocaml convention (former ZDivOcaml.v) - ZDivEucl.v for "Mathematical" convention 0<=r (former ZDivMath.v) These property functors are more or less finished (except that sign and abs stuff should be migrated to a separate file). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12594 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-12-16Division in Numbers: more properties proved (still W.I.P.)letouzey
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12591 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-12-15A generic euclidean division in Numbers (Still Work-In-Progress)letouzey
- For Z, we propose 3 conventions for the sign of the remainder... - Instanciation for nat in NPeano. - Beginning of instanciation in ZOdiv. Still many proofs to finish, etc, etc, but soon we will have a decent properties database for all divisions of all instances of Numbers (e.g. BigZ). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12590 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-30Fix backtracking heuristic in typeclass resolution. msozeau
Now that backtracking is working correctly, we need to avoid a non-termination issue introduced by the [RelCompFun] definition in RelationPairs, by adding a [Measure] typeclass. It could be used to have a uniform notation for measures/interpretations in Numbers and be but in the interfaces too, only the mimimal change was implemented. Fix syntax change in test-suite scripts. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12547 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-12BigQ / BigN / BigZ syntax and scope improvements (sequel to 12504)letouzey
- In fact, Bind Scope has no retrospective effect. Since we don't want it inside functor, we use it late, and hence we are forced to use manual "Arguments Scope" commands. - Added syntax for power in BigN / BigZ / BigQ. - Added syntax p#q in BigQ for representing fractions (constructor BigQ.Qq) as in QArith. Display of a rational numeral is hence either an integer (constructor BigQ.Qz) or something like 6756 # 8798. - Fix of function BigQ.Qred that was not simplifing (67#1) into 67. - More tests in test-suite/output/NumbersSyntax.v A nice one not in the test-suite: Time Eval vm_compute in BigQ.red ((2/3)^(-100000) * (2/3)^(100000)). = 1 : bigQ Finished transaction in 3. secs (3.284206u,0.004s) :-) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12507 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-12Repair interpretation of numeral for BigQ, add a printer (close #2160)letouzey
on the way: - Added a testsuite output file - Try to avoid nasty unfolding (fix nfun ...) in type of I31. Idealy we would need a "Eval compute in" for the type of a inductive constructor - Stop opening Scopes for BigQ, BigN, BigZ by default The user should do some Open Scope. TODO: there's a bug that prevent BigQ.opp to have arg in bigQ_scope (and so on for other operations), even with some Bind Scope around. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12504 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-10SpecViaZ.NSig: all-in-one spec for [pred] and [sub] based on ZMaxletouzey
To retrieve the old behavior of spec_sub0 and spec_sub with precondition on order, just chain spec_sub with Zmax_r or Zmax_l. Idem with spec_pred0 and spec_pred. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12490 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-10Simplification of Numbers, mainly thanks to Includeletouzey
- No more nesting of Module and Module Type, we rather use Include. - Instead of in-name-qualification like NZeq, we use uniform short names + modular qualification like N.eq when necessary. - Many simplification of proofs, by some autorewrite for instance - In NZOrder, we instantiate an "order" tactic. - Some requirements in NZAxioms were superfluous: compatibility of le, min and max could be derived from the rest. - NMul removed, since it was containing only an ad-hoc result for ZNatPairs, that we've inlined in the proof of mul_wd there. - Zdomain removed (was already not compiled), idea of a module with eq and eqb reused in DecidableType.BooleanEqualityType. - ZBinDefs don't contain any definition now, migrate it to ZBinary. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12489 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-06Numbers: more (syntactic) changes toward new style of type classesletouzey
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12475 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-11-03Numbers: start using Classes stuff, Equivalence, Proper, Instance, etcletouzey
TODO: finish removing the "Add Relation", "Add Morphism" fun_* fun2_* TODO: now that we have Include, flatten the hierarchy... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12464 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-10-08Init/Tactics.v: tactic with nicer name 'exfalso' for 'elimtype False'letouzey
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12380 85f007b7-540e-0410-9357-904b9bb8a0f7
2009-09-17Delete trailing whitespaces in all *.{v,ml*} filesglondu
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-12-12Uniformity with the rest of the StdLib : _symm --> _symletouzey
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11675 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-09-14Add user syntax for creating hint databases [Create HintDb foomsozeau
[discriminated]] with a switch for using the more experimantal dnet impl for every hint. Also add [Hint Transparent/Opaque] which parameterize the dnet and the unification flags used by auto/eauto with a particular database. Document all this. Remove [Typeclasses unfold] directives that are no longer needed (everything is unfoldable by default) and move to [Typeclasses Transparent/Opaque] syntax. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11409 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-07-26Even better test for choosing rewrite or setoid_rewrite.msozeau
Now there is a class "SetoidRelation" for registering relations that should always be considered as setoids and never unfolded. Every "Add Relation" command adds an instance and impl,iff are there by default. Now the test is: if there is a SetoidRelation instance, use it ; otherwise, allow unfolding to find an eq or fallback on setoid_rewrite. To avoid searching for SetoidRelation instances repeateadly we check that it is really needed first by unfolding the hyp. Only two scripts relied on the now-forbidden semantics of rewriting by an @eq inside a setoid relation, in Numbers. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11269 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-07-04Fix bug #1899: no more strange notations for Qge and Qgtletouzey
In fact, Qge and Ggt disappear, and we only leave notations for > and >= that map directly to Qlt and Qle. We also adopt the same approach for BigN, BigZ, BigQ. By the way, various clean-up concerning Zeq_bool, Zle_bool and similar functions for Q. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11205 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-06-27Enhanced discrimination nets implementation, which can now work withmsozeau
goals containing existentials and use transparency information on constants (optionally). Only used by the typeclasses eauto engine for now, but could be used for other hint bases easily (just switch a boolean). Had to add a new "creation" hint to be able to set said boolean upon creation of the typeclass_instances hint db. Improve the proof-search algorithm for Morphism, up to 10 seconds gained in e.g. Field_theory, Ring_polynom. Added a morphism declaration for [compose]. One needs to declare more constants as being unfoldable using the [Typeclasses unfold] command so that discrimination is done correctly, but that amounts to only 6 declarations in the standard library. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11184 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-06-03In abstract parts of theories/Numbers, plus/times becomes add/mul, letouzey
for increased consistency with bignums parts (commit part II: names of files + additional translation minus --> sub) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11040 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-06-02In abstract parts of theories/Numbers, plus/times becomes add/mul, letouzey
for increased consistency with bignums parts (commit part I: content of files) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11039 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-06-01Enhance the BigN and BigZ infrastructure: letouzey
* Isolate and put forward the interfaces NSig and ZSig that describe what should contain structures of natural numbers and integers (specs are done by translation to ZArith). * Functors NSigNAxioms and ZSigZAxioms proving that these NSig and ZSig implements the fully-abstract NAxioms and ZAxioms module types. * BigN and BigZ now contains more notations, plus an export of all abstract results proved by Evgeny instantiated thanks to NSigNAxioms and ZSigZAxioms. In addition, BigN and BigZ are declared as (semi/full)-rings. * as a consequence, some incompatibities have to be fixed in BigQ: - take care of some name masking (via Import, Open Scope ...) - some additionnal constants like BigN.lt to deal with git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11027 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-05-22switch theories/Numbers from Set to Type (both the abstract and the bignum ↵letouzey
part). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10964 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-05-16ZTreeMod was meant to prove that BigZ correspond to the Integer Axioms.letouzey
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
2008-05-16More BigNum cleanup: letouzey
* 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
2008-05-15In practice, the new setoid rewrite (and the "at" syntax) allows to avoid letouzey
using the ad-hoc qsetoid_rewrite. Could QRewrite.v be made completely obsolete ? For the moment rewrite under fun and exists don't work. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10935 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-05-15Coq headers + $ in theories/Numbers filesletouzey
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10934 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-05-11- Changement du code de Zplus pour accomoder ring qui sinon prend uneherbelin
complexité exponentielle dans la machine lazy depuis que l'algo de compilation du filtrage évite systématiquement d'expanser quand le filtrage n'est pas dépendant. - Un peu plus de colorisation dans coqide. - Utilisation de formats pour améliorer de l'affichage des notations Utf8. - Systématisation paire Local/Global dans g_vernac.ml4 (même si le défaut n'est pas toujours le même) - Bug Makefile git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10918 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-05-07Integration of theories/Ints into theories/Numbers, part 1: moving filesletouzey
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
2008-04-27Suite r10857herbelin
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10858 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-03-07Fix bug #1704 (ordering of condition goals for (setoid)rewrite). As partmsozeau
of the fix I added an optional "by" annotation for rewrite to solve said conditions in the same tactic call. Most of the theories have been updated, only FSets is missing, Pierre will take care of it. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10634 85f007b7-540e-0410-9357-904b9bb8a0f7
2008-03-06Plug the new setoid implemtation in, leaving the original one commentedmsozeau
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
2007-11-22An update on Numbers. Added two files dealing with recursion, for ↵emakarov
information only. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10330 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-11-16Added theorems; created NZPlusOrder from NTimesOrder.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10325 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-11-14Update on Numbers; renamed ZOrder.v to ZLt to remove clash with ↵emakarov
ZArith/Zorder on MacOS. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10323 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-11-07Replaced BinNat with a new version that is based on ↵emakarov
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. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10298 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-11-06Integration of theories/Ints/Z/* in ZArith and large cleanup and extension ↵letouzey
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
2007-11-03An update of theories/Numbersemakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10285 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-10-23Added Numbers/Natural/Abstract/NIso.v that proves that any two models of ↵emakarov
natural numbers are isomorphic. Added NatScope and IntScope for abstract developments. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10247 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-10-16Added transitivity and irreflexivity of <, as well as < -elimination for ↵emakarov
binary positive numbers. Added directory contribs/micromega with the generalization of Frédéric Besson's micromega tactic for an arbitrary ordered ring. So far no tactic has been defined. One has to apply the theorems and find the certificate, which is necessary to solve inequations, manually. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10226 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-10-04Added the proof (in Numbers/Integers/TreeMod) that tree-like representation ↵emakarov
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. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10178 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-10-02The following now compiles: abstract integers with plus, minus and times, ↵emakarov
binary implementation and integers as pairs of natural numbers git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10167 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-10-01Added the compilation of theories/Numbers to Makefile.common. The following ↵emakarov
things compile: abstract natural numbers and integers with plus, times, minus, and order; Peano and binary implementations for natural numbers. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10161 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-09-25An update on theories/Numbers.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10142 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-09-21Update on theories/Numbersemakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10133 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-09-21Update on theories/Numbers. Natural numbers are mostly complete,emakarov
need to make NZOrdAxiomsSig a subtype of NAxiomsSig. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10132 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-09-13Update before joining all signatures into one.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10119 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-08-13An update on axiomatic number classes.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10075 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-07-24An update on axiomatization of numbers.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10041 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-07-13An update on axiomatization of number classes.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10002 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-07-06Update of theories/Numbers directory.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9955 85f007b7-540e-0410-9357-904b9bb8a0f7
2007-07-05Update on numbers.emakarov
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9947 85f007b7-540e-0410-9357-904b9bb8a0f7
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