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* Arithemtic: more concerning compare, eqb, leb, ltbGravatar letouzey2011-06-20
| | | | | | | | | | | | | | | | | | | | Start of a uniform treatment of compare, eqb, leb, ltb: - We now ensure that they are provided by N,Z,BigZ,BigN,Nat and Pos - Some generic properties are derived in OrdersFacts.BoolOrderFacts In BinPos, more work about sub_mask with nice implications on compare (e.g. simplier proof of lt_trans). In BinNat/BinPos, for uniformity, compare_antisym is now (y ?= x) = CompOpp (x ?=y) instead of the symmetrical result. In BigN / BigZ, eq_bool is now eqb In BinIntDef, gtb and geb are kept for the moment, but a comment advise to rather use ltb and leb. Z.div now uses Z.ltb and Z.leb. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14227 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
* CompareSpec: a slight generalization/reformulation of CompSpecGravatar letouzey2011-03-17
| | | | | | | | | | | | | | | | | | | CompareSpec expects 3 propositions Peq Plt Pgt instead of 2 relations eq lt and 2 points x y. For the moment, we still always use (Peq=eq x y), (Plt=lt x y) (Pgt=lt y x), but this may not be always the case, especially for Pgt. The former CompSpec is now defined in term of CompareSpec. Compatibility is preserved (except maybe a rare unfold or red to break the CompSpec definition). Typically, CompareSpec looks nicer when we have infix notations, e.g. forall x y, CompareSpec (x=y) (x<y) (y<x) (x?=x) while CompSpec is shorter when we directly refer to predicates: forall x y, CompSpec eq lt x y (compare x y) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13914 85f007b7-540e-0410-9357-904b9bb8a0f7
* ZBits,ZdivEucl,ZDivFloor: a few lemmas with weaker preconditionsGravatar letouzey2011-03-10
| | | | | | Initial patch by Robbert Krebbers. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13900 85f007b7-540e-0410-9357-904b9bb8a0f7
* An automatic substitution of scope at functor applicationGravatar letouzey2011-02-11
| | | | | | | | | | | | | | | | | | | For Argument Scope, we now record types (more precisely classes cl_typ) in addition to scope list. After substitution (e.g. at functor application), the new types are used to search for corresponding concrete scopes. Currently, this automatic scope substitution of argument scope takes precedence (if successful) over scope declared in the functor (even by the user). On the opposite, the manual scope substitution (cf last commit introducing annotation [scope foo to bar]) is done _after_ the automatic scope substitution. TODO: if this behavior is satisfactory, document it ... Note that Classops.find_class_type lose its env args since it was actually unused, and is now used for Notation.find_class git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13840 85f007b7-540e-0410-9357-904b9bb8a0f7
* Annotations at functor applications:Gravatar letouzey2011-02-11
| | | | | | | | | | | | | - The experimental syntax "<30>F M" is transformed into "F M [inline at level 30]" - The earlier syntax !F X should now be written "F X [no inline]" (note that using ! is still possible for compatibility) - A new annotation "F M [scope foo_scope to bar_scope]" allow to substitute foo_scope by bar_scope in all arguments scope of objects in F. BigN and BigZ are cleaned from the zillions of Arguments Scope used earlier. Arguments scope for lemmas are fixed for instances of Numbers. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13839 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: simplier spec for testbitGravatar letouzey2011-01-20
| | | | | | | | | | | | We now specify testbit by some initial and recursive equations. The previous spec (via a complex split of the number in low and high parts) is now a derived property in {N,Z}Bits.v This way, proofs of implementations are quite simplier. Note that these new specs doesn't imply anymore that testbit is a morphism, we have to add this as a extra spec (but this lead to trivial proofs when implementing). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13792 85f007b7-540e-0410-9357-904b9bb8a0f7
* f_equiv : a clone of f_equal that handles setoid equivalencesGravatar letouzey2011-01-04
| | | | | | | | | | | For example, if we know that [f] is a morphism for [E1==>E2==>E], then the goal [E (f x y) (f x' y')] will be transformed by [f_equiv] into the subgoals [E1 x x'] and [E2 y y']. This way, we can remove most of the explicit use of the morphism instances in Numbers (lemmas foo_wd for each operator foo). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13763 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: some improvements in proofsGravatar letouzey2011-01-03
| | | | | | | | | | - a ltac solve_proper which generalizes solve_predicate_wd and co - using le_elim is nicer that (apply le_lteq; destruct ...) - "apply ->" can now be "apply" most of the time. Benefit: NumPrelude is now almost empty git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13762 85f007b7-540e-0410-9357-904b9bb8a0f7
* Cosmetic : let's take advantage of the n-ary exists notationGravatar letouzey2010-12-17
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13721 85f007b7-540e-0410-9357-904b9bb8a0f7
* First release of Vector library.Gravatar pboutill2010-12-10
| | | | | | | | | | To avoid names&notations clashs with list, Vector shouldn't be "Import"ed but one can "Import Vector.VectorNotations." to have notations. SetoidVector at least remains to do. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13702 85f007b7-540e-0410-9357-904b9bb8a0f7
* ZArith: for uniformity, Zdiv2 becomes Zquot2 while Zdiv2' becomes Zdiv2Gravatar letouzey2010-12-09
| | | | | | | | | | | | | | | Now we have: - Zdiv and Zdiv2 : round toward bottom, no easy sign rule, remainder of a/2 is 0 or 1, operations related with two's-complement Zshiftr. - Zquot and Zquot2 : round toward zero, Zquot2 (-a) = - Zquot2 a, remainder of a/2 is 0 or Zsgn a. Ok, I'm introducing an incompatibility here, but I think coherence is really desirable. Anyway, people using Zdiv on positive numbers only shouldn't even notice the change. Otherwise, it's just a matter of sed -e "s/div2/quot2/g". git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13695 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers and bitwise functions.Gravatar letouzey2010-12-06
| | | | | | | | | | | | | | | | | | | | | | | 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
* NZSqrt: we define sqrt_up, a square root that rounds up instead of down as sqrtGravatar letouzey2010-11-18
| | | | | | Some more results about sqrt. Similar results for sqrt_up. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13649 85f007b7-540e-0410-9357-904b9bb8a0f7
* NZLog: we define log2_up, a base-2 logarithm that rounds up instead of down ↵Gravatar letouzey2010-11-18
| | | | | | | | as log2 Some more results about log2. Similar results for log2_up. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13648 85f007b7-540e-0410-9357-904b9bb8a0f7
* Division: avoid imposing rem as an infix keyword in Z_scope and bigZ_scope.Gravatar letouzey2010-11-16
| | | | | | | | | | | No infix notation "rem" for Zrem (that will probably become Z.rem in a close future). This way, we avoid conflict with people already using rem for their own need. Same for BigZ. We still use infix rem, but only in the abstract layer of Numbers, in a way that doesn't inpact the rest of Coq. Btw, the axiomatized function is now named rem instead of remainder. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13640 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
* Numbers: axiomatization, properties and implementations of gcdGravatar letouzey2010-11-05
| | | | | | | | | | | | | | | | | | | - For nat, we create a brand-new gcd function, structural in the sense of Coq, even if it's Euclid algorithm. Cool... - We re-organize the Zgcd that was in Znumtheory, create out of it files Pgcd, Ngcd_def, Zgcd_def. Proofs of correctness are revised in order to be much simpler (no omega, no advanced lemmas of Znumtheory, etc). - Abstract Properties NZGcd / ZGcd / NGcd could still be completed, for the moment they contain up to Gauss thm. We could add stuff about (relative) primality, relationship between gcd and div,mod, or stuff about parity, etc etc. - Znumtheory remains as it was, apart for Zgcd and correctness proofs gone elsewhere. We could later take advantage of ZGcd in it. Someday, we'll have to switch from the current Zdivide inductive, to Zdivide' via exists. To be continued... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13623 85f007b7-540e-0410-9357-904b9bb8a0f7
* NZSqrt : since spec is complete, no need for morphism axiom sqrt_wdGravatar letouzey2010-11-02
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13609 85f007b7-540e-0410-9357-904b9bb8a0f7
* NZLog : since spec is complete, no need for morphism axiom log2_wdGravatar letouzey2010-11-02
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13608 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers : log2. Abstraction, properties and implementations.Gravatar letouzey2010-11-02
| | | | | | | | | | Btw, we finally declare the original Zpower as the power on Z. We should switch to a more efficient one someday, but in the meantime BigN is proved with respect to the old one. TODO: reform Zlogarithm with respect to Zlog_def git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13606 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: specs about sqrt and pow of neg numbers, even in NZGravatar letouzey2010-11-02
| | | | | | | These additional specs are useless (but trivially provable) for N. They are quite convenient when deriving properties in NZ. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13603 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: NZPowProp as a Module Type, some module variable renamingGravatar letouzey2010-11-02
| | | | | | | | | We temporary use a hack to convert a module type into a module Module M := T is refused, so we force an include via Module M := Nop <+ T where Nop is an empty module. To be fixed later more beautifully... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13602 85f007b7-540e-0410-9357-904b9bb8a0f7
* Add sqrt in NumbersGravatar letouzey2010-10-19
| | | | | | | | | | | | | | | | | | | | | | As for power recently, we add a specification in NZ,N,Z, derived properties, implementations for nat, N, Z, BigN, BigZ. - For nat, this sqrt is brand new :-), cf NPeano.v - For Z, we rework what was in Zsqrt: same algorithm, no more refine but a pure function, based now on a sqrt for positive, from which we derive a Nsqrt and a Zsqrt. For the moment, the old Zsqrt.v file is kept as Zsqrt_compat.v. It is not loaded by default by Require ZArith. New definitions are now in Psqrt.v, Zsqrt_def.v and Nsqrt_def.v - For BigN, BigZ, we changed the specifications to refer to Zsqrt instead of using characteristic inequations. On the way, many extensions, in particular BinPos (lemmas about order), NZMulOrder (results about squares) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13564 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers : also axiomatize constants 1 and 2.Gravatar letouzey2010-10-14
| | | | | | | | | | | | | | | | | Initially, I was using notation 1 := (S 0) and so on. But then, when implementing by NArith or ZArith, some lemmas statements were filled with Nsucc's and Zsucc's instead of 1 and 2's. Concerning BigN, things are rather complicated: zero, one, two aren't inlined during the functor application creating BigN. This is deliberate, at least for the other operations like BigN.add. And anyway, since zero, one, two are defined too early in NMake, we don't have 0%bigN in the body of BigN.zero but something complex that reduce to 0%bigN, same for one and two. Fortunately, apply or rewrite of generic lemmas seem to work, even if there's BigZ.zero on one side and 0 on the other... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13555 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: new functions pow, even, odd + many reorganisationsGravatar letouzey2010-10-14
| | | | | | | | | | | | | | | | | | | | | | | | - Simplification of functor names, e.g. ZFooProp instead of ZFooPropFunct - The axiomatisations of the different fonctions are now in {N,Z}Axioms.v apart for Z division (three separate flavours in there own files). Content of {N,Z}AxiomsSig is extended, old version is {N,Z}AxiomsMiniSig. - In NAxioms, the recursion field isn't that useful, since we axiomatize other functions and not define them (apart in the toy NDefOps.v). We leave recursion there, but in a separate NAxiomsFullSig. - On Z, the pow function is specified to behave as Zpower : a^(-1)=0 - In BigN/BigZ, (power:t->N->t) is now pow_N, while pow is t->t->t These pow could be more clever (we convert 2nd arg to N and use pow_N). Default "^" is now (pow:t->t->t). BigN/BigZ ring is adapted accordingly - In BigN, is_even is now even, its spec is changed to use Zeven_bool. We add an odd. In BigZ, we add even and odd. - In ZBinary (implem of ZAxioms by ZArith), we create an efficient Zpow to implement pow. This Zpow should replace the current linear Zpower someday. - In NPeano (implem of NAxioms by Arith), we create pow, even, odd functions, and we modify the div and mod functions for them to be linear, structural, tail-recursive. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13546 85f007b7-540e-0410-9357-904b9bb8a0f7
* Updated all headers for 8.3 and trunkGravatar herbelin2010-07-24
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13323 85f007b7-540e-0410-9357-904b9bb8a0f7
* Made option "Automatic Introduction" active by default before too manyGravatar herbelin2010-06-08
| | | | | | | people use the undocumented "Lemma foo x : t" feature in a way incompatible with this activation. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13090 85f007b7-540e-0410-9357-904b9bb8a0f7
* Remove the svn-specific $Id$ annotationsGravatar letouzey2010-04-29
| | | | | | | | | | | - Many of them were broken, some of them after Pierre B's rework of mli for ocamldoc, but not only (many bad annotation, many files with no svn property about Id, etc) - Useless for those of us that work with git-svn (and a fortiori in a forthcoming git-only setting) - Even in svn, they seem to be of little interest git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12972 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: properties of min/max with respect to 0,S,P,add,sub,mulGravatar letouzey2010-02-09
| | | | | | | | | With these properties, we can kill Arith/MinMax, NArith/Nminmax, and leave ZArith/Zminmax as a compatibility file only. Now the instanciations NPeano.Nat, NBinary.N, ZBinary.Z, BigZ, BigN contains all theses facts. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12718 85f007b7-540e-0410-9357-904b9bb8a0f7
* ZBinary (impl of Numbers via Z) reworked, comes earlier, subsumes ZOrderedTypeGravatar letouzey2010-02-09
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12714 85f007b7-540e-0410-9357-904b9bb8a0f7
* Division in numbers: kills some Include to avoid bad alias Zsucc = ZDiv.Z.Z'.SGravatar letouzey2010-01-29
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12704 85f007b7-540e-0410-9357-904b9bb8a0f7
* More improvements of BigN, BigZ, BigQ:Gravatar letouzey2010-01-18
| | | | | | | | | | | | | | | - ring/field: detection of constants for ring/field, detection of power, potential use of euclidean division. - for BigN and BigZ, x^n now takes a N as 2nd arg instead of a positive - mention that we can use (r)omega thanks to (ugly) BigN.zify, BigZ.zify. By the way, BigN.zify could still be improved (no insertion of positivity hyps yet, unlike the original zify). - debug of BigQ.qify (autorewrite was looping on spec_0). - for BigQ, start of a generic functor of properties QProperties. - BigQ now implements OrderedType, TotalOrder, and contains facts about min and max. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12681 85f007b7-540e-0410-9357-904b9bb8a0f7
* BigN, BigZ, BigQ: presentation via unique module with both ops and propsGravatar letouzey2010-01-17
| | | | | | | | | | | | | | | | | | | | | We use the <+ operation to regroup all known facts about BigN (resp BigZ, ...) in a unique module. This uses also the new ! feature for controling inlining. By the way, we also make sure that these new BigN and BigZ modules implements OrderedTypeFull and TotalOrder, and also contains facts about min and max (cf. GenericMinMax). Side effects: - In NSig and ZSig, specification of compare and eq_bool is now done with respect to Zcompare and Zeq_bool, as for other ops. The order <= and < are also defined via Zle and Zlt, instead of using compare. Min and max are axiomatized instead of being macros. - Some proofs rework in QMake - QOrderedType and Qminmax were in fact not compiled by make world Still todo: OrderedType + MinMax for BigQ, etc etc git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12680 85f007b7-540e-0410-9357-904b9bb8a0f7
* Avoid some more re-declarations of Equivalence instancesGravatar letouzey2010-01-14
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12671 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: two more Local Obligation TacticGravatar letouzey2010-01-12
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12652 85f007b7-540e-0410-9357-904b9bb8a0f7
* Support "Local Obligation Tactic" (now the default in sections).Gravatar msozeau2010-01-11
| | | | | | | | Update Numbers that was implicitely using [simpl_relation] instead of the default tactic [program_simpl]. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12647 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: BigN and BigZ get instantiations of all properties about div and modGravatar letouzey2010-01-08
| | | | | | | | | NB: for declaring div and mod as a morphism, even when divisor is zero, I've slightly changed the definition of div_eucl: it now starts by a check of whether the divisor is zero. Not very nice, but this way we can say that BigN.div and BigZ.div _always_ answer like Zdiv.Zdiv. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12646 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: axiomatization + generic properties of abs and sgn.Gravatar letouzey2010-01-08
| | | | | | | This allow to really finish files about division. An abs and sgn is added to BigZ. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12644 85f007b7-540e-0410-9357-904b9bb8a0f7
* Include can accept both Module and Module TypeGravatar letouzey2010-01-07
| | | | | | | | Syntax Include Type is still active, but deprecated, and triggers a warning. The syntax M <+ M' <+ M'', which performs internally an Include, also benefits from this: M, M', M'' can be independantly modules or module type. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12640 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: separation of funs, notations, axioms. Notations via module, ↵Gravatar letouzey2010-01-07
| | | | | | without scope. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12639 85f007b7-540e-0410-9357-904b9bb8a0f7
* "by" becomes officially a reserved keyword of Coq (fixes "rewrite ... at ... ↵Gravatar letouzey2010-01-06
| | | | | | | | by ...") Application in some proofs of Numbers's abstract division git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12630 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers abstract layer: more Module Type, used especially for divisions.Gravatar letouzey2010-01-05
| | | | | | | Properties are now rather passed as functor arg instead of via Include or some inner modules. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12629 85f007b7-540e-0410-9357-904b9bb8a0f7
* Avoid declaring hints about refl/sym/trans of eq in DecidableType2Gravatar letouzey2010-01-05
| | | | | | | | This used to be convenient in FSets, but since we now try to integrate DecidableType and OrderedType as foundation for other part of the stdlib, this should be avoided, otherwise some eauto take a _long_ time. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12626 85f007b7-540e-0410-9357-904b9bb8a0f7
* Division in Numbers: proofs with less auto (less sensitive to hints, in ↵Gravatar letouzey2010-01-05
| | | | | | particular about eq) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12625 85f007b7-540e-0410-9357-904b9bb8a0f7
* Division in Numbers: factorisation of signaturesGravatar letouzey2010-01-05
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12624 85f007b7-540e-0410-9357-904b9bb8a0f7
* Specific syntax for Instances in Module Type: Declare InstanceGravatar letouzey2010-01-04
| | | | | | | | | NB: the grammar entry is placed in vernac:command on purpose even if it should have gone into vernac:gallina_ext. Camlp4 isn't factorising rules starting by "Declare" in a correct way otherwise... git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12623 85f007b7-540e-0410-9357-904b9bb8a0f7
* RelationPairs: stop loading it in all Numbers, stop maximal args with fst/sndGravatar letouzey2009-12-18
| | | | | | | As a consequence, revert to some pedestrian proofs of Equivalence here and there, without the need for the Measure class. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12598 85f007b7-540e-0410-9357-904b9bb8a0f7
* Division in Numbers : more properties, new filenames based on a paper by R. ↵Gravatar letouzey2009-12-17
| | | | | | | | | | | | | | 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
* Division in Numbers: more properties proved (still W.I.P.)Gravatar letouzey2009-12-16
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12591 85f007b7-540e-0410-9357-904b9bb8a0f7
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