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* Modularization of BinNat + fixes of stdlibGravatar letouzey2011-05-05
| | | | | | | | | | | | A sub-module N in BinNat now contains functions add (ex-Nplus), mul (ex-Nmult), ... and properties. In particular, this sub-module N directly instantiates NAxiomsSig and includes all derived properties NProp. Files Ndiv_def and co are now obsolete and kept only for compat git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14100 85f007b7-540e-0410-9357-904b9bb8a0f7
* Modularization of BinPos + fixes in StdlibGravatar letouzey2011-05-05
| | | | | | | | | | | | | | | | | | | | | | | BinPos now contain a sub-module Pos, in which are placed functions like add (ex-Pplus), mul (ex-Pmult), ... and properties like add_comm, add_assoc, ... In addition to the name changes, the organisation is changed quite a lot, to try to take advantage more of the orders < and <= instead of speaking only of the comparison function. The main source of incompatibilities in scripts concerns this compare: Pos.compare is now a binary operation, expressed in terms of the ex-Pcompare which is ternary (expecting an initial comparision as 3rd arg), this ternary version being called now Pos.compare_cont. As for everything else, compatibility notations (only parsing) are provided. But notations "_ ?= _" on positive will have to be edited, since they now point to Pos.compare. We also make the sub-module Pos to be directly an OrderedType, and include results about min and max. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14098 85f007b7-540e-0410-9357-904b9bb8a0f7
* Definitions of positive, N, Z moved in Numbers/BinNums.vGravatar letouzey2011-05-05
| | | | | | | | | | | | In the coming reorganisation, the name Z in BinInt will be a module containing all code and properties about binary integers. The inductive type Z hence cannot be at the same location. Same for N and positive. Apart for this naming constraint, it also have advantages : presenting the three types at once is clearer, and we will be able to refer to N in BinPos (for instance for output type of a predecessor function on positive). git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14097 85f007b7-540e-0410-9357-904b9bb8a0f7
* Fix generated script for NMake, a rewrite necessitates full conversion forGravatar msozeau2011-04-18
| | | | | | checking types. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14023 85f007b7-540e-0410-9357-904b9bb8a0f7
* Cyclic: a small optimisation with nice effect on BigN.mul (thinks Benjamin)Gravatar letouzey2011-03-30
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13943 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
* - Add modulo_delta_types flag for unification to allow fullGravatar msozeau2011-03-13
| | | | | | | | | | | | | | | | conversion when checking types of instanciations while having restricted delta reduction for unification itself. This makes auto/eauto... backward compatible. - Change semantics of [Instance foo : C a.] to _not_ search for an instance of [C a] automatically and potentially slow down interaction, except for trivial classes with no fields. Use [C a := _.] or [C a := {}] to search for an instance of the class or for every field. - Correct treatment of transparency information for classes declared in sections. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13908 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
* BigQ : setting correct arguments scopesGravatar letouzey2011-02-23
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13851 85f007b7-540e-0410-9357-904b9bb8a0f7
* - Use transparency information all the way through unification andGravatar msozeau2011-02-17
| | | | | | | | | | conversion. - Fix trans_fconv* to use evars correctly. - Normalize the goal with respect to evars before rewriting in [rewrite], allowing to see instanciations from other subgoals. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13844 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
* A fine-grain control of inlining at functor application via priority levelsGravatar letouzey2011-01-31
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | As said in CHANGES: << The inlining done during application of functors can now be controlled more precisely. In addition to the "!F G" syntax preventing any inlining, we can now use a priority level to select parameters to inline : "<30>F G" means "only inline in F the parameters whose levels are <= 30". The level of a parameter can be fixed by "Parameter Inline(30) foo". When levels aren't given, the default value is 100. One can also use the flag "Set Inline Level ..." to set a level. >> Nota : the syntax "Parameter Inline(30) foo" is equivalent to "Set Inline Level 30. Parameter Inline foo.", and "Include <30>F G" is equivalent to "Set Inline Level 30. Include F G." For instance, in ZBinary, eq is @Logic.eq and should rather be inlined, while in BigZ, eq is (fun x y => [x]=[y]) and should rather not be inlined. We could achieve this behavior by setting a level such as 30 to the parameter eq, and then tweaking the current level when applying functors. This idea of levels might be too restrictive, we'll see, but at least the implementation of this change was quite simple. There might be situation where parameters cannot be linearly ordered according to their "inlinablility". For these cases, we would need to mention names to inline or not at a functor application, and this is a bit more tricky (and might be a pain to use if there are many names). No documentation for the moment, since this feature is experimental and might still evolve. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13807 85f007b7-540e-0410-9357-904b9bb8a0f7
* Remove the "Boxed" syntaxes and the const_entry_boxed fieldGravatar letouzey2011-01-28
| | | | | | | | | | | | | | | | According to B. Gregoire, this stuff is obsolete. Fine control on when to launch the VM in conversion problems is now provided by VMcast. We were already almost never boxing definitions anymore in stdlib files. "(Un)Boxed Definition foo" will now trigger a parsing error, same with Fixpoint. The option "(Un)Set Boxed Definitions" aren't there anymore, but tolerated (as no-ops), since unknown options raise a warning instead of an error by default. Some more cleaning could be done in the vm. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13806 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
* Ndigits: a Pshiftl_nat used in BigN (was double_digits there)Gravatar letouzey2011-01-04
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13764 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
* NPeano.modulo : another trick a la "minus" for having a decreasing argGravatar letouzey2010-12-17
| | | | | | | | | | By writing y instead of 0 in the branch where y is 0, Coq can see that (modulo x y) is a structural subterm of y (but not necessarily a strict one). Same trick for div, but here it doesn't help. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13722 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
* Nicer log2 function for nat (suggested by Hugo)Gravatar letouzey2010-12-17
| | | | | | | | | | | | | | The auxiliary variable q is now increased continuously instead of being doubled from time to time. Interest: this version is obviously linear, and specification proofs are slightly simplier. NB: the previous version was in fact also linear I think, but proving this requires a proper complexity analysis. I'm sure this algorithm is related with some cellular automata stuff in the spirit of the firing squad :-) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13720 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
* Some more revision of {P,N,Z}Arith + bitwise ops in NdigitsGravatar letouzey2010-11-18
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Initial plan was only to add shiftl/shiftr/land/... to N and other number type, this is only partly done, but this work has diverged into a big reorganisation and improvement session of PArith,NArith,ZArith. Bool/Bool: add lemmas orb_diag (a||a = a) and andb_diag (a&&a = a) PArith/BinPos: - added a power function Ppow - iterator iter_pos moved from Zmisc to here + some lemmas - added Psize_pos, which is 1+log2, used to define Nlog2/Zlog2 - more lemmas on Pcompare and succ/+/* and order, allow to simplify a lot some old proofs elsewhere. - new/revised results on Pminus (including some direct proof of stuff from Pnat) PArith/Pnat: - more direct proofs (limit the need of stuff about Pmult_nat). - provide nicer names for some lemmas (eg. Pplus_plus instead of nat_of_P_plus_morphism), compatibility notations provided. - kill some too-specific lemmas unused in stdlib + contribs NArith/BinNat: - N_of_nat, nat_of_N moved from Nnat to here. - a lemma relating Npred and Nminus - revised definitions and specification proofs of Npow and Nlog2 NArith/Nnat: - shorter proofs. - stuff about Z_of_N is moved to Znat. This way, NArith is entirely independent from ZArith. NArith/Ndigits: - added bitwise operations Nand Nor Ndiff Nshiftl Nshiftr - revised proofs about Nxor, still using functional bit stream - use the same approach to prove properties of Nand Nor Ndiff ZArith/BinInt: huge simplification of Zplus_assoc + cosmetic stuff ZArith/Zcompare: nicer proofs of ugly things like Zcompare_Zplus_compat ZArith/Znat: some nicer proofs and names, received stuff about Z_of_N ZArith/Zmisc: almost empty new, only contain stuff about badly-named iter. Should be reformed more someday. ZArith/Zlog_def: Zlog2 is now based on Psize_pos, this factorizes proofs and avoid slowdown due to adding 1 in Z instead of in positive Zarith/Zpow_def: Zpower_opt is renamed more modestly Zpower_alt as long as I dont't know why it's slower on powers of two. Elsewhere: propagate new names + some nicer proofs NB: Impact on compatibility is probably non-zero, but should be really moderate. We'll see on contribs, but a few Require here and there might be necessary. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13651 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
* Oups, fix last commit, a missing file in a vo.itargetGravatar letouzey2010-11-10
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13634 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: misc improvementsGravatar letouzey2010-11-02
| | | | | | | | | - Add alternate specifications of pow and sqrt - Slightly more general pow_lt_mono_r - More explicit equivalence of Plog2_Z and log_inf - Nicer proofs in Zpower git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13607 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
* NPeano: A log2 function for natGravatar letouzey2010-11-02
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13604 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
* Numbers: no need for advanced functions (e.g. sqrt) in NStrongRec, NDefOps, etcGravatar letouzey2010-10-19
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13565 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
* Minor fixes of 'make doc'Gravatar pboutill2010-09-28
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13472 85f007b7-540e-0410-9357-904b9bb8a0f7
* NMake : another round of heavy reworkGravatar letouzey2010-09-09
| | | | | | | | | | | | | | | | - generic iterator [iter] factorized in the same way as [same_level] - as a consequence, remaining operations [mul] [compare] [div_gt] are now defined and proved in a short and nice way and moved to NMake.v. - lots of other simplifications / factorisations in NMake_gen. This file is still macro-generated, but is much shorter, and the major part of it is now invariant. - As advised by B. Gregoire, try to (re)create clever partial applications in code of operators, in order to avoid projecting ZnZ fields all the time in base cases. Case 0 can still be improved, but it's already better this way :-) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13402 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
* Reverted 13293 commited mistakenly. Sorry for the noise.Gravatar herbelin2010-07-18
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13294 85f007b7-540e-0410-9357-904b9bb8a0f7
* Tentative de suppression de l'import automatique des hints et coercions.Gravatar herbelin2010-07-18
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13293 85f007b7-540e-0410-9357-904b9bb8a0f7
* Fix compilation by replacing some "auto with zarith" with "ring"Gravatar glondu2010-06-28
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* Fixing commit r13090 (forgot to commit the file generating Nmake_gen.v).Gravatar herbelin2010-06-08
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13095 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
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