aboutsummaryrefslogtreecommitdiffhomepage
path: root/theories/Numbers
Commit message (Collapse)AuthorAge
* Give inner fixpoint of gcd31 a name, to avoid excessive unfoldingGravatar glondu2011-08-17
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14413 85f007b7-540e-0410-9357-904b9bb8a0f7
* SearchAbout and similar: add a customizable blacklistGravatar letouzey2011-08-11
| | | | | | | | | | | | | | | | | | | | | | | | Instead of hard-coding in search.ml some substrings such as "_admitted" or "_subproof" we don't want to see in results of SearchAbout and co, we now have a user command: Add Search Blacklist "foo". Remove Search Blacklist "foo". (* the opposite *) Print Table Search Blacklist. (* the current state *) In Prelude.v, three substrings are blacklisted originally: - "_admitted" for internal lemmas due to admit. - "_subproof" for internal lemmas due to abstract. - "Private_" for hiding auxiliary modules not meant for global usage. Note that substrings are searched in the fully qualified names of the available lemmas (e.g. "Coq.Init.Peano.plus"). This commit also adds the prefix "Private_" to some internal modules in Numbers, Z, N, etc. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14408 85f007b7-540e-0410-9357-904b9bb8a0f7
* Cleanup of files related with power over Z.Gravatar letouzey2011-07-01
| | | | | | | | | | | | | | - 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
* Cleanup in SpecViaZGravatar letouzey2011-06-30
| | | | | | | | | Note that in NSig (and hence NMake and BigN), to_N is now Z.to_N (to_Z ...) instead of Z.abs_N (to_Z ...). This doesn't change the result (since to_Z create non-negative integers), but some proofs may have to be adapted git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14250 85f007b7-540e-0410-9357-904b9bb8a0f7
* Cleanup of NdigitsGravatar letouzey2011-06-30
| | | | | | | | | | - No need for compatibility notations for stuff introduced strictly after branching of 8.3, for instance Nor, Nand, etc. - Properties for N.lor, N.lxor, etc are now in BinNat.N, no need to duplicate them in Ndigits, apart from the few compatibility results about xor. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14249 85f007b7-540e-0410-9357-904b9bb8a0f7
* Deletion of useless Zdigits_defGravatar letouzey2011-06-28
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14247 85f007b7-540e-0410-9357-904b9bb8a0f7
* Deletion of useless Zlog_defGravatar letouzey2011-06-28
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14246 85f007b7-540e-0410-9357-904b9bb8a0f7
* Deletion of useless Zsqrt_defGravatar letouzey2011-06-28
| | | | 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_defGravatar letouzey2011-06-28
| | | | 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_defGravatar letouzey2011-06-24
| | | | | | | | | | | 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
* Numbers: a particular case of div_uniqueGravatar letouzey2011-06-24
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14238 85f007b7-540e-0410-9357-904b9bb8a0f7
* Numbers: change definition of divide (compat with Znumtheory)Gravatar letouzey2011-06-24
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14237 85f007b7-540e-0410-9357-904b9bb8a0f7
* Some more cleanup of ZorderGravatar letouzey2011-06-23
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14234 85f007b7-540e-0410-9357-904b9bb8a0f7
* Some migration of results from BinInt to NumbersGravatar letouzey2011-06-20
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14230 85f007b7-540e-0410-9357-904b9bb8a0f7
* Zcompare.destr_zcompare subsumed by case Z.compare_specGravatar letouzey2011-06-20
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14229 85f007b7-540e-0410-9357-904b9bb8a0f7
* 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
* Some simplifications in NZDomainGravatar letouzey2011-06-20
| | | | git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14226 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
* 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
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-01 17:12:56 +0000