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Add headers to a few files which were missing them.
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15715 85f007b7-540e-0410-9357-904b9bb8a0f7
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- For instance, refl_equal --> eq_refl
- Npos, Zpos, Zneg now admit more uniform qualified aliases
N.pos, Z.pos, Z.neg.
- A new module BinInt.Pos2Z with results about injections from
positive to Z
- A result about Z.pow pushed in the generic layer
- Zmult_le_compat_{r,l} --> Z.mul_le_mono_nonneg_{r,l}
- Using tactic Z.le_elim instead of Zle_lt_or_eq
- Some cleanup in ring, field, micromega
(use of "Equivalence", "Proper" ...)
- Some adaptions in QArith (for instance changed Qpower.Qpower_decomp)
- In ZMake and ZMake, functor parameters are now named NN and ZZ
instead of N and Z for avoiding confusions
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15515 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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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
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- 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
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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
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- 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
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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
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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
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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
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(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
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- 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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13609 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13608 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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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
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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
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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
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- 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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13323 85f007b7-540e-0410-9357-904b9bb8a0f7
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- 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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12714 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12671 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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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
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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
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- 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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12475 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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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
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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
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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
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ZArith/Zorder on MacOS.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10323 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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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
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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
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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
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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
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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
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