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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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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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13721 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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To avoid names¬ations 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
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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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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
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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
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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
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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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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13634 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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- 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
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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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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13604 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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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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13565 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@13472 85f007b7-540e-0410-9357-904b9bb8a0f7
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- 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
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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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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13294 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13293 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13212 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13095 85f007b7-540e-0410-9357-904b9bb8a0f7
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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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Ocaml 3.10.0 is already three year old...
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13015 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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This is a fairly large commit (around 140 files and 7000 lines of code
impacted), it will cause some troubles for sure (I've listed the know
regressions below, there is bound to be more).
At this state of developpement it brings few features to the user, as
the old tactics were
ported with no change. Changes are on the side of the developer mostly.
Here comes a list of the major changes. I will stay brief, but the code
is hopefully well documented so that it is reasonably easy to infer the
details from it.
Feature developer-side:
* Primitives for a "real" refine tactic (generating a goal for each
evar).
* Abstract type of tactics, goals and proofs
* Tactics can act on several goals (formally all the focused goals). An
interesting consequence of this is that the tactical (. ; [ . | ... ])
can be separated in two
tacticals (. ; .) and ( [ . | ... ] ) (although there is a conflict for
this particular syntax). We can also imagine a tactic to reorder the
goals.
* Possibility for a tactic to pass a value to following tactics (a
typical example is
an intro function which tells the following tactics which name it
introduced).
* backtracking primitives for tactics (it is now possible to implement a
tactical '+'
with (a+b);c equivalent to (a;c+b;c) (itself equivalent to
(a;c||b;c)). This is a valuable
tool to implement tactics like "auto" without nowing of the
implementation of tactics.
* A notion of proof modes, which allows to dynamically change the parser
for tactics. It is controlled at user level with the keywords Set
Default Proof Mode (this is the proof mode which is loaded at the start
of each proof) and Proof Mode (switches the proof mode of the current
proof) to control them.
* A new primitive Evd.fold_undefined which operates like an Evd.fold,
except it only goes through the evars whose body is Evar_empty. This is
a common operation throughout the code,
some of the fold-and-test-if-empty occurences have been replaced by
fold_undefined. For now,
it is only implemented as a fold-and-test, but we expect to have some
optimisations coming some day, as there can be a lot of evars in an
evar_map with this new implementation (I've observed a couple of
thousands), whereas there are rarely more than a dozen undefined ones.
Folding being a linear operation, this might result in a significant
speed-up.
* The declarative mode has been moved into the plugins. This is made
possible by the proof mode feature. I tried to document it so that it
can serve as a tutorial for a tactic mode plugin.
Features user-side:
* Unfocus does not go back to the root of the proof if several Focus-s
have been performed.
It only goes back to the point where it was last focused.
* experimental (non-documented) support of keywords
BeginSubproof/EndSubproof:
BeginSubproof focuses on first goal, one can unfocus only with
EndSubproof, and only
if the proof is completed for that goal.
* experimental (non-documented) support for bullets ('+', '-' and '*')
they act as hierarchical BeginSubproof/EndSubproof:
First time one uses '+' (for instance) it focuses on first goal, when
the subproof is
completed, one can use '+' again which unfocuses and focuses on next
first goal.
Meanwhile, one cas use '*' (for instance) to focus more deeply.
Known regressions:
* The xml plugin had some functions related to proof trees. As the
structure of proof changed significantly, they do not work anymore.
* I do not know how to implement info or show script in this new engine.
Actually I don't even know what they were suppose to actually mean in
earlier versions either. I wager they would require some calm thinking
before going back to work.
* Declarative mode not entirely working (in particular proofs by
induction need to be restored).
* A bug in the inversion tactic (observed in some contributions)
* A bug in Program (observed in some contributions)
* Minor change in the 'old' type of tactics causing some contributions
to fail.
* Compilation time takes about 10-15% longer for unknown reasons (I
suspect it might be linked to the fact that I don't perform any
reduction at QED-s, and also to some linear operations on evar_map-s
(see Evd.fold_undefined above)).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12961 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12856 85f007b7-540e-0410-9357-904b9bb8a0f7
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destr_t, etc etc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12855 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12854 85f007b7-540e-0410-9357-904b9bb8a0f7
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This allow for instance to remove the dependency of List.v toward Min.v
To prove max_l and co, we push Le.le_pred and Le.le_S_n into Peano.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12784 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12728 85f007b7-540e-0410-9357-904b9bb8a0f7
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There was already a Ndiv and Nmod, but hiddent in ZOdiv_def. We
higlight it by putting it in a separate file, prove its specification
without using Z (but for the moment can't avoid a detour via nat,
though), and then instantiate general results from Natural/Abstract/NDiv
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12726 85f007b7-540e-0410-9357-904b9bb8a0f7
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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
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12717 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12716 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12715 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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- Records of operations and specs in CyclicAxioms are now
type classes (under a module ZnZ for qualification).
We benefit from inference and from generic names:
(ZnZ.mul x y) instead of (znz_mul (some_ops...) x y).
- Beware of typeclasses unfolds: the line about
Typeclasses Opaque w1 w2 ... is critical for decent
compilation time (x2.5 without it).
- Functions defined via same_level are now obtained from a
generic version by (Eval ... in ...) during definition.
The code obtained this way should be just as before, apart
from some (minor?) details. Proofs for these functions
are _way_ simplier and lighter.
- The macro-generated NMake_gen.v contains only generic iterators
and compare, mul, div_gt, mod_gt. I hope to be able to adapt
these functions as well soon.
- Spec of comparison is now fully done with respect to Zcompare
- A log2 function has been added.
- No more unsafe_shiftr, we detect the underflow directly with sub_c
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12713 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12704 85f007b7-540e-0410-9357-904b9bb8a0f7
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we export the "safe" version of these functions, working for all
input and not only reasonably small shifting arg. The former
"unsafe" shiftr and shiftl are now unsafe_shiftr and unsafe_shiftl.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12688 85f007b7-540e-0410-9357-904b9bb8a0f7
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letouzey
pboutill
herbelin
glondu
aspiwack