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See file PreOmega for more details and/or test-suite/succes/*Omega*.v
The zify tactic performs a Z-ification of your current goal,
transforming parts of type nat, N, positive, taking advantage of many
equivalences of operations, and of the positivity implied by these
types.
Integration with omega and romega:
(r)omega : the earlier tactics, 100% compatible
(r)omega with * : full zify applied before the (r)omega run
(r)omega with <types>, where <types> is a sub-list of {nat,N,positive,Z},
applies only specific parts of zify (btw "with Z" means take advantage
of Zmax, Zmin, Zabs and Zsgn).
As a particular consequence, "romega with nat" should now be a
close-to-perfect replacement for omega. Slightly more powerful, since
(forall x:nat, x*x>=0) is provable and also slightly less powerful: if
False is somewhere in the hypothesis, it doesn't use it.
For the moment zify is done in a direct way in Ltac, using rewrite
when necessary, but crucial chains of rewrite may be made reflexive
some day.
Even though zify is designed to help (r)omega, I think it might be
of interest for other tactics (micromega ?). Feel free to complete
zify if your favorite operation / type isn't handled yet.
Side-effects:
- additional results for ZArith, NArith, etc...
- definition of Ple, Plt, Pgt, Pge and notations for them in positive_scope
- romega now start by doing "intros". Since the conclusion will be negated,
and this operation will be justified by means of decidability, it helps
to have as little as possible in the conclusion.
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complains.
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frais (par exemple pour "intro") ou pas forcément (par exemple pour
"fresh")
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noté cette erreur de ma part (copier/coller mon amour).
Ça créait des soucis dans les dépendance dans l'ancienne architecture de
Makefile, probablement dans la nouvelle aussi dans certaines
circonstances. Exit les bêtise, c'est plus propre maintenant.
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- Make sure make notices when a command fails
- don't leave behind half-baked output files of commands that failed
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anymore.
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The -MG option causes gcc to add any non-found .h file verbatim in the
dependencies. This naturally doesn't include the path to it (because
the path is unknown) and thus make doesn't know how to build it; it
knows how to build kernel/byterun/coq_jumptbl.h, not "coq_jumptbl.h".
--This line, and those below, will be ignored--
M Makefile.common
M Makefile.build
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Removed parsing/lexer.ml4 special case
No file depends on pa_extend_m.cmo anymore, Wierd ...
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include path
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- deletion of some dead code
- grouping all stuff depending on Z in a nice module Int
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répertoire Num. Suppression de ce dernier de l'archive courante.
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after commit 9983 of Bruno concerning kernel/closure.ml,
a few firstorder were awfully slow.
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Documented in dev/doc/build-system.txt .
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* explicitation of some types
* tags for grammar entries
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realizers)
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Not maintained, probably broken, of no interest except (maybe) for
myself, bad interaction with tools that work recursively (coqdep).
===> I move it to a personal repository
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utilities from Util. Some additions in Util, and simplifications
in various files.
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and generic romega tactic...
For the moment, nothing is visible yet from the user's point of view
(hopefully). But internally, we prepare a romega that can works on
any integer types. ReflOmegaCore is now separated in several modules:
* First, an interface Int that specifies the minimal amount of things
needed on our integer type for romega to work:
- int should be a ring (re-use of ring_theory definition ;-)
- it should come with an total order, compatible with + * -
- we should have a decidable ternary comparison function
- moreover, we ask one (and only one!) critical property specific to
integers: a<b <-> a<=b-1
* Then a functor IntProperties derives from this interface all the
various lemmas on integers that are used in the romega part,
in particular the famous OMEGA?? lemmas.
* The romega reflexive part is now in another functor IntOmega,
that rely on some Int: no more Z inside. The main changes is
that Z0 was a constructor whereas our abstract zero isn't. So
matching Z0 is transformed into (if beq ... 0 then ...). With
extensive use of && and if then else, it's almost clearer this way.
* Finally, for the moment Z_as_Int show that Z fulfills our interface,
and ZOmega = IntOmega(Z_as_Int) is used by the tactic.
Remains to be done:
- revision of the refl_omega to use any Int instead of just Z,
and creating a user interface.
- Int has no particular reason to use the leibniz equality (only
rely on the beq boolean test). Setoids someday ?
- a version with "semi-ring" for nat ? or rather a generic way to plug
additional equations on the fly, e.g. n>=0 for every nat subpart ?
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