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This file contains low-level stuff for FSets/FMaps. Switching it to
the new version (the one using Equivalence and so on instead of
eq_refl/eq_sym/eq_trans and so on) only leads to a few changes in
FSets/FMaps that are minor and probably invisible to standard users.
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FSets, and improve it
As soon as you have a eq, a lt and a le (that may be lt\/eq, or (complement (flip (lt)))
and a few basic properties over them, you can instantiate functor MakeOrderTac
and gain an "order" tactic. See comments in the file for the scope of this tactic.
NB: order doesn't call auto anymore. It only searches for a contradiction in the
current set of (in)equalities (after the goal was optionally turned into hyp
by double negation). Thanks to S. Lescuyer for his suggestions about this tactic.
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1) compilation of Library.tex was failing on a "Ext_" in Diaconescu.v
In fact coqdoc was trying to recognize the end of a _emphasis_ and
hence inserted a bogus }. For the moment I've enclosed the phrase
with [ ], but this emphasis "feature" of coqdoc seems _really_
easy to broke. Matthieu ?
2) By the way, this Library document was made from latin1 and utf8
source file, hence bogus characters. All .v containing special
characters are converted to utf8, and their first line is now
mentionning this. (+ killed some old french comments and some
other avoidable special characters).
PLEASE: let's stick to this convention and avoid latin1, at least
in .v files.
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pattern unification
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a Coq meeting some time ago. NB: this syntax is an alias for (x,(y,(z,t)))
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and idem for |||, thanks to a specific scope lazy_bool_scope.
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As for FSetAVL vs. FSetFullAVL, preservation of the balancing of trees
is not necessary anymore for just fulfilling the Map interface. But we
still want theses proofs to exists somewhere, since they ensure the
correct efficiency of the FMapAVL operations.
In addition, FSetFullAVL also contains the non-structural,
ocaml-faithful version of compare.
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* pure functions comes first, proofs are isolated in a sub-module
* lazy (&&&) = if ... then ... else true instead of strict (&&) = andb
* equal and compare done via continuations
* a more clever map2_opt suggested by B. Gregoire: no more
intermediate conversion to lists, some sub-functions can handle
trivial situations, etc.
* map2 is now done via map2_opt and another new iterator: map_option.
By the way, this map_option allows to define easily an efficient
filter function. Both map2_opt and map_option are currently not
available through FMapInterface.S, but they can be used by direct
reference to the underlying Raw module.
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* FSetAVL is greatly lightened : modulo a minor change in bal, formal
proofs of avl invariant is not needed for building a functor
implementing FSetInterface.S (even if this invariant is still true)
* Non-structural functions (union, subset, compare, equal) are
transformed into efficient structural versions
* Both proofs of avl preservation and non-structural functions are
moved to a new file FSetFullAVL, that can be ignored by the average
user.
Same for FMapAVL (still work in progress...)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10679 85f007b7-540e-0410-9357-904b9bb8a0f7
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- clarifications about Equality on maps
Caveat: name change, what used to be Equal is now Equivb
- the prefered equality predicate (the new Equal) is declared
a setoid equality, along with several morphisms
- beginning of a filter/for_all/exists_/partition section in FMapFacts
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Sequel of commit 10545 on FSetAVL. This time, no compile-time penality
since there are fewer non-structural functions in FMapAVL.
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14097)
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more general.
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subtype of the FSet Interface (and idem for FMapWeak / FMap).
1) No eq_dec is officially required in FSetWeakInterface.S.E
(EqualityType instead of DecidableType). But of course,
implementations still needs this eq_dec.
2) elements_3 differs in FSet and FSetWeak (sort vs. nodup). In
FSetWeak we rename it into elements_3w, whereas in FSet we
artificially add elements_3w along to the original elements_3.
Initial steps toward factorization of FSetFacts and FSetWeakFacts,
and so on...
Even if it's not required, FSetWeakList provides a eq_dec on sets,
allowing weak sets of weak sets.
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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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(A:Type) instead of a (A:Set).
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+ bug correction in proof of structural principles
+ up do to date test-suite/success/Funind.v
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The old version is, for now, still available by prefixing any command/tactic with Old/old (eg. old functional induction ...).
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* quelques unfold E.eq en cas de changement de la semantique des foncteurs
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-> OrderedTypeEx: des exemples de OrderedType
-> OrderedTypeAlt: une definition alternative de OrderedType
-> FSetAVL et FMapAVL: realisation a coup d'AVL
-> FMapPositive: realisation a coup d'arbre binaire
(selon les chiffres binaires de la cle)
-> FMapIntMap : realisation en utilisant IntMap
-> FSetToFiniteSet: un ensemble de FSet est un ensemble de Ensemble.v
FSetAVL et FMapAVL prenent 30 secondes chacuns sur ma machine:
on peut ne pas les compiler en passant l'option "-fsets no" a
configure, de facon similaire a "-reals no"
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