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Fixed some bugs in -beautify and robustness of {struct} clause.
Note: I tried to make the Automatic Introduction mode on by default
for version >= 8.3 but it is to complicated to adapt even in the
standard library.
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Improve generalization by equalities tactic, now allowing to
generalize an arbitrary application, e.g. in preparation for applying an
elimination principle for a function. This adds a flag to generalize_dep
so that it doesn't abstract the variable if it is defined, just
introducing a let-in.
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NZBase -- NZAdd -- NZMul
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NZOrder ---------- NZAddOrder -- NZMulOrder -- NZProperties
This is done by transforming NZBase into a
functorial module type, and making NZAdd NZMul NZOrder
accept an instance of NZBase as parameter. This is possible
thanks to a combination of various new features of modules:
- interactive proofs in module type (ie functors can be
turned into type functors)
- Include Type in Module (ie type functors can be turned
into functors)
- Include Self, <+ , etc, etc...
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Any place where <: was legal can now contain many <: declarations.
Moreover we can say that the module type we are declaring is a subtype
of an earlier module type. See DecidableType2 for examples.
Also try to handle correctly the freeze/unfreeze summaries
when simulating start/include/end (syntax ... := ... <+ ...)
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"Module M (...) := M1 <+ M2 <+ M3 <+ ..." is now a shortcut for
"Module M (...). Include M1. Include M2. Include M3... End M."
Moreover M2,M3,etc can be functors as long as they find what they need in what
comes before them (see new command "Include Self").
The only real constraint is that M1,M2,M3,... should not have common elements
(for the moment (?)).
Same behavior for signature : Module Type M := M1 <+ M2 <+ M3.
Note that this <+ is _not_ a primitive construct of the module language,
for instance it cannot be used in signature (Module M <: M1 <+ M2 is
illegal for the moment).
Some example of use in Decidable2 and NZAxioms
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We can now have a diamond-like approch to extentions of signatures,
instead of a linear-only chains as earlier...
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synonyms in Le.v, Lt.v, Gt.v.
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[Generalizable (All|No) Variables (ident+)?], also update
type classes documentation to reflect the latest changes
in instance decls. Fix a bug in [Util.list_split_when].
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expected, not introducing the [forall ...] variables to avoid
unnecessary eta-expansions. Force to use { } in instance declarations
when the class is a record even if it's a singleton.
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- In fact, Bind Scope has no retrospective effect. Since we don't want
it inside functor, we use it late, and hence we are forced to use manual
"Arguments Scope" commands.
- Added syntax for power in BigN / BigZ / BigQ.
- Added syntax p#q in BigQ for representing fractions (constructor BigQ.Qq)
as in QArith. Display of a rational numeral is hence either an integer
(constructor BigQ.Qz) or something like 6756 # 8798.
- Fix of function BigQ.Qred that was not simplifing (67#1) into 67.
- More tests in test-suite/output/NumbersSyntax.v
A nice one not in the test-suite:
Time Eval vm_compute in BigQ.red ((2/3)^(-100000) * (2/3)^(100000)).
= 1
: bigQ
Finished transaction in 3. secs (3.284206u,0.004s)
:-)
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on the way:
- Added a testsuite output file
- Try to avoid nasty unfolding (fix nfun ...) in type of I31.
Idealy we would need a "Eval compute in" for the type of a inductive
constructor
- Stop opening Scopes for BigQ, BigN, BigZ by default
The user should do some Open Scope.
TODO: there's a bug that prevent BigQ.opp to have arg in bigQ_scope
(and so on for other operations), even with some Bind Scope around.
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As show by contrib TreeAutomata, the Peqb now placed in BinPos
was using 1st arg as "struct", instead of 2nd arg as earlier.
Fix that, and remove the "Import BinPos BinNat" hack in Ndec
(merci Hugo :-).
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- Deactivation of short names registration and printing for
abbreviations to identical names, what avoids printing uselessly
qualified names binding where the short name is in fact equivalent.
- New treatment of abbreviations to names: don't insert any maximally
inserted implicit arguments at all at the time of the abbreviation
and use the regular internalization strategy to have them inserted
at use time.
- The previous modifications altogether make redirections of
qualified names easier and avoid the semantic change of r12349 and
hence allows to keep "Notation b := @a" as it was before, i.e. as a
notation for the deactivation of the implicit arguments of a.
- Took benefit of these changes and updated nil/cons/list/app
redefinition in "List.v".
- Fixed parsing/printing notation bugs (loop on partially applied
abreviations for constructors in constrintern.ml + bad reverting of
notations with holes that captured non anonymous variables in
match_cases_pattern).
- Add support for parsing/printing abbreviations to @-like constructors
and for reverting printing for abbreviations to constructors applied
to parameters only (function extern_symbol_pattern).
- Minor error messages fixes and minor APIs cleaning.
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To retrieve the old behavior of spec_sub0 and spec_sub with
precondition on order, just chain spec_sub with Zmax_r or Zmax_l.
Idem with spec_pred0 and spec_pred.
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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.
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+ adaptation of {Nat,N,P,Z,Q,R}_as_DT for them to provide both eq_dec and eqb
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- Cleaning and uniformisation in command.ml:
- For better modularity and better visibility, two files got isolated
out of command.ml:
- lemmas.ml is about starting and saving a proof
- indschemes.ml is about declaring inductive schemes
- Decomposition of the functions of command.ml into a functional part
and the imperative part
- Inductive schemes:
- New architecture in ind_tables.ml for registering scheme builders,
and for sharing and generating on demand inductive schemes
- Adding new automatically generated equality schemes (file eqschemes.ml)
- "_congr" for equality types (completing here commit 12273)
- "_rew_forward" (similar to vernac-level eq_rect_r), "_rew_forward_dep",
"_rew_backward" (similar to eq_rect), "_rew_backward_dep" for
rewriting schemes (warning, rew_forward_dep cannot be stated following
the standard Coq pattern for inductive types: "t=u" cannot be the
last argument of the scheme)
- "_case", "_case_nodep", "_case_dep" for case analysis schemes
- Preliminary step towards discriminate and injection working on any
equality-like type (e.g. eq_true)
- Restating JMeq_congr under the canonical form of congruence schemes
- Renamed "Set Equality Scheme" into "Set Equality Schemes"
- Added "Set Rewriting Schemes", "Set Case Analysis Schemes"
- Activation of the automatic generation of boolean equality lemmas
- Partial debug and error messages improvements for the generation of
boolean equality and decidable equality
- Added schemes for making dependent rewrite working (unfortunately with
not a fully satisfactory design - see file eqschemes.ml)
- Some names of ML function made more regular (see dev/doc/changes.txt)
- Incidentally, added a flush to obsolete Local/Global syntax warning
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not just type class applications.
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Since length and app were defined inside a Section in List.v,
their type argument A wasn't inside the fixpoint. Restoring
the initial definition repairs (at least) Cachan/IntMap.
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- NStrongRec provides a "strong" recursor based on the usual one:
recursive calls can be done here on any lower value.
See binary log in NDefOps for an example of use.
- NDefOps contains alternative definitions of usual operators
(add, mul, ltb, pow, even, half, log)
via usual or strong recursor, and proofs of correctness and/or
of equivalence with axiomatized operators.
These files were in the archive but not being compiled,
some proofs of correction for functions defined there were missing.
By the way, some more iff-style lemmas in Bool.
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TODO: finish removing the "Add Relation", "Add Morphism" fun_* fun2_*
TODO: now that we have Include, flatten the hierarchy...
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This way we get properties of Rmin / Rmax (almost) for free.
TODO: merge Rbasic_fun and Rminmax...
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- A richer OrderedTypeFull interface : OrderedType + predicate "le"
- Implementations {Nat,N,P,Z,Q}OrderedType.v, also providing "order" tactics
- By the way: as suggested by S. Lescuyer, specification of compare is
now inductive
- GenericMinMax: axiomatisation + properties of min and max out of
OrderedTypeFull structures.
- MinMax.v, {Z,P,N,Q}minmax.v are specialization of GenericMinMax,
with also some domain-specific results, and compatibility layer
with already existing results.
- Some ML code of plugins had to be adapted, otherwise wrong "eq",
"lt" or simimlar constants were found by functions like coq_constant.
- Beware of the aliasing problems: for instance eq:=@eq t instead of
eq:=@eq M.t in Make_UDT made (r)omega stopped working (Z_as_OT.t
instead of Z in statement of Zmax_spec).
- Some Morphism declaration are now ambiguous: switch to new syntax
anyway.
- Misc adaptations of FSets/MSets
- Classes/RelationPairs.v: from two relations over A and B, we
inspect relations over A*B and their properties in terms of classes.
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ForallPairs, etc
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Indeed, since sqrt is a total function, most lemmas are true, even for
negative inputs. For instance, sqrt_le_1 was
0 <= x -> 0 <= y -> x <= y -> sqrt x <= sqrt y
while sqrt_le_1_alt is just
x <= y -> sqrt x <= sqrt y.
Naming is done by adding _alt suffixes. In an ideal world (Coq 9.0?), these
new lemmas should just replace the original ones.
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like ring)
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This allows easier handling of dependencies, for instance RelationClasses
won't have to requires List (which itself requires part of Arith, etc).
One of the underlying ideas is to provide setoid rewriting in Init someday.
Thanks to some notations in List, this change should be fairly transparent
to the user. For instance, one could see that List.length is a notation for
(Datatypes.)length only when doing a Print List.length.
For these notations not to be too intrusive, they are hidden behind an explicit
Export of Datatypes at the end of List. This isn't very pretty, but quite handy.
Notation.ml is patched to stop complaining in the case of reloading the same
Delimit Scope twice.
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branch
and remove equations stuff which moves to a separate plugin.
Classes:
- Ability to define classes post-hoc from constants or inductive types.
- Correctly rebuild the hint database associated to local hypotheses when
they are changed by a [Hint Extern] in typeclass resolution.
Tactics and proofs:
- Change [revert] so that it keeps let-ins (but not [generalize]).
- Various improvements to the [generalize_eqs] tactic to make it more robust
and produce the smallest proof terms possible.
Move [specialize_hypothesis] in tactics.ml as it goes hand in hand with
[generalize_eqs].
- A few new general purpose tactics in Program.Tactics like [revert_until]
- Make transitive closure well-foundedness proofs transparent.
- More uniform testing for metas/evars in pretyping/unification.ml
(might introduce a few changes in the contribs).
Program:
- Better sorting of dependencies in obligations.
- Ability to start a Program definition from just a type and no obligations,
automatically adding an obligation for this type.
- In compilation of Program's well-founded definitions, make the functional a
separate definition for easier reasoning.
- Add a hint database for every Program populated by [Hint Unfold]s for
every defined obligation constant.
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variables with syntax:
[Local?|Global] Generalizable Variable(s)? [all|none|id1 idn].
By default no variable is generalizable, so this patch breaks backward
compatibility with files that used implicit generalization (through
Instance declarations for example). To get back the old behavior, one
just needs to use [Global Generalizable Variables all].
Make coq_makefile more robust using [mkdir -p].
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Implicit Arguments, Arguments Scope and Coercion fixed, noneffective
Global in sections for Hints and Notation detected).
Misc. improvements (comments + interpretation of Hint Constructors +
dev printer for hint_db).
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unconstrained goals (e.g. PreOrder A ?). Allow the unconstrained use of
[proper_reflexive] again.
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Thanks to the functors in FSetCompat, the three implementations
of FSets (FSetWeakList, FSetList, FSetAVL) are just made of a few
lines adapting the corresponding MSets implementation to the old
interface.
This approach breaks FSetFullAVL. Since this file is of little use
for stdlib users, we migrate it into contrib Orsay/FSets.
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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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In particular we remove them from the hint db, a few autos become
calls to order. Moreover, lt_antirefl --> lt_irrefl for uniformity.
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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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I forgot to mention in last commit message about MSets that
the corresponding OrderedType2 comes with a redesigned "order"
tactic. It should now be complete for its purpose (that is
solve systems of (in)equations of variables over == < <= <>).
Non-linear matching is cool, I love Ltac :-). Unlike the old "order",
this new version is meant to completely solve the goal or fail.
Speed might be an issue for big systems, but in pratice it is
quite efficient on the examples encountered in FSets.
This commit:
- propagages this new "order" to the original OrderedType.v file
used for the old FSet.
- fixes a bug : the ltac loop shouldn't fail otherwise strange
backtrack occurs. I hate Ltac :-(
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Same global ideas (in particular the use of modules/functors), but:
- frequent use of Type Classes inside interfaces/implementation.
For instance, no more eq_refl/eq_sym/eq_trans, but Equivalence.
A class StrictOrder for lt in OrderedType. Extensive use of Proper
and rewrite.
- now that rewrite is mature, we write specifications of set operators
via iff instead of many separate requirements based on ->. For instance
add_spec : In y (add x s) <-> E.eq y x \/ In x s.
Old-style specs are available in the functor Facts.
- compare is now a pure function (t -> t -> comparison) instead of
returning a dependent type Compare.
- The "Raw" functors (the ones dealing with e.g. list with no
sortedness proofs yet, but morally sorted when operating on them)
are given proper interfaces and a generic functor allows to obtain
a regular set implementation out of a "raw" one.
The last two points allow to manipulate set objects that are completely free
of proof-parts if one wants to. Later proofs will rely on type-classes
instance search mechanism.
No need to emphasis the fact that this new version is severely incompatible
with the earlier one. I've no precise ideas yet on how allowing an easy
transition (functors ?). For the moment, these new Sets are placed alongside
the old ones, in directory MSets (M for Modular, to constrast with forthcoming
CSets, see below). A few files exist currently in version foo.v and foo2.v,
I'll try to merge them without breaking things. Old FSets will probably move
to a contrib later.
Still to be done:
- adapt FMap in the same way
- integrate misc stuff like multisets or the map function
- CSets, i.e. Sets based on Type Classes : Integration of code contributed by
S. Lescuyer is on the way.
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