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Fix inheritances from countalg to finalg
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Line 426 in `integral.v` diverged to over 40 minutes with the new
`finfun.v`, because matching `mod_Iirr` to `quo_Iirr` goes into
exponential backtracking. This is currently averted by limiting the
repetition of `mod_IirrE` in this `rewrite` line.
Making `finfun` mixing opaque brings this down to 40 seconds, and
locking `cfIirr` to a tractable 0.15 seconds, hopefully improving the
instances. This line also takes 47 seconds to execute in the master
branch, so this is likely an undetected Coq performance regression.
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Coq currently fails to resolve Miller patterns against open evars
(issue coq/#9663), in particular it fails to unify `T -> ?R` with
`forall x : T, ?dR x` even when `?dR` does not have `x` in its context.
As a result canonical structures and constructor notations for the
new generalised dependent `finfun`s fail for the non-dependent use
cases, which is an unacceptable regression.
This commit mitigates the problem by specialising the canonical
instances and most of the constructor notation to the non-dependent
case, and introducing an alias of the `finfun_of` type that has
canonical instances for the dependent case, to allow experimentation
with that feature.
With this fix the whole `MathComp` library compiles, with a few
minor changes. The change in `integral_char` fixes a performance issue
that appears to be the consequence of insufficient locking of both
`finfun_eqType` and `cfIirr`; this will be explored in a further commit.
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Clarified that the sample use provided is an example rather than a
misplaced unit test.
Added the definition of generic recursors to the examples, for both
non-dependent and dependent use cases.
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Construct `finfun_of` directly from a bespoke indexed inductive type,
which both makes it structurally positive (and therefore usable as a
container in an `Inductive` definition), and accommodates naturally
dependent functions.
This is still WIP, because this PR exposed a serious shortcoming of
the Coq unification algorithm’s implantation of Miller patterns. This
bug defeats the inference of `Canonical` structures for `{ffun S -> T}`
when the instances are defined in the dependent case!
This causes unmanageable regressions starting in `matrix.v`, so I
have not been able to check for any impact past that. I’m pushing this
commit so that the Coq issue may be addressed.
Made `fun_of_fin` structurally decreasing: Changed the primitive
accessor of `finfun_of` from `tfgraph` to the `Funclass` coercion
`fun_of_fin`. This will make it possible to define recursive functions
on inductive types built using finite functions. While`tfgraph` is
still useful to transport the tuple canonical structures to
`finfun_of`, it is no longer central to the theory so its role has
been reduced.
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Add extra eta lemmas for the under tactic
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compat sumn with bigop
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Related: coq/coq#9651
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while some refs (see e.g. [1]) don't assume that the "transitive closure" is
reflexive; so one won't need to look at lemma "connect0" to figure this out.
[1] https://en.wikipedia.org/wiki/Transitive_closure
[ci skip]
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Anticipating coq/coq#9170, remove numeric occurrence selector affected
by the (invisible) presence of explicit types for variables bound in
`match` branch patterns. The proof could be further simplified if this
change is implemented.
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pmap_cat, pmap_perm and perm_map_inj added
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itv_intersection, redefine prev_of_itv and itv_decompose using lersif, extend itv_rewrite, simplify proofs (#271)
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Namely:
-projection-no-head-constant
-redundant-canonical-projection
-notation-overridden
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* Add some theorems on lersif and intervals
* Add more theorems on lersif
* Remove needless parens
* ChangeLog
* Move lersifN
* Add lersif_anti
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* (Update make's path accordingly)
* This patch is required for opam 2.0 pinning
* As a result, these *.opam files are now similar to the opam files in
https://github.com/coq/opam-coq-archive/blob/master/extra-dev/packages/coq-mathcomp-*/coq-mathcomp-*.dev/
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swap mingroup / maxgroup arguments
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Moved set argument before predicate argument for mingroup and maxgroup
because Coq only displays notation with identifier parameters that are
both bound and free if there is at least one free occurrence to the
left of the binder.
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Refactored and completed implicit and scope signatures of constants of
MatrixGenField, the module that contains the construction of an
extension field for an irreducible representation, and for decidability
definitions.
Completed and corrected some errors in the corresponding header
documentation.
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Like injectivity lemmas, instances of cancellation lemmas (whose
conclusion is `cancel ? ?`, `{in ?, cancel ? ?}`, `pcancel`, or
`ocancel`) are passed to
generic lemmas such as `canRL` or `canLR_in`. Thus such lemmas should
not have trailing on-demand implicits _just before_ the `cancel`
conclusion, as these would be inconvenient to insert (requiring
essentially an explicit eta-expansion).
We therefore use `Arguments` or `Prenex Implicits` directives to make
all such arguments maximally inserted implicits. We don’t, however make
other arguments implicit, so as not to spoil direct instantiation of
the lemmas (in, e.g., `rewrite -[y](invmK injf)`).
We have also tried to do this with lemmas whose statement matches a
`cancel`, i.e., ending in `forall x, g (E[x]) = x` (where pattern
unification will pick up `f = fun x => E[x]`).
We also adjusted implicits of a few stray injectivity
lemmas, and defined constants.
We provide a shorthand for reindexing a bigop with a permutation.
Finally we used the new implicit signatures to simplify proofs that
use injectivity or cancellation lemmas.
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fix TFAE
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```
Warning: Adding and removing hints in the core database implicitly is
deprecated. Please specify a hint database.
[implicit-core-hint-db,deprecated]
```
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This increases performance 10% - 15% for Coq v8.6.1 - v8.9.dev.
Tested on a Debain-based 16-core build server and
a Macbook Pro laptop with 2,3 GHz Intel Core i5.
| | Compilation time, old | Compilation | Speedup |
| | (mathcomp commit 967088a6f87) | time, new | |
| Coq 8.6.1 | 10min 33s | 9min 10s | 15% |
| Coq 8.7.2 | 10min 12s | 8min 50s | 15% |
| Coq 8.8.2 | 9min 39s | 8min 32s | 13% |
| Coq 8.9.dev(05d827c800544) | 9min 12s | 8min 16s | 11% |
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It seems Coq at some point fixed the problem `_ : Type` was
supposed to solve.
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Document parameter names whenever possible
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As suggested by @ggonthier
[here](https://github.com/math-comp/math-comp/pull/249#pullrequestreview-177938295)
> One of the design ideas for the `Arguments` command was that it would allow
to centralise the documentation of the application of constants.
In that spirit it would be in my opinion better to make as much use of this
as possible, and to document the parameter names whenever possible,
especially that of implicit parameters.
and
[here](https://github.com/math-comp/math-comp/pull/253#discussion_r237434163):
> As a general rule, defined functional constants should have maximal prenex
implicit arguments, as this facilitates their use as arguments to functionals,
because this mimics the way function constants are treated in functional
programming languages with Hindley-Milner type inference. Conversely, lemmas and
theorems should have on-demand implicit arguments, possibly interspersed with
explicit ones, as it's fairly common for other lemmas to have universally
quantified premises; also, this makes it easier to specify such arguments with
the apply: tactic. This policy may be amended for lemmas that are used as
functional arguments, such as reflection or cancellation lemmas. Unfortunately
there is currently no easy way to tell Coq to use different defaults for
definitions and lemmas, so MathComp sticks to the on-demand default, as there
are significantly more lemmas than definition, and use the Prenex Implicits to
redress matters in bulk for definitions. However, this is not completely
systematic, and is sometimes omitted for constants that are not used as
functional arguments in the library, or inside the sections in which the
definition occur, since such commands need to be repeated after the section is
closed. Since Arguments commands should document the intended constant usage as
best as possible, they should follow the implicits policy - even in cases such
as this where the Prenex Implicits had been skipped.
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Documentation of FieldUnitMixin and FieldMixin corrected to reflect
actual arguments, with mulVf and inv0 made explicit arguments for
FieldMixin (they were implicit due to the extended signature of
Field.mixin_of). Type of FieldMixin changed to a convertible variant to
facilitate construction of on-the-fly in-proof construction of
fieldType instances, exposing an idomainType instance.
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See the discussion here:
https://github.com/math-comp/math-comp/pull/242#discussion_r233778114
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Remove some unused canonical mixins.
Change simplification behavior of concrete comparison functions to allow for
better simplification using unfolding and sebsequent folding back e.g. with
`rewrite !eqE /= -!eqE`.
A bit of cleanup for `Prenex Implicits` declarations.
Document some explanations by G. Gonthier.
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Adding missing documentation for mixin and class constructors for
Equality, Choice, Countable, and Finite.
Renaming Equality mixin constructor comparableClass to the more
consistent comparableMixin.
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should fix #238
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This reverts commit 044634dcc2f645e3afbdad6cb8dcc66f3eb4a87e.
See issue https://github.com/math-comp/odd-order/pull/5
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fix some bugs in Makefile
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Statement of `bool_irrelevance` more consistent with its name.
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