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Added lemmas `big_enum_cond`, `big_enum` and `big_enumP` to handle more
explicitly big ops iterating over explicit enumerations in a `finType`.
The previous practice was to rely on the convertibility between
`enum A` and `filter A (index_enum T)`, sometimes explicitly via the
`filter_index_enum` equality, more often than not implicitly.
Both are likely to fail after the integration of `finmap`, as the
`choiceType` theory can’t guarantee that the order in selected
enumerations is consistent.
For this reason `big_enum` and the related (but currently unused)
`big_image` lemmas are restricted to the abelian case. The `big_enumP`
lemma can be used to handle enumerations in the non-abelian case, as
explained in the `bigop.v` internal documentation.
The Changelog entry enjoins clients to stop relying on either
`filter_index_enum` and convertibility (though this PR still provides
both), and warns about the restriction of the `big_image` lemma set to
the abelian case, as it it a possible source of incompatibility.
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Replaced the legacy generalised induction idiom with a more robust one
that does not rely on the `{-2}` numerical occurrence selector, using
either new helper lemmas `ubnP` and `ltnSE` or a specific `nat`
induction principle `ltn_ind`.
Added (non-strict in)equality induction helper lemmas
Added `ubnP[lg]?eq` helper lemmas that abstract an integer expression
along with some (in)equality, in preparation for some generalised
induction. Note that while `ubnPleq` is very similar to `ubnP` (indeed
`ubnP M` is basically `ubnPleq M.+1`), `ubnPgeq` is used to remember
that the inductive value remains below the initial one.
Used the change log to give notice to users to update the generalised
induction idioms in their proofs to one of the new forms before
Mathcomp 1.11.
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* missing exports of lemmas `commrB`, `commr_sum` and `commr_prod`
* missing `regular_*` canonical exports
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* Lemmas on commutation with big sum and prod
* Added commrB Lemma
* @CohenCyril review
* apply -> apply:
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add existsPn/forallPn lemmas
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Commutative Algebras
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Initial properties of polynomials in R-algebras
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from
`ltngtP m n : compare_nat m n (m <= n) (n <= m) (m < n) (n < m) (n == m) (m == n)`
to
`ltngtP m n : compare_nat m n (n == m) (m == n) (n <= m) (m <= n) (n < m) (m < n)`,
to make it tries to match subterms with `m < n` first, `m <= n`, then `m == n`.
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`V` was wrongly eta-expanded before:
GRing.scale
: forall (R : ringType) (V : lmodType R),
R -> GRing.Zmodule.Pack (GRing.Lmodule.class V) ->
GRing.Zmodule.Pack (GRing.Lmodule.class V)
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* Modified the definition of sort to work on any type
* Other Generalizations, fixes and CHANGELOG entry
* Add stability lemmas for `path.sort`
- Inverse the comparison in `merge` and swap arguments of it everywhere.
- Add `sort_rec1` and `sortE` to simplify inductive proofs on `sort`.
- Add `seq.mask_filter`, `mem2E`, `path_mask`, `path_filter`, and `sorted_mask`.
- Generalize `sorted_filter`, `homo_path_in`, `mono_path_in`, `homo_sorted_in`,
and `mono_sorted_in` to non-`eqType`s.
- Add the following lemmas to state the stability of `path.merge` and `path.sort`.
sorted_merge
: forall (T : Type) (leT : rel T),
transitive leT ->
forall s t : seq T, sorted leT (s ++ t) -> merge leT s t = s ++ t
merge_stable_path
: forall (T : Type) (leT leT' : rel T),
total leT ->
forall (x : T) (s1 s2 : seq T),
all (fun y : T => all (leT' y) s2) s1 ->
path [rel x0 y | leT x0 y && (leT y x0 ==> leT' x0 y)] x s1 ->
path [rel x0 y | leT x0 y && (leT y x0 ==> leT' x0 y)] x s2 ->
path [rel x0 y | leT x0 y && (leT y x0 ==> leT' x0 y)] x
(merge leT s1 s2)
merge_stable_sorted
: forall (T : Type) (leT leT' : rel T),
total leT ->
forall s1 s2 : seq T,
all (fun x : T => all (leT' x) s2) s1 ->
sorted [rel x y | leT x y && (leT y x ==> leT' x y)] s1 ->
sorted [rel x y | leT x y && (leT y x ==> leT' x y)] s2 ->
sorted [rel x y | leT x y && (leT y x ==> leT' x y)] (merge leT s1 s2)
sorted_sort
: forall (T : Type) (leT : rel T),
transitive leT -> forall s : seq T, sorted leT s -> sort leT s = s
sort_stable
: forall (T : Type) (leT leT' : rel T),
total leT -> transitive leT' ->
forall s : seq T,
sorted leT' s ->
sorted [rel x y | leT x y && (leT y x ==> leT' x y)] (sort leT s)
filter_sort
: forall (T : Type) (leT : rel T),
total leT -> transitive leT ->
forall (p : pred T) (s : seq T),
[seq x <- sort leT s | p x] = sort leT [seq x <- s | p x]
mask_sort
: forall (T : Type) (leT : rel T),
total leT -> transitive leT ->
forall (s : seq T) (m : bitseq),
{m_s : bitseq | mask m_s (sort leT s) = sort leT (mask m s)}
mask_sort'
: forall (T : Type) (leT : rel T),
total leT -> transitive leT ->
forall (s : seq T) (m : bitseq),
sorted leT (mask m s) ->
{m_s : bitseq | mask m_s (sort leT s) = mask m s}
subseq_sort
: forall (T : eqType) (leT : rel T),
total leT -> transitive leT -> {homo sort leT : t s / subseq t s}
subseq_sort'
: forall (T : eqType) (leT : rel T),
total leT -> transitive leT ->
forall t s : seq T, subseq t s -> sorted leT t -> subseq t (sort leT s)
mem2_sort
: forall (T : eqType) (leT : rel T),
total leT -> transitive leT ->
forall (s : seq T) (x y : T),
leT x y -> mem2 s x y -> mem2 (sort leT s) x y
* Avoid some eta-expansions
* Get the proper fix of `order_path_min` and remove `sort_map_in`
* Update documentation and CHANGELOG entries
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Also changed eqsVneq.
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- Change the naming of permutation lemmas so they conform to a
consistent policy: `perm_eq` lemmas have a `perm_` (_not_ `perm_eq`)
prefix, or sometimes a `_perm` suffix for lemmas that _prove_ `perm_eq`
using a property when there is also a lemma _using_ `perm_eq` for the
same property. Lemmas that do not concern `perm_eq` do _not_ have
`perm` in their name.
- Change the definition of `permutations` for a time- and space-
back-to-front generation algorithm.
- Add frequency tally operations `tally`, `incr_tally`, `wf_tally` and
`tally_seq`, used by the improved `permutation` algorithm.
- add deprecated aliases for renamed lemmas
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Use `{pred T}` systematically for generic _collective_ boolean
predicate.
Use `PredType` to construct `predType` instances.
Instrument core `ssreflect` files to replicate these and other new
features introduces by coq/coq#9555 (`nonPropType` interface,
`simpl_rel` that simplifies with `inE`).
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Replace improper use of non-dependent `return` clause in `if` with a
type cast; an upcoming coq-side PR will discontinue support for this,
in order to support dependent return clauses with an implicit `as`
annotation.
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Fix inheritances from countalg to finalg
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Related: coq/coq#9651
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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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* 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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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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```
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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