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* This patch is a quick fix that removes part of the features of coq/coq#10022,
namely the ability to directly use setoid_rewrite with a (Under_rel)-tagged
relation R. This just means we'll need to do an extra step [rewrite UnderE.]
which was unnecessary with Coq 8.11+alpha.
* This PR stays backward-compatible w.r.t. Coq 8.10 and also keeps the salient
feature of coq/coq#10022 (generalize under & over to any Reflexive relation).
* Related: coq-community/atbr#23
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(namely, [RewriteRelation]s beyond Equivalence ones)
Thanks to @CohenCyril for suggesting this enhancement
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* Borrow ideas from the Setoid refman documentation:
https://coq.inria.fr/refman/addendum/generalized-rewriting.html#first-class-setoids-and-morphisms
* Introduce a relation with the following signature:
[Rel : forall (m n : nat) (s : Setoid m n), car s -> car s -> Prop]
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Changes:
* Add ssrclasses.v that redefines [Reflexive] and [iff_Reflexive];
* Add ssrsetoid.v that links
[ssrclasses.Reflexive] and [RelationClasses.Reflexive];
* Add [Require Coq.ssr.ssrsetoid] in Setoid.v;
* Update ssrfwd.ml accordingly, using a helper file ssrclasses.ml that
ports some non-exported material from rewrite.ml;
* Some upside in passing: ssrfwd.ml no more depends on Ltac_plugin;
* Update doc and tests as well.
Summary:
* We can now use the under tactic in two flavors:
- with the [eq] or [iff] relations: [Require Import ssreflect.]
- or a [RewriteRelation]: [Require Import ssreflect. Require Setoid.]
(while [ssreflect] does not require [RelationClasses] nor [Setoid],
and conversely [Setoid] does not require [ssreflect]).
* The file ssrsetoid.v could be skipped when porting under to stdlib2.
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* Add an extra test with an Equivalence.
* Update the doc accordingly.
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So if the underlying tactic "contains a ;" one should actually write:
under eq_bigl => i do [rewrite andb_idl; first by move/eqP->].
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so it acts "more naturally" like (under eq_bigl; [hnf|]); move=> [*|].
Also: replace "by over." in the doc example with "over."
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* Add tests accordingly.
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As a result, the following:
under i: eq_bigr by rewrite adnnC. (* ensure 1 Under subogal is created *)
under i: eq_big by [rewrite adnnC | rewrite addnC]. (* 2 Under subgoals *)
amounts to:
under i: eq_bigr; [rewrite adnnC; over | cbv beta iota].
under i: eq_big; [rewrite adnnC; over | rewrite adnnC; over | cbv beta iota].
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* Rely on a new tactic unify_helper that workarounds the fact
[apply Under.under_done] cannot unify (?G i...) with (expr i...) in
[|- @Under T (expr i...) (?G i...)]
when expr is a constant expression, or has more than one var (i...).
Idea: massage the expression with Ltac to obtain a beta redex.
* Simplify test-suite/ssr/under.v by using TestSuite.ssr_mini_mathcomp
and add a test-case [test_big_andb].
* Summary of commands to quickly test [under]:
$ cd .../coq
$ make plugins/ssr/ssreflect.vo plugins/ssr/ssrfun.vo plugins/ssr/ssrbool.vo
$ cd test-suite
$ touch prerequisite/ssr_mini_mathcomp.v
$ make
$ emacs under.v
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Both can be use to close the "under goals", in rewrite style or in
closing-tactic style.
Contrarily to the previous implementation that assumed
"over : forall (T : Type) (x : T), @Under T x x <-> True"
this new design won't require the Setoid library.
Extend the test-suite (in test-suite/ssr/under.v)
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Rename the bound variables of the last (lambda) argument of the redex
w.r.t. the varnames specified by the user.
Co-authored-by: Erik Martin-Dorel <erik.martin-dorel@irit.fr>
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Still to do: renaming the bound variables afterwards
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