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perf(CategoryTheory): let aesop_cat attempt rfl before aesop #21330

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@JovanGerb JovanGerb commented Feb 1, 2025

This PR modifies the aesop_cat tactic so that it tries a proof by rfl before doing the more expensive aesop tactic.

This ran into a problem that is discussed here: https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/changing.20a.20proof.20can.20break.20a.20later.20proof/near/497313462

The issue is that a proof by rfl doesn't have the same type as the expected type. Starting the proof with refine id ?_` is a trick to make sure that the type matches exactly with the expected type.


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@JovanGerb JovanGerb marked this pull request as draft February 1, 2025 20:27
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PR summary b5bc210b0a

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.CategoryTheory.Category.Basic 262 263 +1 (+0.38%)
Mathlib.CategoryTheory.DiscreteCategory 302 303 +1 (+0.33%)
Mathlib.CategoryTheory.Monoidal.Mod_ 463 464 +1 (+0.22%)
Mathlib.Algebra.Homology.DifferentialObject 652 653 +1 (+0.15%)
Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover 968 969 +1 (+0.10%)
Import changes for all files
Files Import difference
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@github-actions github-actions bot added the t-category-theory Category theory label Feb 1, 2025
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Here are the benchmark results for commit 11db251.
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Here are the benchmark results for commit 775ba62.
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Here are the benchmark results for commit 55aba30.
There were significant changes against commit 213a36c:

  Benchmark                                                                Metric         Change
  ==============================================================================================
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+ ~Mathlib.Topology.Order.Category.AlexDisc                                instructions   -62.7%
+ ~Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts               instructions   -10.2%
+ ~Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover                    instructions   -20.5%
+ ~Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections           instructions   -37.1%

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github-actions bot commented Feb 2, 2025

File Instructions %
build -2104.144⬝10⁹ (-1.37%)
2 files, Instructions +7.0⬝10⁹
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File Instructions %
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2 files, Instructions +3.0⬝10⁹
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13 files, Instructions +1.0⬝10⁹
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38 files, Instructions -3.0⬝10⁹
File Instructions %
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15 files, Instructions -4.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks -3.282⬝10⁹ (-2.62%)
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Mathlib.CategoryTheory.Grothendieck -3.719⬝10⁹ (-3.64%)
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Mathlib.Algebra.Homology.ShortComplex.SnakeLemma -3.834⬝10⁹ (-3.88%)
Mathlib.Algebra.Category.MonCat.Adjunctions -3.881⬝10⁹ (-32.85%)
Mathlib.CategoryTheory.Monad.EquivMon -3.896⬝10⁹ (-9.19%)
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13 files, Instructions -5.0⬝10⁹
File Instructions %
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Mathlib.Topology.Sheaves.CommRingCat -4.289⬝10⁹ (-6.15%)
Mathlib.Algebra.Category.Ring.Adjunctions -4.313⬝10⁹ (-26.52%)
Mathlib.CategoryTheory.Localization.Resolution -4.422⬝10⁹ (-18.68%)
Mathlib.Algebra.Homology.DifferentialObject -4.523⬝10⁹ (-8.14%)
Mathlib.CategoryTheory.Category.TwoP -4.561⬝10⁹ (-41.59%)
Mathlib.CategoryTheory.Limits.Opposites -4.610⬝10⁹ (-4.87%)
Mathlib.Algebra.Category.Grp.Basic -4.647⬝10⁹ (-10.89%)
Mathlib.CategoryTheory.Sites.SheafOfTypes -4.713⬝10⁹ (-18.76%)
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18 files, Instructions -6.0⬝10⁹
File Instructions %
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Mathlib.Topology.Category.LightProfinite.Basic -5.237⬝10⁹ (-13.40%)
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Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal -5.462⬝10⁹ (-18.41%)
Mathlib.Order.Category.CompleteLat -5.550⬝10⁹ (-37.13%)
Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric -5.558⬝10⁹ (-41.31%)
Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat -5.582⬝10⁹ (-10.91%)
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Mathlib.CategoryTheory.MorphismProperty.Concrete -5.745⬝10⁹ (-44.49%)
Mathlib.CategoryTheory.Functor.Category -5.788⬝10⁹ (-19.36%)
Mathlib.AlgebraicTopology.SimplicialSet.Horn -5.825⬝10⁹ (-26.45%)
Mathlib.CategoryTheory.Endofunctor.Algebra -5.938⬝10⁹ (-9.15%)
Mathlib.Topology.Category.TopCommRingCat -5.974⬝10⁹ (-44.82%)
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10 files, Instructions -7.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Limits.Shapes.Types -6.443⬝10⁹ (-12.15%)
Mathlib.Topology.Sheaves.Alexandrov -6.448⬝10⁹ (-21.74%)
Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Strong -6.520⬝10⁹ (-13.57%)
Mathlib.Topology.Category.TopCat.Adjunctions -6.584⬝10⁹ (-59.08%)
Mathlib.CategoryTheory.Category.Preorder -6.820⬝10⁹ (-48.70%)
Mathlib.Order.Category.LinOrd -6.933⬝10⁹ (-47.33%)
5 files, Instructions -8.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Products.Associator -7.401⬝10⁹ (-53.07%)
Mathlib.CategoryTheory.Action.Limits -7.709⬝10⁹ (-14.95%)
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4 files, Instructions -9.0⬝10⁹
File Instructions %
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Mathlib.Algebra.Homology.Functor -8.477⬝10⁹ (-52.61%)
Mathlib.Order.Category.FinPartOrd -8.520⬝10⁹ (-59.50%)
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7 files, Instructions -10.0⬝10⁹
File Instructions %
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Mathlib.Algebra.Category.AlgebraCat.Monoidal -9.121⬝10⁹ (-30.62%)
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Mathlib.Topology.Sheaves.LocalPredicate -9.578⬝10⁹ (-37.59%)
Mathlib.Order.Category.BddOrd -9.645⬝10⁹ (-55.85%)
Mathlib.Order.Category.BddDistLat -9.768⬝10⁹ (-49.28%)
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7 files, Instructions -11.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Action.Basic -10.283⬝10⁹ (-17.81%)
Mathlib.Algebra.Category.ModuleCat.ChangeOfRings -10.362⬝10⁹ (-3.30%)
Mathlib.CategoryTheory.Limits.Lattice -10.525⬝10⁹ (-46.34%)
Mathlib.Algebra.Homology.Augment -10.632⬝10⁹ (-16.55%)
Mathlib.CategoryTheory.Functor.Trifunctor -10.718⬝10⁹ (-6.30%)
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5 files, Instructions -12.0⬝10⁹
File Instructions %
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Mathlib.Topology.Order.Category.AlexDisc -11.402⬝10⁹ (-62.73%)
Mathlib.Algebra.Category.ModuleCat.Sheaf -11.554⬝10⁹ (-28.68%)
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Mathlib.Order.Category.BoolAlg -11.871⬝10⁹ (-43.33%)
4 files, Instructions -13.0⬝10⁹
File Instructions %
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Mathlib.RepresentationTheory.Rep -12.520⬝10⁹ (-9.61%)
Mathlib.Algebra.Homology.Opposite -12.940⬝10⁹ (-18.74%)
Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer -12.963⬝10⁹ (-14.12%)
9 files, Instructions -14.0⬝10⁹
File Instructions %
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Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf -13.168⬝10⁹ (-16.74%)
Mathlib.Algebra.Category.Grp.EquivalenceGroupAddGroup -13.179⬝10⁹ (-53.68%)
Mathlib.Algebra.Category.ModuleCat.Basic -13.241⬝10⁹ (-15.92%)
Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory -13.350⬝10⁹ (-8.86%)
Mathlib.CategoryTheory.Limits.ExactFunctor -13.444⬝10⁹ (-25.09%)
Mathlib.AlgebraicTopology.SimplicialSet.Nerve -13.545⬝10⁹ (-70.97%)
Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_ -13.576⬝10⁹ (-43.85%)
Mathlib.Geometry.RingedSpace.LocallyRingedSpace -13.976⬝10⁹ (-24.61%)
File Instructions %
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Mathlib.Order.Category.NonemptyFinLinOrd -15.933⬝10⁹ (-50.32%)
2 files, Instructions -17.0⬝10⁹
File Instructions %
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Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence -16.317⬝10⁹ (-15.91%)
6 files, Instructions -18.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Bicategory.Coherence -17.399⬝10⁹ (-14.26%)
Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic -17.468⬝10⁹ (-23.08%)
Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover -17.498⬝10⁹ (-20.48%)
Mathlib.CategoryTheory.Monad.Products -17.570⬝10⁹ (-28.94%)
Mathlib.Order.Category.FinBoolAlg -17.740⬝10⁹ (-48.27%)
File Instructions %
Mathlib.Algebra.Category.Grp.Adjunctions -18.223⬝10⁹ (-54.44%)
2 files, Instructions -21.0⬝10⁹
File Instructions %
Mathlib.CategoryTheory.Products.Basic -20.67⬝10⁹ (-22.73%)
Mathlib.Condensed.Discrete.Colimit -20.456⬝10⁹ (-16.49%)
2 files, Instructions -22.0⬝10⁹
File Instructions %
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Mathlib.CategoryTheory.Limits.Constructions.Over.Products -21.660⬝10⁹ (-26.00%)
File Instructions %
Mathlib.Topology.Category.TopCat.OpenNhds -22.226⬝10⁹ (-65.41%)
Mathlib.Algebra.Category.ModuleCat.Presheaf -23.322⬝10⁹ (-8.91%)
4 files, Instructions -25.0⬝10⁹
File Instructions %
Mathlib.CategoryTheory.Square -24.111⬝10⁹ (-33.41%)
Mathlib.CategoryTheory.Limits.ConeCategory -24.171⬝10⁹ (-27.80%)
Mathlib.Algebra.Category.ModuleCat.Pseudofunctor -24.717⬝10⁹ (-51.52%)
Mathlib.CategoryTheory.Elements -24.965⬝10⁹ (-35.30%)
3 files, Instructions -26.0⬝10⁹
File Instructions %
Mathlib.CategoryTheory.Comma.Over -25.161⬝10⁹ (-8.20%)
Mathlib.CategoryTheory.Comma.Basic -25.427⬝10⁹ (-13.02%)
Mathlib.CategoryTheory.Limits.Cones -25.979⬝10⁹ (-8.24%)
File Instructions %
Mathlib.CategoryTheory.Subobject.Types -26.885⬝10⁹ (-57.45%)
Mathlib.CategoryTheory.Comma.Presheaf.Basic -27.305⬝10⁹ (-18.34%)
2 files, Instructions -29.0⬝10⁹
File Instructions %
Mathlib.Topology.Category.TopCat.Opens -28.709⬝10⁹ (-54.38%)
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor -28.932⬝10⁹ (-56.27%)
File Instructions %
Mathlib.Condensed.Discrete.Module -31.950⬝10⁹ (-27.92%)
Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections -33.41⬝10⁹ (-37.07%)
Mathlib.CategoryTheory.Triangulated.Opposite.Triangle -34.196⬝10⁹ (-25.19%)
Mathlib.CategoryTheory.Monoidal.Internal.Types -36.565⬝10⁹ (-68.71%)
Mathlib.Condensed.Discrete.LocallyConstant -37.208⬝10⁹ (-49.49%)
Mathlib.CategoryTheory.Functor.Currying -42.715⬝10⁹ (-38.92%)
Mathlib.CategoryTheory.Monoidal.Internal.Module -50.723⬝10⁹ (-35.34%)
Mathlib.CategoryTheory.Limits.Final -51.135⬝10⁹ (-27.49%)
Mathlib.AlgebraicGeometry.Modules.Tilde -52.875⬝10⁹ (-38.91%)
Mathlib.CategoryTheory.Limits.Shapes.Biproducts -53.141⬝10⁹ (-19.28%)
Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward -54.458⬝10⁹ (-42.72%)
Mathlib.AlgebraicTopology.SimplicialObject.Basic -56.709⬝10⁹ (-26.65%)
Mathlib.CategoryTheory.Comma.StructuredArrow.Basic -63.465⬝10⁹ (-19.95%)
Mathlib.AlgebraicTopology.SimplicialNerve -86.948⬝10⁹ (-63.86%)
CI run

@joelriou joelriou added the t-meta Tactics, attributes or user commands label Feb 2, 2025
@grunweg
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grunweg commented Feb 2, 2025

Thanks for trying this; the gains looks impressive! I took a look already and have a few comments - which maybe you were intending to address all along. In case one of them is new, let me share them here:

  • Would you like to split out the unused variable removal and the @simp un-tagging? I'll approve the former change immediately.
  • Can you say something about why the refine id ?_ change is necessary? (Both in the PR description and code, say.)
  • Can you make the same change to aesop_cat?, please?

@JovanGerb
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One question I have is whether this is the right solution, or if this is something that can be improved in aesop internally.

@grunweg
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grunweg commented Feb 2, 2025

Good question! @JLimperg Can you comment on the above question: would it be useful to have an "easy pre-pass" in aesop, trying proofs like "rfl" first, before running all of aesop? This PR does this for the auto-params in category theory, with dramatic effects.

@JLimperg
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JLimperg commented Feb 3, 2025

The most natural way to do this would be to make rfl a high-priority (low-penalty) Aesop normalisation rule. So something like

add_aesop_rules norm -10 (rule_sets := [CategoryTheory]) (by rfl)

This will make Aesop try rfl before most other rules, in particular simp.

However, it'll also retry rfl on each normalisation round, which is not ideal. Aesop used to have an option to use a rule at most n times (here n = 1), but I removed it at some point because it was unused. I could bring that back.

So for now, the approach used in this PR is probably optimal.

@JLimperg
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JLimperg commented Feb 3, 2025

Btw, might be worth trying with_reducible rfl instead of rfl as well.

@JovanGerb
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I think rfl instead of with_reducible rfl is the right tactic. with_reducible rfl is also used by simp, so any goal that can be closed by with_reducible rfl would be closed by aesop fairly quickly.

@JovanGerb
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To make aesop_cat? work nicely, I've added a macro rfl_cat which gets suggested by aesop_cat? and which is short for refine id ?_; intros; rfl.

@grunweg
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grunweg commented Feb 5, 2025

Thanks for your PR. As far as I can, the two dependent changes have been merged, this PR is documented and seems like a good approach for now. Is there anything else this PR is waiting on?
@JovanGerb If there's nothing else you'd like to do, if you merge master and un-draft this PR, I'll be happy to maintainer merge it.

@JovanGerb
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I think I found an underlying reason today for why the simp calls in category theory were so slow in the first place. I've posted it on Zulip now. So I think it would be better to wait with this PR until that is figured out further.

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5 participants