linear_algebra.tensor_algebra.grading | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

2a7ceb0e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

6b31d1ee

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.LinearAlgebra.TensorAlgebra.Basic
-import Mathbin.RingTheory.GradedAlgebra.Basic
+import LinearAlgebra.TensorAlgebra.Basic
+import RingTheory.GradedAlgebra.Basic
 
 #align_import linear_algebra.tensor_algebra.grading from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"

6b31d1ee

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.grading
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.TensorAlgebra.Basic
 import Mathbin.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.tensor_algebra.grading from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # Results about the grading structure of the tensor algebra

6b31d1ee

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -30,22 +30,27 @@ open scoped DirectSum
 
 variable (R M)
 
+#print TensorAlgebra.GradedAlgebra.ι /-
 /-- A version of `tensor_algebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `tensor_algebra.graded_algebra`. -/
 def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ℕ, ↥((ι R : M →ₗ[_] _).range ^ i) :=
   DirectSum.lof R ℕ (fun i => ↥((ι R : M →ₗ[_] _).range ^ i)) 1 ∘ₗ
     (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m
 #align tensor_algebra.graded_algebra.ι TensorAlgebra.GradedAlgebra.ι
+-/
 
+#print TensorAlgebra.GradedAlgebra.ι_apply /-
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι R M m =
       DirectSum.of (fun i => ↥((ι R : M →ₗ[_] _).range ^ i)) 1
         ⟨ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩ :=
   rfl
 #align tensor_algebra.graded_algebra.ι_apply TensorAlgebra.GradedAlgebra.ι_apply
+-/
 
 variable {R M}
 
+#print TensorAlgebra.gradedAlgebra /-
 /-- The tensor algebra is graded by the powers of the submodule `(tensor_algebra.ι R).range`. -/
 instance gradedAlgebra :
     GradedAlgebra ((· ^ ·) (ι R : M →ₗ[R] TensorAlgebra R M).range : ℕ → Submodule R _) :=
@@ -67,6 +72,7 @@ instance gradedAlgebra :
       rw [AlgHom.map_mul, ih, lift_ι_apply, graded_algebra.ι_apply R M, DirectSum.of_mul_of]
       exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)
 #align tensor_algebra.graded_algebra TensorAlgebra.gradedAlgebra
+-/
 
 end TensorAlgebra

6b31d1ee

bump to nightly-2023-06-10-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

e13a28eb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.grading
-! leanprover-community/mathlib commit 2a7ceb0e411e459553a303d48eecdbb8553bd7ed
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.GradedAlgebra.Basic
 /-!
 # Results about the grading structure of the tensor algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main result is `tensor_algebra.graded_algebra`, which says that the tensor algebra is a
 ℕ-graded algebra.
 -/

2a7ceb0e

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -23,7 +23,7 @@ namespace TensorAlgebra
 
 variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]
 
-open DirectSum
+open scoped DirectSum
 
 variable (R M)

2a7ceb0e

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -58,10 +58,8 @@ instance gradedAlgebra :
     refine'
       Submodule.pow_induction_on_left' _ (fun r => _) (fun x y i hx hy ihx ihy => _)
         (fun m hm i x hx ih => _) hx
-    · rw [AlgHom.commutes, DirectSum.algebraMap_apply]
-      rfl
-    · rw [AlgHom.map_add, ihx, ihy, ← map_add]
-      rfl
+    · rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
+    · rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
     · obtain ⟨_, rfl⟩ := hm
       rw [AlgHom.map_mul, ih, lift_ι_apply, graded_algebra.ι_apply R M, DirectSum.of_mul_of]
       exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)

2a7ceb0e

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

2a7ceb0e

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -52,7 +52,7 @@ instance gradedAlgebra :
     fun i x => by
     cases' x with x hx
     dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
-    -- porting note: use new `induction using` support that failed in Lean 3
+    -- Porting note: use new `induction using` support that failed in Lean 3
     induction hx using Submodule.pow_induction_on_left' with
     | algebraMap r =>
       rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl

2a7ceb0e

chore: rename induction principle arguments around CliffordAlgebra (#10908)

In order to improve the ergonomics of the induction tactic, this renames the arguments of:

ExteriorAlgebra.induction
TensorAlgebra.induction
CliffordAlgebra.induction
CliffordAlgebra.left_induction
CliffordAlgebra.right_induction
CliffordAlgebra.even_induction
CliffordAlgebra.odd_induction
Submodule.iSup_induction'
Submodule.pow_induction_on_left'
Submodule.pow_induction_on_right'

This is slightly awkward for name-resolution within these induction principles, as the argument names end up clashing with the function they are about. Thankfully, this pain is not transferred to the caller using induction _ using _.

0257770c

Diff

@@ -54,14 +54,14 @@ instance gradedAlgebra :
     dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
     -- porting note: use new `induction using` support that failed in Lean 3
     induction hx using Submodule.pow_induction_on_left' with
-    | hr r =>
+    | algebraMap r =>
       rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
-    | hadd x y i hx hy ihx ihy =>
+    | add x y i hx hy ihx ihy =>
       -- Note: #8386 had to specialize `map_add` to avoid a timeout
       -- (the extra typeclass search seems to have pushed this already slow proof over the edge)
       rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]
       rfl
-    | hmul m hm i x hx ih =>
+    | mem_mul m hm i x hx ih =>
       obtain ⟨_, rfl⟩ := hm
       rw [AlgHom.map_mul, ih, lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.of_mul_of]
       exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)

2a7ceb0e

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -57,7 +57,10 @@ instance gradedAlgebra :
     | hr r =>
       rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
     | hadd x y i hx hy ihx ihy =>
-      rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
+      -- Note: #8386 had to specialize `map_add` to avoid a timeout
+      -- (the extra typeclass search seems to have pushed this already slow proof over the edge)
+      rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]
+      rfl
     | hmul m hm i x hx ih =>
       obtain ⟨_, rfl⟩ := hm
       rw [AlgHom.map_mul, ih, lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.of_mul_of]

2a7ceb0e

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -18,7 +18,7 @@ The main result is `TensorAlgebra.gradedAlgebra`, which says that the tensor alg
 
 namespace TensorAlgebra
 
-variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]
+variable {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
 
 open scoped DirectSum

2a7ceb0e

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.grading
-! leanprover-community/mathlib commit 2a7ceb0e411e459553a303d48eecdbb8553bd7ed
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.TensorAlgebra.Basic
 import Mathlib.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.tensor_algebra.grading from "leanprover-community/mathlib"@"2a7ceb0e411e459553a303d48eecdbb8553bd7ed"
+
 /-!
 # Results about the grading structure of the tensor algebra

2a7ceb0e

feat: port LinearAlgebra.TensorAlgebra.Grading (#4803)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

6f39ffab

`linear_algebra.tensor_algebra.grading` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.Grading`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 474

linear_algebra.tensor_algebra.grading ⟷ Mathlib.LinearAlgebra.TensorAlgebra.Grading

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 474

`linear_algebra.tensor_algebra.grading` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.Grading`

`simp` not firing sometimes