refactor(Algebra/Quaternion): intermediate Module instance

[YaelDillies]

This Module instance allows me to not ungeneralise the NoZeroSMulDivisors R ℍ[R,c₁,c₂,c₃] in #30563.

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[github-actions]

PR summary 0231ea944e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ addEquivTuple
+ coe_addEquivTuple
+ coe_symm_addEquivTuple
+ instance : Add ℍ[R,c₁,c₂,c₃] := fast_instance% (equivProd c₁ c₂ c₃).add
+ instance : Neg ℍ[R,c₁,c₂,c₃] := fast_instance% (equivProd c₁ c₂ c₃).Neg
+ instance : SMul S ℍ[R,c₁,c₂,c₃] := fast_instance% (equivProd ..).smul _
+ instance : Sub ℍ[R,c₁,c₂,c₃] := fast_instance% (equivProd c₁ c₂ c₃).sub
+ instance : Zero ℍ[R,c₁,c₂,c₃] := fast_instance% (equivProd c₁ c₂ c₃).zero
+ instance [Monoid S] [MulAction S R] : MulAction S ℍ[R,c₁,c₂,c₃]
+ instance [Monoid S] [MulAction S R] : MulAction S ℍ[R]
+ instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂,c₃] := (equivTuple ..).smulCommClass ..
+ instance [Semiring S] [AddCommGroup R] [DistribMulAction S R] : DistribMulAction S ℍ[R,c₁,c₂,c₃]
+ instance [Semiring S] [AddCommGroup R] [Module S R] : Module S ℍ[R,c₁,c₂,c₃]
+ instance [Semiring S] [DistribMulAction S R] : DistribMulAction S ℍ[R]
+ instance [Semiring S] [Module S R] : Module S ℍ[R]
- instance : Add ℍ[R,c₁,c₂,c₃]
- instance : Neg ℍ[R,c₁,c₂,c₃] := ⟨fun a => ⟨-a.1, -a.2, -a.3, -a.4⟩⟩
- instance : SMul S ℍ[R,c₁,c₂,c₃] where smul s a := ⟨s • a.1, s • a.2, s • a.3, s • a.4⟩
- instance : Sub ℍ[R,c₁,c₂,c₃]
- instance : Zero ℍ[R,c₁,c₂,c₃] := ⟨⟨0, 0, 0, 0⟩⟩
- instance [SMulCommClass S T R] : SMulCommClass S T ℍ[R,c₁,c₂,c₃]

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[eric-wieser]

Can you add a sentence in the PR description explaining what motivated these?

[eric-wieser]

Doesn't this produce a worse term?

[YaelDillies]

Sure, but the simp lemmas are just the same as before, so that should be no difference

[eric-wieser]

In terms of unification I think the previous approach was better.

[YaelDillies]

But unification with what? With other instances? They are all like that now

[eric-wieser]

Are you sure? Can you show me the effect of #print on the AddCommGroup instance before and after this line being changed?

[YaelDillies]

This is not possible. fast_instance% complains about the data fields not matching up to some transparency

[eric-wieser]

Ah, that's useful information! I was hoping it would use a higher level of transparency here.

In that case, I think it would be best to define things via the Function.Injective constructors. One argument for why this new zero instance is bad is that at runtime it's now a bunch of if statements to index a vector, rather than a hard-coded zero.

[YaelDillies]

No actually it is not using vectors. It used to be, because I was using equivTuple : _ \equiv (Fin 4 \r R), but I am now using equivProd : _ \equiv R \times R \times R \times R... unless you're claiming this too is bad at runtime?

[eric-wieser]

Ah, I missed that! Indeed equivProd is less bad, but still not as good as the direct constructor.

[YaelDillies]

Bad enough that I should use Function.Injective.foo? I was quite happy that I finally got to use the TransferInstance files!