Introduce MutableTangent

[oxinabox]

Will close #105

• Move functionality to StructuralTangent
• Add MutableTangent
• Make co-PR to ChainRules.jl to add setindex
• Make more optimal re: stable backing type

[codecov]

Codecov Report

Attention: 7 lines in your changes are missing coverage. Please review.

Comparison is base (6664e8f) 93.91% compared to head (95e63d0) 94.15%.

❗ Current head 95e63d0 differs from pull request most recent head 73b7508. Consider uploading reports for the commit 73b7508 to get more accurate results

Files	Patch %	Lines
src/tangent_types/structural_tangent.jl	94.87%	6 Missing ⚠️
src/tangent_types/abstract_zero.jl	97.22%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #626      +/-   ##
==========================================
+ Coverage   93.91%   94.15%   +0.24%     
==========================================
  Files          15       15              
  Lines         904      976      +72     
==========================================
+ Hits          849      919      +70     
- Misses         55       57       +2     

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[oscardssmith]

This is a pretty big change, but It looks good.

[willtebbutt]

This is cool. Glad to see it added. I've a few things to say about zero_tangent because I'm implemented something similar recently.

[github-actions]

[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

	# TODO: we might be able to do better than this. even without.
	# TODO: we might be able to do better than this. even without.

[willtebbutt]

It might make sense to test that this works for self-referential types c.f. something like this example from the docs. Maybe add a differentiable field of some kind? I'm not entirely sure how this will work -- I'm still trying to figure out how to avoid an infinite-loop in some of my work.

[ToucheSir]

I don't see any mention of self-referential types in the Swift docs on automatic tangent type synthesis, but I imagine they must've run into this so perhaps the implementation could have some clues?

[oxinabox]

Ok this has now been massively overhauled.
Mostly in the zero_tangent code.
Special attention has been paid to achieve type stability where possibly,
and to have correct behavour where the primal has nonconcretely typed fields or where it has
With the intent that we can also use zero_tangent rather than ZeroTangent when we need type stable for literals or other other times we get it from frules if that is the AD's preference.
Doing this kinda sucked but I think i worked all the edge cases out.

However, in the process some things may have been broken.
So the next step will be to fix all those and get CI passing.

I expect MutableTangent will be missing some of the nicer overloads for linear operators etc.,
but those can come later as we find they are needed.

[oxinabox]

zero_tangent should be more or less idempotent.
Anything it returns should also be a valid zero for itself. More or less.
We should have tests for this.

This property, in general, holds for all valid tangent types.
We should document this.

[oscardssmith]

This looks reasonable to me.

[oxinabox]

The error in the projection tests is unrelated to this PR and is fixed in
#645 (by deleting those tests)

[willtebbutt]

This is cool.