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Comment by tikhonj | Hacker News Reader

No idea if this book does it, but this seems like a perfect fit for automatic differentiation. You can get a simple implementation of automatic differentiation for one dimension in a small amount of surprisingly clear code, without needing to pull in any dependencies or extraneous concepts.

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That is along the lines of the motivation for my question. Automatic differentiation is such a natural fit with Haskell...

> this seems like a perfect fit for automatic differentiation.

Why?

It would let you represent physical systems as normal Haskell functions and get accurate derivatives "for free". At least in the one-dimensional case it's probably simpler than numeric differentiation while also letting you worry far less about accuracy and stability.

I've never worked this through to a full conclusion, but you could even write it in a way that would let you get symbolic differentiation out of it too.

Yes, if you get to automatic differentiation by overloading your operators to also take a “differential” type, you can further overload them to do symbolic arithmetic and then symbolic differentiation falls out for free.

See https://sritchie.github.io/emmy/src/emmy/differential.html for detail!

Makes sense. I initially thought, that automatic differentiation would be mostly useful for long derivative chains, but of course even for single derivatives it does have advantages.

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