Hacker News Reader

Comment by tobinfricke | Hacker News Reader

Does this implement symbolic algebra/calculus, or is it entirely numerical?

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.

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.

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.

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!

Reply on news.ycombinator.com