Wednesday, September 17, 2014

expanding the derivative

The arithmetic derivative (discussed here: is cute but perhaps not that important.

However differentiable functors seem important for programming. They take data structures and return a "one hole context" for that structure. This makes it possible to write code that traverses data structures in a very general way.
In, Connor McBride shows how this can involve partial differentiation. Wow.

As we see it is pretty messy in Haskell, even with multifarious optional features enabled. I suspect that this is stuff which is an indicator of whether you've got your programming language design right.

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