I've been watching this stuff with great interest for a while now. Glad to see it's getting press here. Conal also has a paper on using this approach for automatic differentiation.

https://www.youtube.com/watch?v=MmkNSsGAZhw

http://conal.net/papers/essence-of-ad/

I've been playing around with his approach. It's super cool.

http://www.philipzucker.com/reverse-mode-differentiation-is-...

http://www.philipzucker.com/approximating-compiling-categori...