Differentiable programming allows one to specify any parametrized function and allows one to use optimization to learn the objective.

There is definitely some need for an EDSL of some sort, but I think a general method is pretty useless. Being able to arbitrarily come up with automatic jacobians for a function isn't really language specific, and usually much better results are obtained using manually calculated jacobians. By starting from scratch you lose all the language theory poured into all the pre-existing languages.

I'm sure there'll be a nice haskell version that works in a much simpler manner. Here's a good start: https://github.com/hasktorch/hasktorch/blob/master/examples/...

I think it's pretty trivial to generalize and extend it beyond multilinear functions.