These blog posts try to explain a bit about what is going on here
http://www.philipzucker.com/reverse-mode-auto-differentiation-kind-like-lens/
http://www.philipzucker.com/reverse-mode-differentiation-is-kind-of-like-a-lens-ii/
http://www.philipzucker.com/bidirectional-applicative-programming-and-automatic-differentation/
http://www.philipzucker.com/neural-networks-with-weighty-lenses-dioptics/
Check out the test directory for some usage examples
A lens is a getter and setter pair a -> (b, (b->a)). This is also the signature of reverse mode automatic differentiation. The function (b->a) is the transposed Jacobian (using a function representation of Matrices. Matrices are a certain kind of Vector -> Vector functions).
We use the standard Lens trick to make these functions composable via (.).
TODO: Higher order derivatives ReExport safe pieces of standard Lens library Try Accelerate GPU lib More Combinators Recursion Schemes