You're absolutely right, it is totally redundant. You could reduce the entire thing even more in size by doing only `D Float Float`, removing the `TypeSynonymIn

You're absolutely right, it is totally redundant. You could reduce the entire thing even more in size by doing only `D Float Float`, removing the `TypeSynonymInstances` pragma and removing the `VectorSpace`, instead using normal Float operations for the derivatives in the Num, Floating and Fractional instances. Further, you can remove the `diff` function entirely if you want, since it's doing something very simple; calling `f` using a `D` instead of a normal Float, Int, etc. So you would simply get the function applied to x and it's derivative by doing `(\x -> x^2) (D 2 1)`, setting the derivative to 1 and x=2. However, I think the Float' and `diff` etc. is at least a little helpful in understanding it. I got it from SPJ's talk, which I linked to in the file. Also, it makes it easier (e.g. in the case of `diff`) to later add onto the Autodiff, for example by implementing reverse mode, Jacobians, etc.