> But is there a way to somehow construct this modulus automatically for some functions? In a sense. You would end up with https://en.wikipedia.org/wiki/Automa

> But is there a way to somehow construct this modulus automatically for some functions? In a sense. You would end up with https://en.wikipedia.org/wiki/Automatic_differentiation https://en.wikipedia.org/wiki/Automatic_differentiation. The amount of functions you can construct in this manner is massive, along with their derivatives, but it is not an operator that given an arbitrary computable function gives you its derivative.