Compute next element of list based on previous elements

Question

I want to define an infinite list where each element is a function of all the previous elements.

So, the n+1th element of the list would be f [x1, x2, ..., xn].

This seems simple, but I cannot seem to get my head around how to do it. Can anyone help?

Answer 1

gen f = xs where xs = map f $ inits xs

Or

gen f = fix $ map f . inits