Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Functional programming, design and analysis of algorithms (resit) / 4 / b

The standard Haskell definition and principal type are

iterate :: (a -> a) -> a -> [a]
iterate f x = x : iterate f (f x)

Under lazy evaluation, this produces successive states $x,f(x),f(f(x)),\dots$ as demanded. An infinite spine does not require all elements to be evaluated at once; productivity still depends on the demanded computations terminating.