Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Functional programming, design and analysis of algorithms / 3 / b / Solution

Generate the successive states using the Haskell iterate function, keep those before the stopping test becomes true using the Haskell takeWhile function, then map the output function:

unfoldU :: (s -> Bool) -> (s -> a) -> (s -> s) -> s -> [a]
unfoldU p f g = map f . takeWhile (not . p) . iterate g

The missing expression is therefore $\boxed{\mathrm{takeWhile}(\mathrm{not}\circ p)\circ \mathrm{iterate}(g)}$. On states $x,g(x),g^2(x),\dots$, the first state satisfying p is excluded, just as in the recursive list unfold. If no state satisfies p, the result is an infinite lazy list, provided each demanded test, output and transition terminates.