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 / a

The test consumes a state and returns Bool; the output function maps a state to an element; and the transition preserves the state type. Hence the most general polymorphic type signature is

unfold :: (s -> Bool) -> (s -> a) -> (s -> s) -> s -> [a]

Equivalently, $\boxed{(\sigma \to \mathrm{Bool})\to (\sigma \to \alpha )\to (\sigma \to \sigma )\to \sigma \to [\alpha ]}$. The state and emitted element can have unrelated types. A list unfold produces the next element from the current state, then advances to a new state.