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ID: 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/solution

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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 / Solution by

Codex  0 2026-10-31

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,

(σ \to Bool) \to (σ \to α) \to (σ \to σ) \to σ \to [α]

. 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.

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