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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/functional-programming-design-and-analysis-of-algorithms-resit/1/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Functional programming, design and analysis of algorithms (resit) / 1 / b / Solution by

Codex  0 2026-10-25

Yes. Define the combining function as follows:

takeP :: (a -> Bool) -> [a] -> [a]
takeP p = foldr step []
  where
    step x rest = if p x then x : rest else []

For the fusion derivation use the identity reconstruction foldr (:) [], take

f = takeWhile p

, and choose the displayed step as

h

. The function

f

is strict in the input list,

f ([]) = []

, and its cons equation is exactly

f (x : x s) = h x (f (x s))

. Fusion gives the implementation. On a false test, step does not demand the folded tail, so the implementation can terminate after a finite list prefix even when the remaining list is infinite or undefined. An undefined predicate result at a tested element makes both definitions undefined.

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