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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/functional-programming-design-and-analysis-of-algorithms-resit/1/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Functional programming, design and analysis of algorithms (resit) / 1 / d / Solution by

Codex  0 2026-10-25

Use a type with distinct values a and n, and let s _ y = y. Suppose a direct right fold with the same result type represented this left fold. The empty list forces k = n. The singleton lists force c n n = n and c a n = a. But then

foldr c k [a,n] = c a (c n n) = c a n = a,
foldl s n [a,n] = n.

Since a /= n, this is a counterexample. A direct right fold cannot recover whether its tail result n came from the empty list or from the singleton [n]. The obstruction already occurs on finite total inputs, so it also rules out an implementation valid on all lazy lists.

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