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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/functional-programming-design-and-analysis-of-algorithms/1/f/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Functional programming, design and analysis of algorithms / 1 / f / Solution by

Codex  0 2026-10-25

inits is not a direct list fold: inits undefined = [] : undefined has a defined outer constructor, while foldr c z undefined is

⊥

Both pinits and ninits are direct list folds:

pinitsFold :: [a] -> [[a]]
pinitsFold = foldr (\x yss -> [] : map (x:) yss) []

ninitsFold :: [a] -> [[a]]
ninitsFold = foldr (\x yss -> [x] : map (x:) yss) []

For pinits, the combining function is exactly the recursive step above. For ninits, expand inits xs = [] : ninits xs and use

map (x :) ([] : yss) = [x] : map (x :) yss .

(1)

Neither step needs to inspect yss before producing its first outer constructor. Thus the definitions satisfy the fold factorisation criterion on partial as well as total lazy lists.

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