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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/functional-programming-design-and-analysis-of-algorithms/2/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Functional programming, design and analysis of algorithms / 2 / d / Solution by

Codex  0 2026-10-25

Both versions preserve left-to-right leaf order:

flatten :: Tree a -> [a]
flatten (One x)   = [x]
flatten (Two l r) = flatten l ++ flatten r

flattenFold :: Tree a -> [a]
flattenFold = foldTree (\x -> [x]) (++)

The tree fold replaces each leaf by a singleton list and each internal node by list concatenation. The defining equations of flattenFold are consequently those of flatten, proving their equality by structural induction.

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