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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/2/e/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) / 2 / e / Solution by

Codex  0 2026-10-25

A tree fold replaces each constructor by its interpretation:

foldTree :: (b -> [a] -> b -> b) -> b -> Tree a -> b
foldTree combine zero Empty = zero
foldTree combine zero (Node left equal right) =
  combine (foldTree combine zero left)
          equal
          (foldTree combine zero right)

fromTreeFold :: Tree a -> [a]
fromTreeFold = foldTree (\left equal right -> left ++ equal ++ right) []

Induction on the finite tree shows equality with fromTree: the empty tree produces the empty output, and the combining function concatenates the two correctly flattened children around the node's bucket. The result type

b

is independent of the key type; other choices can compute a size or another summary using the same structural recursion.

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