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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/functional-programming-design-and-analysis-of-algorithms/4/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Functional programming, design and analysis of algorithms / 4 / c / Solution by

Codex  0 2026-10-31

A tree fold replaces Empty by a seed and Node by a combining function. The combining function receives the already folded left subtree, the node's label and the already folded right subtree:

foldSTree :: (b -> a -> b -> b) -> b -> STree a -> b
foldSTree combine empty Empty = empty
foldSTree combine empty (Node left x right) =
  combine (foldSTree combine empty left)
          x
          (foldSTree combine empty right)

Its polymorphic type signature is

(β \to α \to β \to β) \to β \to STree α \to β .

(1)

The result type need not be the label type: it may be a list, a number or another structure. No ordering constraint is needed because this tree fold follows constructors without comparing labels.

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