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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/2/g/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) / 2 / g / Solution by

Codex  0 2026-10-25

Repeated root removal gives the conventional list:

toList :: List a -> [a]
toList rs
  | null rs   = []
  | otherwise = head rs : toList (tail rs)

The representation interpretation satisfies toList (cons x rs) = x : toList rs; alternatively, structural induction on the number of stored elements proves that each step emits exactly the next preorder traversal value. The output has

n

cons cells, and each step takes constant time, so fully consuming it costs $Θ (n)$ time. No repeated list concatenation is needed.

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