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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/functional-programming-design-and-analysis-of-algorithms/3/h/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 3 / h / Solution by

Codex  0 2026-10-31

Compose the three functions:

reverse :: [a] -> [a]
reverse = abs . rev . rep

The representation built by rep has

2 n + 1

constructors. rev preserves that count, and abs traverses it once. Their three linear bounds add to $Θ (n + 1)$ total time, improving the direct quadratic reversal. The correctness equations for representation, reversal and abstraction compose to the required reversed list.

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