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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/functional-programming-design-and-analysis-of-algorithms/4/b/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Functional programming, design and analysis of algorithms / 4 / b / i / Solution by

Codex  0 2026-10-31

A recursive transpose removes the first column, then transposes the remaining columns:

transpose :: Matrix a -> Matrix a
transpose [] = []
transpose ([] : _) = []
transpose rows = map head rows : transpose (map tail rows)

The internal recursive calls eventually reach rows of length zero, even though the original input has positive dimensions; the second equation handles this terminating case. Rectangularity ensures that the rows become empty together, so no head or tail is applied to an empty row in the third equation. The output is an $n \times m$ matrix with entry $b_{ji} = a_{ij}$ . The element type is unrestricted.

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