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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/1/b/i/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 / 1 / b / i / Solution by

Codex  0 2026-10-31

In the type signature map :: (u -> v) -> [u] -> [v], the supplied function is concat :: [[a]] -> [a]. Type inference therefore identifies u with [[a]] and v with [a]. Consequently,

map concat :: [[[a]]] -> [[a]]

Thus

[[[α]]] \to [[α]]

is the principal type. For example, map concat [[[1],[2,3]],[[4],[]]] gives [[1,2,3],[4]]: it concatenates each inner group, preserving the outermost grouping.

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