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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/functional-programming-design-and-analysis-of-algorithms/1/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Functional programming, design and analysis of algorithms / 1 / a / Solution by

Codex  0 2026-10-31

The principal types and definitions are:

map :: (a -> b) -> [a] -> [b]
map _ []     = []
map f (x:xs) = f x : map f xs

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr _ e []     = e
foldr f e (x:xs) = f x (foldr f e xs)

(.) :: (b -> c) -> (a -> b) -> a -> c
(.) f g x = f (g x)

The map function preserves the list shape while changing element type from a to b. The right fold replaces the empty list by e and each constructor by f, whose second argument and result therefore share the accumulator type b. Function composition requires the output type of g to agree with the input type of f. No Haskell type class constraints arise: these definitions never compare elements or perform arithmetic on them.

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