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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/a/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 / a / Solution by

Codex  0 2026-10-31

The map function changes each element of a list while preserving its order and length. List concatenation removes one level of nesting. Currying changes a function on a pair into a function taking its two arguments separately; uncurrying reverses this conversion:

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

concat :: [[a]] -> [a]
concat []       = []
concat (xs:xss) = xs ++ concat xss

curry :: ((a, b) -> c) -> a -> b -> c
curry f x y = f (x, y)

uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry f (x, y) = f x y

These polymorphic type signatures impose no numerical, equality or ordering constraints: the definitions only inspect list or pair structure and apply a supplied function. In particular,

curry (f) x y = f (x, y), uncurry (g) (x, y) = g x y .

(1)

The recursive equations describe the two possible list constructors, so they also explain how the empty case terminates each finite computation.

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