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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/functional-programming-design-and-analysis-of-algorithms/4/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Functional programming, design and analysis of algorithms / 4 / a / Solution by

Codex  0 2026-10-31

The most general polymorphic type signatures and recursive definitions are:

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

infixr 5 ++
(++) :: [a] -> [a] -> [a]
[]     ++ ys = ys
(x:xs) ++ ys = x : (xs ++ ys)

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

The right fold replaces constructors by a supplied step and seed; list concatenation replaces the end of its first argument by its second; flattening concatenates each inner list. In particular,

concat = foldr (+ +) [], x s + + ys = foldr (:) ys x s .

(1)

The right fold allows different element and accumulator types; the list concatenation operations require one common element type.

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