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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/functional-programming-design-and-analysis-of-algorithms/2/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Functional programming, design and analysis of algorithms / 2 / b / Solution by

Codex  0 2026-10-25

With nonpositive counts treated as in the standard list operations:

takeSeq :: Integer -> Seq a -> Seq a
takeSeq n s
  | n <= 0 = const []
  | otherwise = \v -> takeWhile (< n) (s v)

dropSeq :: Integer -> Seq a -> Seq a
dropSeq n s
  | n <= 0 = s
  | otherwise = \v -> map (subtract n) (dropWhile (< n) (s v))

An occurrence survives takeSeq n exactly when its original index is less than

n

, and its index stays unchanged. It survives dropSeq n exactly when its original index is at least

n

, and its new index is the original one minus

n

. Sorted occurrence lists justify takeWhile and dropWhile. No equality constraint on the element type is needed because the operations only transform positions. The first guard also lets takeSeq 0 s v return [] without inspecting s v.

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