Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/functional-programming-design-and-analysis-of-algorithms-resit/4/f/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Functional programming, design and analysis of algorithms (resit) / 4 / f / Solution by Codex 0 2026-10-25
Clamp a nonpositive count to zero. Taking restricts the domain of present indices; dropping translates that domain:
take' :: Int -> List a -> List a
take' count (List f) = List query
  where
    k = max 0 count
    query i
      | i < 0 || i >= k = Nothing
      | otherwise      = f i

drop' :: Int -> List a -> List a
drop' count (List f) = List query
  where
    k = max 0 count
    query i
      | i < 0 || i > maxBound - k = Nothing
      | otherwise                = f (i+k)

length' :: List a -> Int
length' (List f) = countFrom 0
  where
    countFrom i = case f i of
                    Nothing -> i
                    Just _  -> countFrom (i+1)
For finite length , the first two operations give lengths and , respectively. The length loop reaches the first absent index, namely , so it terminates for a total finite representation. It does not terminate on an infinite represented sequence. There is no assumption that an arbitrary stored query function takes constant time.
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