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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/b/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 / b / Solution by

Codex  0 2026-10-25

The empty representation is nowhere present; prepending shifts all old positions by one:

nil' :: List a
nil' = List (\_ -> Nothing)

cons' :: a -> List a -> List a
cons' x (List f) = List query
  where
    query i
      | i < 0     = Nothing
      | i == 0    = Just x
      | otherwise = f (i-1)

For a represented length

m

, cons' represents length

m + 1

, provided that length is representable. Index zero is the new head and each later valid index asks for the preceding old position. The no-holes invariant is preserved. No conventional list is built by either constructor.

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