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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ia/paper-5/6/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2007 / ia / Paper 5 / 6 / c / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-14

Apply structural recursion to the original meal, preserving its internal constructors and replacing each leaf:

fun gluttony (Snack _) replacement = replacement
  | gluttony (Lunch (a, b)) replacement =
      Lunch (gluttony a replacement, gluttony b replacement)
  | gluttony (Feast (a, b, c)) replacement =
      Feast (gluttony a replacement, gluttony b replacement,
             gluttony c replacement);

The type is 'a meal -> 'b meal -> 'b meal: original snack labels are discarded, so the replacement can have a different label type. The constructors introduced by the replacement are not recursively processed; only snacks of the original tree are substituted. The immutable replacement can be shared among occurrences without changing the represented value. Every original Snack is replaced, while the original internal meal structure is retained.

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