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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/functional-programming-data-structures-and-algorithms-procedural-programming-and-digital-hardware/2/a/iii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Functional programming, data structures and algorithms, procedural programming, and digital hardware / 2 / a / iii / Solution by

Codex  0 2026-10-31

Idempotence concerns applying an operation to the same whole value. It says more than saying that the equal-entry pairs are unchanged. Choose the idempotent binary operation min. Then

[1, 2] X_{m i n} [1, 2] = [1, 1, 1, 2] \neq = [1, 2] .

(1)

More generally, a finite list of length

m

paired with itself produces

m^{2}

entries, so length alone contradicts idempotence when

m > 1

. Therefore

False: the lifted operation need not be idempotent.

(2)

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