 Solution

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/ii/solution

Commutativity of the element binary operation does not remove the ordering of a list comprehension. For ordinary addition, take xs = [1,2] and ys = [10,20]. Then

[1, 2] X_{+} [10, 20] = [11, 21, 12, 22], [10, 20] X_{+} [1, 2] = [11, 12, 21, 22] .

The middle entries occur in opposite orders. Hence

False: the lifted operation need not be commutative.

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