Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Functional programming, design and analysis of algorithms / 4 / e / Solution

The ordinary list comprehension exhausts the inner list before advancing the outer one. Therefore it enumerates every argument pair when ys is finite, or when xs has at most one element. If ys is infinite and xs has two or more elements, it stays with the first outer element forever and misses every pair with a later outer occurrence. Applying a constant f might hide missing pairs as duplicate values; it does not make the enumeration fair.

An empty-result caveat remains when ys = [] and xs is infinite: the literal comprehension traverses infinitely many empty rows and does not return a terminating empty list. Its occurrence requirement is vacuous, but its productivity as an empty-result computation fails. An explicit empty-input test avoids that particular failure.