Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Functional programming, design and analysis of algorithms / 2 / a / Solution

Swap the components of every ordered pair using a list comprehension:

invert :: [(a, a)] -> [(a, a)]
invert r = [(y, x) | (x, y) <- r]

Thus $\boxed{\mathrm{invert}(R)=R^{-1}}$, the converse relation. Swapping is a bijection, since doing it twice restores the original pair. Therefore distinct input pairs remain distinct; no equality constraint or duplicate removal is necessary.