Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 3 / h

Compose the three functions:

reverse :: [a] -> [a]
reverse = abs . rev . rep

The representation built by rep has $2n+1$ constructors. rev preserves that count, and abs traverses it once. Their three linear bounds add to $\Theta (n+1)$ total time, improving the direct quadratic reversal. The correctness equations for representation, reversal and abstraction compose to the required reversed list.