I didn't think of optimising, it's just the first solution I found, and didn't think of asking myself how I could do it differently. If I were to attempt to remove explicit recursion, I think I would use iterate and take to generate the intermediate list.

Isn't this optimising by hand something that GHC will optimise automagically perfectly fine?

Create an intermediate list, run maximum on it, see GHC optimise away the intermediate list. That's what all the build / foldr rewriting is for.

This is less readable ( because more monolithical ), and less optimisable for the compiler ( which might very well be able to optimise better than you can yourself ).

not an issue

Oh, right, thanks a lot.

use let in the definition of next so that the sum is only computed once (the compiler is likely to optimize, but still).