Have you run it through hlint? What does it say? Let us know if there's anything in hlint's output that's befuddling -- treat it more as a syntax h(l)inter than a syntax (h)linter.

p.s. A note about exposition: consider providing some input & output examples to illustrate what these functions are up to. The preceding paragraphs indicate twisty exceptions and special cases that are hard-going for the casual reader. Which means fewer eyeballs on your email.

p.p.s. Are there any interesting properties of these functions that you could leverage quickcheck on?