Studying Wadler's "Comprehending Monads" and "Theorems for free!",
I've been unable to derive law (iv) and I'm not sure about (iii). Will
appreciate a pointer to similar examples or a massive hint. Here's my
attempt at (iii):
map f . unit x = map f [x]
= [f x]
= unit (f x)
= (unit . f) x
map f . unit = unit .f