For more on monoids, see Brent Yorgey's paper _Monoids: Theme and Variations (Functional Pearl)_ at <http://www.cis.upenn.edu/~byorgey/pub/monoid-pearl.pdf>; (there's also a video of his talk at the Haskell Symposium at <http://www.youtube.com/watch?v=X-8NCkD2vOw>).