The extent of my experience on the topic is in half-comprehending hobbyist's awe and the inclusion of okmij on my "personal heroes and demigods" list. The only word I could half-heartedly associate with this structure is the incredibly lame "hylomorphism"... which actually kinda generally expresses the pattern of much of computing. It's 5 AM and I'm going to sleep, but I'll leave you with the the most plausible leaves of a very brief search towards finding some recognized formal name for this structure:

http://blog.sigfpe.com/2009/07/monad-for-combinatorial-searc... http://spivey.oriel.ox.ac.uk/mike/search-jfp.pdf http://www.cs.au.dk/~gerth/papers/jfp96.pdf

If you really don't like yourself, try digging here:

http://hackage.haskell.org/packages/archive/pointless-haskel... http://comonad.com/reader/2009/recursion-schemes/