Pertinent to this thread (though perhaps overkill) is the work of Flajolet et al on (fast) random generation of combinatorial structures for any structure given as a context-free grammar, including Permutation. In particular see http://citeseer.nj.nec.com/flajolet93calculus.html http://citeseer.nj.nec.com/flajolet95computer.html There is a complete implementation of this in Maple as well as a partial port to MuPAD. The Maple version is available at http://pauillac.inria.fr/algo/libraries/libraries.html. Also worth a look is the set of fully documented example applications (available in various formats) at http://pauillac.inria.fr/algo/libraries/autocomb/autocomb.html A translation of the random generation parts of this work to Haskell would not be too difficult, and might in fact be easier than the original, although a full translation would require Template Haskell. Translating the automatic generation of the 'counting' functions would be very challenging [as no one has, as far as I know, yet to create a workable, truly statically-typed computer algebra system!] Jacques