I found a couple of shortcomings in arity computation, and did
quite a bit of refactoring as a result.  Regrettably, I have
forgotten the details, but I do remember that one part was to
do with the infamous "state hack".  If we're going to use the
state-hack at all, we'd better do it right.

Anyway I think this is an improvement. The comments are more
up to date too, and more voluminous.