I'm going to argue there are no special cases that don't fit.
the set of all possible for loops (no side effects) \subset the set of all possible hylomorphisms (generalizations of map reduce) \subset of all possible recursions.
That's why I wanted to see a real example, because of mathematically they can't exist.
As for accumulators over loops those can be usually handled via. a fold providing the reduction operation is associative. The initial and final state never present a problem.
I'll agree I was considering lazy part of functional. At this point I think purity allows for laziness and laziness demonstrates a lot of the advantages of purity. Otherwise you are backed to mixed paradigm which I dealt with other places in this thread. As for lazy with large amounts of data, Hadoop is lazy. So I'm not sure what you are saying.