I think you've (re)discovered the -morphisms. E.g. anamorphism, catamorphism, hylomorphism. Data structure traversals of various kinds can usually be cast in te

I think you've (re)discovered the -morphisms. E.g. anamorphism, catamorphism, hylomorphism. Data structure traversals of various kinds can usually be cast in terms of these morphisms. As it turns out GHC is usually pretty good at optimizing this kind of thing due to the extremely aggressive inlining which is possible when you know that there are no side effects. It'll often handle compositions of traversals with no sweat. (I think it's sort of all lumped in as "fusion".) EDIT: See tel's comment in this thread. He always understands and explains it much better than I can.