1) I have written many functors in my life without describing them as such

2) "Pure assembly" functor doesn't make much sense. Functors, both in the CS and mathematics sense, require the concept of type. Which is absent once you are dealing with stacks and registers. My best idea is something when you have mixed-width registers - eg, say you've got some 128 bit and 256 bit registers. Your functor could apply a mapping from one to the other (and would probably be nothing more than a move instruction with the appropriate sign extension).