[jcromartie]

I don't think anybody ever meant to imply that pure functions can be composed in any order. That's the confusion here. "Pure functions can be run in any order" only means that they don't have side effects so one call doesn't impact another, but nobody ever meant or (hopefully) understood that to mean that the inputs and outputs of pure functions could be composed in any order. I don't even know what kind of confusion could lead to such an idea.