Pointfree style uses composition (among other operators), currying, and partially applied functions, but it refers to something distinct from the sum of those c

Pointfree style uses composition (among other operators), currying, and partially applied functions, but it refers to something distinct from the sum of those concepts/features. Consider the following function of two parameters, written in Haskell/PureScript syntax: f x y = g x (m (h y)) = (g x . m . h) y We can now eta-reduce/partially apply f instead in the definition (which is possible because f is curried by default): f x = g x . m . h If I were using pointfree style at all (which I almost never do), this is where I'd stop. However, you can go the whole hog and strip out all the arguments: = g x . (m . h) = ((. (m . h)) . g) x f = (. (m . h)) . g I've made use of everything you listed, but it's only when you go this far that your function is truly free of "points".