Parent wasn't slightly wrong, you just tunneled in on the signature of the operator function, when the reason why parent comment brought it up was to illustrate that the operator function is not necessarily associative, and that the function signature was meant to suggest the difference in associativity.

You're wrong about the operations possibly not being commutative; as you pointed out, whether the parameter list is (A, B) or (B, A) doesn't really matter, so it doesn't pose a problem.

An example is the subtraction operator: with just two elements, I can change `(a, b) => b - a` to `(b, a) => b - a` with with no difference in result. But there is no way I can write a subtraction function for foldLeft that gives the same results as a foldRight on subtraction in general. That is, I can write op such that a op b = b - a, but not that (a op b) op c = (c - b) - a. Nevertheless, I can still write op such that a op (b op c) = (c - b) - a due to some dual notion of commutativity.