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Suppose that you have a function f: List a -> a such that f is associative and f(x, y, z) === f(x, f(y, z)). Is there a conventional name for this latter property?
Examples of functions with this property are AND, XOR, sum, product, and GCD. Examples of associative functions without this property are NAND and XNOR.
I believe that the property is equivalent to saying that f(xs) === reduce(f, xs).
It looks like this is also equivalent to saying that f is a catamorphism of an associative binary function and its neutral element. Doesn’t exactly roll off the tongue.
(Also, NAND is not associative. My bad.)