Given a multivariate function $f(x), x \in \Re^n$ for any $n$ and any partition of $x = \bigcup\limits_{i=1}^{m}x_i$, I need
$f(x) = f(x_1, f(x_2, f(x_3, \ldots f(x_m)\ldots)))$
In essence, I have a function that can be appended - meaning, I can compute the function on any subset or partition "recursively" in any order and always get the same final answer. I know that sum, product, min, and max functions all have this property. Is there a general term for this property of functions? Are there some other examples other than the 4 I mentioned that also have this property?