An interesting example is C's pointer-integer addition. p + n == n + p, true, but this is a purely syntactic fact. The actual semantic question of commutativity

An interesting example is C's pointer-integer addition. p + n == n + p, true, but this is a purely syntactic fact. The actual semantic question of commutativity, whether switching the order of the arguments leaves the value unchanged, cannot even be asked of pointer-integer addition since the arguments, having differing types, cannot be switched.