mekso k-ary operator, for natural k and 1 < k < 5: ordered input (f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m=0, or g left-composed with the same if m=1.

S="ro" is default case (making this operator binary or ternary); S must be a set or "ro" (no bare integers); m = 0 is the default case (making this operator binary or ternary); use "mau'au" and "zai'ai" in order to quote f and g each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form (x_{1, x}; thus, notationally, a concrete output of this function, as applied to the aforementioned concrete input tuple, is of form (fa'ai'ai(f, g, S, m))(x_{1, x}. For example, maintaining this notation, if S="ro" and m=0, then the output is f(g(x_{1), g(x}; if S = Set(1, 3, 23) and m=0, then the output is f(g(x_{1), x}; vel sim. If h is the function output by this expression when m=0, then for the same inputs (ignoring m), g \circ h is the function output by the same expression but with m=1. Obviously, in order to be meaningful, the output of each step along the way must be defined. If S is the empty set and g is defined, then the output is just the function f if m=0. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when S or m is omitted (as being equal to the default "ro" or 0 resp.).