 The operation of composition may be understood as a class of functionals which for each \(j,k \in \mathbb{N}\) takes as inputs \(j\) functions \(g_0, \ldots, g_{j-1}\) of arity \(k\) and a single function \(f\) of arity \(j\) and returns as output the \(k\)-ary function \(h\) which composes these functions in the manner just illustrated. This is described by the following scheme: