 Calligraphic letters \(\mathcal{F},\mathcal{G},\mathcal{H},\ldots\) (or abbreviations like \(\mathcal{Comp}^j_k\)) will be used to denote functionals on \(\mathbb{N}^k \rightarrow \mathbb{N}\)—i.e., operations which map one or more functions of type \(\mathbb{N}^k \rightarrow \mathbb{N}\) (possibly of different arities) to other functions.