 Suppose we now consider an alternative class of initial functions \(In_{\mathbf{IT}}\) containing \(s,\pi^k_i\), the binary coding function \(\langle x,y \rangle\), and the decoding functions \((x)_0\) and \((x)_1\) defined at the end of   Section 2.1.2. (Note that these operate analogously to the first and second production functions \(\pi^2_0\) and \(\pi^2_1\) operating on codes of ordered pairs.) Now define \(\mathbf{IT}\) to be the smallest class of functions containing \(In_{\mathbf{IT}}\) and closed under the functionals \(Op_{\mathbf{IT}} = \{\mathcal{Comp}^i_j,\mathcal{Iter}\}\).