 It is easy to see that the function \(h\) defined by (\ref{pureiter}) from \(g\) in this manner is the \(x^{\mathrm{th}}\)–iterate of \(g\)— i.e., \(g^{x}(y)=_{\mathrm{df}} g(g(\ldots g(y)))\) \(x\)–times with the convention that \(g^0(y) = y\).  We will denote this functional by \(\mathcal{Iter}[g,x]\). The scheme (\ref{pureiter}) thus generalizes (\ref{prex1}) by making the value of base case an argument to \(h\). But it is an apparent restriction of (\ref{prscheme}) in the sense that \(h\) cannot depend on either the recursion variable or additional parameters.