 The standard interpretation of PCF consists of a family of cpos \(D^\sigma\), for each type \(\sigma\), where \(D^\texttt{num}= {\mathbb{N}}_{\bot}\) and \(D^\texttt{bool}= {\mathbb{B}}_{\bot}\), \(D^{\sigma \to \tau} = [D^\sigma \to D^\tau]\) and the PCF constants have the natural interpretation as strict continuous functions of the appropriate type, for example \(\texttt{cond}: {\mathbb{B}}_{\bot} \to {\mathbb{N}}_{\bot} \to {\mathbb{N}}_{\bot} \to {\mathbb{N}}_{\bot}\) is interpreted as:   \[\textit{cond}(b)(x)(y) = \left\{    \begin{array}{ll}                             x&amp;\text{if \(b = \texttt{tt}\)}\\                             y &amp;\text{if \(b = \texttt{ff}\)}\\                             \bot    &amp;\text{if \(b = \bot\),}                                 \end{array}                 \right.\]   Furthermore, the operator \({\mathtt{Y}(\cdot)}\) is interpreted as the continuous functional \({\texttt{fix}(\cdot)}\) at the appropriate type. This is the interpretation considered in Scott 1969b) and Milner 1973.