 Given any set \(X\), we write \(X_{\bot}\) for the set \(X \cup \{ \bot \}\) obtained by adding a new element \(\bot\). It is natural to order the elements of \(X_{\bot}\) according to their amount of information, by setting for \(x,y \in X_{\bot}\),   \[\begin{aligned} x \sqsubseteq y &amp;\Longleftrightarrow (x = \bot \ \text{ or } \   x = y).\end{aligned}\]  Partially ordered structures of the form \(X_\bot\) are called flat domains, among which we have \(\texttt{bool}= {\{ {\textit{tt}},{\textit{ff}}\}}_\bot\) and \(\texttt{num}= {\mathbb{N}}_\bot\), that will be used to interpret the ground types of PCF.