 The category whose objects are the concrete data structures and whose morphisms are the sequential functions just defined is, however, not cartesian closed, not unexpectedly. This observation (for a simple proof, see Amadio &amp; Curien 1998 (theorem 14.1.12)) prevents the use of this category as a model of PCF. However, it is possible to define for every two concrete data structures \(M,M'\) a new one \(M \to M'\) whose states represent sequential algorithms and which is the exponential object of \(M\) and \(M'\) in a cartesian closed category whose morphisms are sequential algorithms (Curien 1986: sec. 2.5). The generalizations of the model theory of PCF to categorical models allows us to obtain a model of PCF from this new category, even though its morphisms are not functions in the usual set-theoretic sense. It turns out that the sequential algorithm model is not extensional, because there are distinct PCF terms that denote the same continuous function yet represent distinct algorithms. As an example, consider the following two terms, that denote the same function but different algorithms:   \[\begin{aligned} \texttt{lror}(x,y) &amp;= \texttt{if }x\texttt{ then }({\texttt{if }y\texttt{ then }\texttt{tt}  \texttt{ else }x}) \\ &amp;\quad \texttt{ else }({\texttt{if }y\texttt{ then }\texttt{tt}\texttt{ else }\texttt{ff}}) \\ \texttt{rlor}(x,y) &amp;= \texttt{if }y\texttt{ then }({\texttt{if }x\texttt{ then }\texttt{tt}\texttt{ else }y})\\ &amp;\quad \texttt{ else }({\texttt{if } x\texttt{ then }\texttt{tt}\texttt{ else }\texttt{ff}}).     \end{aligned}\]   By suitably introducing error values \(\textit{error}_1,\textit{error}_2\) in the semantics, and enforcing an error-propagation property of the interpretations of terms (thus enlarging the observables of the language), the functions corresponding to the above terms can then be distinguished: clearly, for the interpreting functions \(\textit{lror}\) and \(\textit{rlor}\) we have   \[\begin{aligned}  \textit{lror}(\textit{error}_1,\textit{error}_2) &amp;= \textit{error}_1 &amp;\textit{rlor}(\textit{error}_1,\textit{error}_2) &amp;= \textit{error}_2\end{aligned}\]   which also points to the possibility of proving full abstraction of this (non-standard) extensional model with respect to an extension of PCF with control operators (Cartwright, Curien, &amp; Felleisen 1994).