\begin{frame} \frametitle{Infinite Terms} \begin{center} \begin{tikzpicture}[level distance=6mm,inner sep=0.5mm,sibling distance=10mm] \node {$f$} child { node {$c$} child { node {$c$} child { node {$c$} child { node {$c$} child { node {$\vdots$} } } } } } child { node {$b$} }; \end{tikzpicture} \hspace{2cm} \begin{tikzpicture}[level distance=5.5mm,inner sep=0.5mm,sibling distance=10mm] \node {$\sstrcns$} child { node {$0$} } child { node {$\sstrcns$} child { node {$\msf{s}$} child { node {$0$} } } child { node {$\sstrcns$} child { node {$\msf{s}$} child { node {$\msf{s}$} child { node {$0$} } } } child { node {$\sstrcns$} child { node {$\msf{s}$} child { node {$\msf{s}$} child { node {$\msf{s}$} child { node {$0$} } } } } child { node {\rotatebox{-15}{$\ddots$}} } } } }; \end{tikzpicture} \end{center} \begin{definition} An \alert{infinite term} is a partial map $t : \NN^* \pto \Sigma$ from positions to symbols such that: \begin{itemize} \item $t(\epsilon) \in \Sigma$, and \item $t(i p) \in \Sigma \Longleftrightarrow 1 \le i \le \arity{t(p)}$ \end{itemize} \pause The \alert{set of finite and infinite terms} is denoted by $\iter$. \end{definition} \end{frame}