\begin{frame}{Parser Tables}
  \begin{block}{}
    The \emph{parser table} for a context-free grammar 
    is a table with
    \begin{itemize}\setlength{\itemsep}{0pt}
      \item columns indexed by terminals $T \cup \{\$\}$,
      \item rows indexed by variables $V$, 
    \end{itemize}
    At place $[a \in T \cup \{\$\},B \in V]$ it contains
    rules $B \to u$
    for which
    \begin{itemize}\setlength{\itemsep}{0pt}
      \item $a \in \first{u}$, or \hfill\textcolor{black!50}{(never the case for $a = \$$)}
      \item $\lambda \in \first{u}$ and $a \in \follow{B}$.
    \end{itemize}
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    \begin{malign}
      S \to aSb\mid\lambda
    \end{malign}
    We have
    \begin{itemize}\setlength{\itemsep}{0pt}
      \item 
        $\first{aSb} = \{a\}$, 
        $\first{\lambda} = \{\lambda\}$, 
        $\first{S} = \{\lambda, a\}$
      \item 
        $\follow{S} = \{b,\$\}$, 
    \end{itemize}
    Thus the parser table is:
    \begin{talign}
      \begin{array}{l|ccc}
      & a & b & \$ \\
      \hline
      S & \mpause[1]{~S \to aSb~} & \mpause{~S \to \lambda~} & \mpause{~S \to \lambda}
      \end{array}
    \end{talign}\vspace{-1ex}
  \end{exampleblock}
\end{frame}