\begin{frame}{Introduction to Grammars}
  \begin{goal}{}
  A \emph{grammar} defines a \emph{language}.
  \end{goal}
  
  Applications areas:
  \begin{itemize}\setlength{\itemsep}{0ex}
    \smallskip
    \item natural language
    \item artificial intelligence
    \item syntax of programming languages
  \end{itemize}
  \pause\medskip
  
  \begin{example}
  \begin{tabular}{rcl}
  $\langle$sentence$\rangle$ & $\to$ & 
    $\langle$article$\rangle$ $\langle$noun$\rangle$ $\langle$verb$\rangle$ $\langle$article$\rangle$ $\langle$noun$\rangle$ \\
  $\langle$article$\rangle$ & $\to$ & the \\
  $\langle$article$\rangle$ & $\to$ & a \\
  $\langle$noun$\rangle$ & $\to$ & farmer \\
  $\langle$noun$\rangle$ & $\to$ & cow \\
  $\langle$verb$\rangle$ & $\to$ & milks
  \end{tabular}
  \end{example}
  With these \emph{grammar rules} we can construct a $\langle$sentence$\rangle$.
  \bigskip
\end{frame}