\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}