\begin{frame}{Grammars}
  \begin{block}{}
    A \emph{grammar} $G = (V,T,S,P)$ consists of:
    
    \begin{itemize}
    \item finite set $V$ of \emph{non-terminals} (or \emph{variables})\\[.5ex]
          
    \item finite set $T$ of \emph{terminals}\\[.5ex]
    
    \item a \emph{start symbol} $S \in V$\\[.5ex]
    
    \item finite set $P$ of \emph{production rules} $x \to y$ where
      \begin{itemize}
        \item $x \in (V \cup T)^+$ containing at least one symbol from $V$
        \item $y \in (V \cup T)^*$
      \end{itemize}
    \end{itemize}
  \end{block}

  \begin{exampleblock}{}
    In the previous example:
    \begin{itemize}
      \item variables: $\langle$sentence$\rangle$, $\langle$article$\rangle$, $\langle$noun$\rangle$, $\langle$verb$\rangle$
      \item terminals: the, a, farmer, cow, milks
      \item starting symbol: $\langle$sentence$\rangle$
    \end{itemize}
  \end{exampleblock}
  \pause
  
  \begin{block}{}
    A grammar is \emph{context-free} if $x \in V$ for every rule $x \to y$.
  \end{block}
\end{frame}