\begin{frame}{Notational Conventions for Grammars}
  \begin{goal}{Notational Conventions}
    When defining grammars, we use the following conventions:
    \begin{itemize}
      \item \emph{upper case} letters for \emph{variables} (non-terminals)
      \item \emph{lower case} letters for \emph{terminals}
      \item $V \to w_1 \mid \ldots \mid w_n$ is \emph{shorthand for} $n$ rules
        \begin{talign}
          V &\to w_1\\[-1.5ex]
          &\;\;\vdots\\[-1ex]
          V &\to w_n
        \end{talign}\vspace{-7mm}
    \end{itemize}
    Often, we only specify the production rules.
  \end{goal}
  \pause

  \begin{exampleblock}{}
    \vspace{-3mm}
    \begin{talign}
      G_1: \quad S &\to Ab  & G_2:\quad S &\to aSb \\
      A &\to aAb \mid \lambda & S &\to b 
    \end{talign}
    \pause
    What languages are generated by these grammars?
    \begin{talign}
      L(G_1) &= \mpause[1]{\{ a^nb^{n+1} \mid n \geq 0 \}} & \mpause[3]{=} &&
      \mpause[2]{ L(G_2) &=} \mpause{\{ a^nb^{n+1} \mid n \geq 0 \}}
    \end{talign}    
  \end{exampleblock}
\end{frame}