\begin{frame}{$\first{A}$}
  \begin{goal}{}
    We consider the first terminal letters derivable from a word:
    \begin{talign}
      \first{w} = 
        \ &\{\, a \in T \mid w \Rightarrow^* a\ldots \,\} \; \cup \; \{\, \lambda \mid w \Rightarrow^* \lambda \,\}
    \end{talign}
  \end{goal}
  \pause
  
  \begin{block}{Algorithm}
    Let \( \text{PreFirst}(w) \) be the smallest set such that:
    \begin{itemize}
      \item \( w \in \text{PreFirst}(w) \)
      \item \( a \in \text{PreFirst}(w) \) if \( av \in \text{PreFirst}(w) \)
      \item \( B \in \text{PreFirst}(w) \) if \( Bv \in \text{PreFirst}(w) \)
      \item \( v \in \text{PreFirst}(w) \) if \( Bv \in \text{PreFirst}(w) \) and \(B\) erasable
      \item \( v \in \text{PreFirst}(w) \) for every \( A \in \text{PreFirst}(w) \) and rule \( A \to v \)
    \end{itemize}
    Then \( \text{First}(w) \) consists of
    \begin{itemize}
      \item all terminal letters \( a \in T \) such that \( a \in \text{PreFirst}(w) \), and
      \item \( \lambda \) if \( w = A_1 A_2 \ldots A_n \) for erasable variables \(A_1,\ldots,A_n\).
    \end{itemize}
  \end{block}
\end{frame}