677   \begin{exercise}\label{ex:contextfree}

   678   Write a parser for the context-free grammar representing arithmetic 

   679   expressions with addition and multiplication. As usual, multiplication 

   680   binds stronger than addition, and both of them nest to the right. 

   681   The context-free grammar is defined as:

   682 

   683   \begin{center}

   684   \begin{tabular}{lcl}

   685   @{text "<Basic>"}  & @{text "::="} & @{text "<Number> | (<Expr>)"}\\

   686   @{text "<Factor>"} & @{text "::="} & @{text "<Basic> * <Factor> | <Basic>"}\\

   687   @{text "<Expr>"}   & @{text "::="} & @{text "<Factor> + <Expr>  | <Factor>"}\\

   688   \end{tabular}

   689   \end{center}

   690 

   691   Hint: Be careful with recursive parsers.

   692   \end{exercise}