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\section*{Homework 8}

\begin{enumerate}

\item Suppose the following grammar for the WHILE-language:

\begin{center}

\begin{tabular}{lcl}

$Stmt$ & $\rightarrow$ &  $\text{skip}$\\

              & $|$ & $Id := AExp$\\

              & $|$ & $\text{if}\; B\!Exp \;\text{then}\; Block \;\text{else}\; Block$\\

              & $|$ & $\text{while}\; B\!Exp \;\text{do}\; Block$\medskip\\

$Stmts$ & $\rightarrow$ &  $Stmt \;\text{;}\; Stmts$\\

              & $|$ & $Stmt$\medskip\\

$Block$ & $\rightarrow$ &  $\{ Stmts \}$\\

                & $|$ & $Stmt$\medskip\\

$AExp$ & $\rightarrow$ & $AExp + AExp$\\

               & $|$ & $AExp * AExp$\\

               & $|$ & $( AExp )$\\

                & $|$ & $Num$\\

                & $|$ & $Id$\medskip\\

$BExp$ & $\rightarrow$ & $AExp = AExp$\\

                 & $|$ & $AExp \not= AExp$\\

                  & $|$ & $\text{false}$\\

                  & $|$ & $\text{true}$\\

\end{tabular}

\end{center}

Transform this grammar into Chomsky normalform.

\item Write a program in the WHILE-language that calculates the factorial function.

\end{enumerate}

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