--- a/handouts/ho04.tex	Mon Oct 19 14:45:50 2015 +0100
+++ b/handouts/ho04.tex	Mon Oct 19 15:03:44 2015 +0100
@@ -730,27 +730,83 @@
 \end{center}
 
 Recall that we want to lex a little programming language,
-called the \emph{While}-language. The main keywords in this
-language are \pcode{while}, \pcode{if}, \pcode{then} and
-\pcode{else}. As usual we have identifiers, operators, numbers
-and so on. For this we would need to design the corresponding
-regular expressions to recognise these syntactic categories. I
-let you do this design task. Having these regular expressions
-at our disposal we can form the regular expression
+called the \emph{While}-language. A simple program in this
+language is shown in Figure~\ref{while}. The main keywords in
+this language are \pcode{while}, \pcode{if}, \pcode{then} and
+\pcode{else}. As usual we have syntactic categories for
+identifiers, operators, numbers and so on. For this we would
+need to design the corresponding regular expressions to
+recognise these syntactic categories. I let you do this design
+task. Having these regular expressions at our disposal, we can
+form the regular expression
+
+\begin{figure}[t]
+\begin{center}
+\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
+\end{center}
+\caption{The Fibonacci program in the While-language.\label{while}}
+\end{figure}
 
 \begin{center}
-\begin{tabular}{rcl}
-\textit{WhileRegs} & $\dn$ & (($k$, KEYWORD) +\\
-                   &     & ($i$, ID) +\\
-                   &     & ($o$, OP) + \\
-                   &     & ($n$, NUM) + \\
-                   &     & ($s$, SEMI) + \\
-                   &     & ($p$, (LPAREN + RPAREN)) +\\ 
-                   &     & ($b$, (BEGIN + END)) + \\
-                   &     & ($w$, WHITESPACE))$^*$
+$\textit{WhileRegs} \;\dn\; 
+\left(\begin{array}{l}
+       (k, KeyWords)\; +\\
+       (i, Ids)\;+\\
+       (o, Ops)\;+ \\
+       (n, Nums)\;+ \\
+       (s, Semis)\;+ \\
+       (p, (LParens + RParens))\;+\\ 
+       (b, (Begin + End))\;+ \\
+       (w, WhiteSpacess)
+      \end{array}\right)\LARGE^\mbox{\LARGE*}$
+\end{center}
+
+\noindent and ask the algorithm by Sulzmann \& Lu to lex, say
+the following string
+
+\begin{center}\large
+\code{"if true then then 42 else +"}
+\end{center}
+
+\noindent
+By using the records and extracting the environment, the 
+result is the following list:
+
+\begin{center}\tt
+\begin{tabular}{l}
+KEYWORD(if),\\ 
+WHITESPACE,\\ 
+IDENT(true),\\ 
+WHITESPACE,\\ 
+KEYWORD(then),\\ 
+WHITESPACE,\\ 
+KEYWORD(then),\\ 
+WHITESPACE,\\ 
+NUM(42),\\ 
+WHITESPACE,\\ 
+KEYWORD(else),\\ 
+WHITESPACE,\\ 
+OP(+)
 \end{tabular}
 \end{center}
 
+\noindent Typically we are not interested in the whitespaces 
+and comments and would filter them out: this gives
+
+\begin{center}\tt
+\begin{tabular}{l}
+KEYWORD(if),\\ 
+IDENT(true),\\ 
+KEYWORD(then),\\ 
+KEYWORD(then),\\ 
+NUM(42),\\ 
+KEYWORD(else),\\ 
+OP(+)
+\end{tabular}
+\end{center}
+
+\noindent
+which will be the input for the next phase of our compiler.
 
 \end{document}