--- a/slides/slides04.tex	Tue Oct 17 13:49:45 2017 +0100
+++ b/slides/slides04.tex	Wed Oct 18 08:36:44 2017 +0100
@@ -338,7 +338,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Lexing}
+\frametitle{Lexing: Test Case}
 
 \mbox{\lstinputlisting[language=While]{../progs/fib.while}}
 
@@ -347,7 +347,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{??}
+\frametitle{?? Test Case}
 
 \mbox{\lstinputlisting[language=While]{../progs/collatz.while}}
 
@@ -368,12 +368,12 @@
 \hspace{5mm}{if}, {then}, {else},\\ 
 WHITESPACE:\\
 \hspace{5mm}{" "}, {$\backslash$n},\\ 
-IDENT:\\
+IDENTIFIER:\\
 \hspace{5mm}LETTER $\cdot$ (LETTER + DIGIT + {\_})$^*$\\ 
 NUM:\\
 \hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {0}\\
 OP:\\
-\hspace{5mm}{+}\\
+\hspace{5mm}+, -, *, \%, <, <=\\
 COMMENT:\\
 \hspace{5mm}{$\slash$*} $\cdot$ $\sim$(ALL$^*$ $\cdot$ (*$\slash$) $\cdot$ ALL$^*$) $\cdot$ {*$\slash$}
 \end{tabular}
@@ -510,7 +510,7 @@
 \draw[->,line width=1mm]  (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};\pause
 \node (r4) [right=of r3] {\bl{$r_4$}};
 \draw[->,line width=1mm]  (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};\pause
-\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};\pause
+\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable?$}}};\pause
 \node (v4) [below=of r4] {\bl{$v_4$}};
 \draw[->,line width=1mm]  (r4) -- (v4);\pause
 \node (v3) [left=of v4] {\bl{$v_3$}};
@@ -586,12 +586,12 @@
 
 \begin{center}
 \begin{tabular}{lcl}
-  \bl{$mkeps\,\ONE$}  & \bl{$\dn$}  & \bl{$Empty$}\\
-  \bl{$mkeps\,r_1 + r_2$} & \bl{$\dn$}  & \bl{if $nullable(r_1)$}  \\
+  \bl{$mkeps\,(\ONE)$}  & \bl{$\dn$}  & \bl{$Empty$}\\
+  \bl{$mkeps\,(r_1 + r_2)$} & \bl{$\dn$}  & \bl{if $nullable(r_1)$}  \\
                           &             & \bl{then $Left(mkeps(r_1))$}\\
                           &             & \bl{else $Right(mkeps(r_2))$}\\
-  \bl{$mkeps\,r_1 \cdot r_2$}  & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),mkeps(r_2))$}\\
-  \bl{$mkeps\,r^*$}      & \bl{$\dn$} & \bl{$[]$}  \\
+  \bl{$mkeps\,(r_1 \cdot r_2)$}  & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),mkeps(r_2))$}\\
+  \bl{$mkeps\,(r^*)$}      & \bl{$\dn$} & \bl{$[]$}  \\
 \end{tabular}
 \end{center}
 
@@ -602,10 +602,10 @@
 \begin{frame}[c]
 \frametitle{Inject}
 
-Injecting (``Adding'') a character to a value\\
+Injecting (``Adding'') a character to a value\\[-12mm]\mbox{}
 
 \begin{center}
-\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
+\begin{tabular}{@{}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
   \bl{$inj\,(c)\,c\,Empty$} & \bl{$\dn$}  & \bl{$Char\,c$}\\
   \bl{$inj\,(r_1 + r_2)\,c\,Left(v)$} & \bl{$\dn$}  & \bl{$Left(inj\,r_1\,c\,v)$}\\
   \bl{$inj\,(r_1 + r_2)\,c\,Right(v)$} & \bl{$\dn$}  & \bl{$Right(inj\,r_2\,c\,v)$}\\
@@ -1253,7 +1253,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Two Rules}
+\frametitle{Lexer: Two Rules}
 
 \begin{itemize}
 \item Longest match rule (``maximal munch rule''): The