
diff -r b728c9dbf120 -r a2d792ed768e slides/slides05.tex
--- a/slides/slides05.tex	Wed Oct 23 01:05:22 2013 +0100
+++ b/slides/slides05.tex	Wed Oct 23 07:28:23 2013 +0100
@@ -378,6 +378,30 @@
 
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{tikzpicture}[scale=1]
+  
+  \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
+  \draw (4.2,1) node {Code Gen};
+  \draw (0.6,1.7) node {\footnotesize Parser};
+  \draw (-2.7,1.7) node {\footnotesize Lexer};
+  
+  \draw[line width=1mm] (-1.8, 0) rectangle (-3.6,2);
+
+  \draw[white] (1.7,1) node (X) {};
+  \draw[white] (3.2,1) node (Y) {};
+  \draw[red, ->, line width = 2mm] (X) -- (Y);
+ 
+  \draw[red, <-, line width = 2mm] (-0.6,1) -- (-1.6,1);
+  \draw[red, <-, line width = 2mm] (-3.8,1) -- (-4.8,1);
+\end{tikzpicture}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -452,28 +476,28 @@
 \mode<presentation>{
 \begin{frame}[c]
 
-\begin{tikzpicture}[scale=1]
-  
-  \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
-  \draw (4.2,1) node {Code Gen};
-  \draw (0.6,1.7) node {\footnotesize Parser};
-  \draw (-2.7,1.7) node {\footnotesize Lexer};
-  
-  \draw[line width=1mm] (-1.8, 0) rectangle (-3.6,2);
+
+There is one small problem with the tokenizer. How should we 
+tokenize:
+
+\begin{center}
+{\consolas "x - 3"}
+\end{center}
 
-  \draw[white] (1.7,1) node (X) {};
-  \draw[white] (3.2,1) node (Y) {};
-  \draw[red, ->, line width = 2mm] (X) -- (Y);
- 
-  \draw[red, <-, line width = 2mm] (-0.6,1) -- (-1.6,1);
-  \draw[red, <-, line width = 2mm] (-3.8,1) -- (-4.8,1);
-\end{tikzpicture}
+\consolas
+\begin{tabular}{@{}l}
+OP:\\
+\hspace{5mm}\texttt{"+"}, \texttt{"-"}\\
+NUM:\\
+\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {''0''}\\
+NUMBER:\\
+\hspace{5mm}NUM +  (\texttt{"-"} $\cdot$ NUM)\\
+\end{tabular}
 
 
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
@@ -536,12 +560,36 @@
 \bl{$zeroable (r_1 \cdot r_2)$} & \bl{$\dn$} &  \bl{$zeroable(r_1) \vee zeroable(r_2)$} \\
 \bl{$zeroable (r^*)$}                 & \bl{$\dn$} & \bl{$f\!alse$} \\
 \end{tabular}
+\end{center}\bigskip\pause
+
+\begin{center}
+\bl{$zeroable(r) \Leftrightarrow L(r) = \varnothing$}
 \end{center}
 
-
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{itemize}
+\item The star-case in our proof about the matcher needs the following lemma
+\begin{center}
+\bl{$Der\,c\,A^* = (Der c A)\,@\, A^*$}
+\end{center}
+\end{itemize}\bigskip\bigskip
+
+\begin{itemize}
+\item If \bl{\texttt{""} $\in A$}, then\\ \bl{$Der\,c\,(A @ B) = (Der\,c\,A) @ B \cup (Der\,c\,B)$}\medskip
+\item If \bl{\texttt{""} $\not\in A$}, then\\ \bl{$Der\,c\,(A @ B) = (Der\,c\,A) @ B$}
+
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
 \newcommand{\qq}{\mbox{\texttt{"}}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{




