diff -r 0da19c346e24 -r 73cf4406b773 slides02.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/slides02.tex	Thu Sep 27 11:59:41 2012 +0100
@@ -0,0 +1,583 @@
+\documentclass[dvipsnames,14pt,t]{beamer}
+\usepackage{beamerthemeplainculight}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{mathpartir}
+\usepackage[absolute,overlay]{textpos}
+\usepackage{ifthen}
+\usepackage{tikz}
+\usepackage{pgf}
+\usepackage{calc} 
+\usepackage{ulem}
+\usepackage{courier}
+\usepackage{listings}
+\renewcommand{\uline}[1]{#1}
+\usetikzlibrary{arrows}
+\usetikzlibrary{automata}
+\usetikzlibrary{shapes}
+\usetikzlibrary{shadows}
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usepackage{graphicx} 
+
+\definecolor{javared}{rgb}{0.6,0,0} % for strings
+\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
+\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
+\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
+
+\lstset{language=Java,
+	basicstyle=\ttfamily,
+	keywordstyle=\color{javapurple}\bfseries,
+	stringstyle=\color{javagreen},
+	commentstyle=\color{javagreen},
+	morecomment=[s][\color{javadocblue}]{/**}{*/},
+	numbers=left,
+	numberstyle=\tiny\color{black},
+	stepnumber=1,
+	numbersep=10pt,
+	tabsize=2,
+	showspaces=false,
+	showstringspaces=false}
+
+\lstdefinelanguage{scala}{
+  morekeywords={abstract,case,catch,class,def,%
+    do,else,extends,false,final,finally,%
+    for,if,implicit,import,match,mixin,%
+    new,null,object,override,package,%
+    private,protected,requires,return,sealed,%
+    super,this,throw,trait,true,try,%
+    type,val,var,while,with,yield},
+  otherkeywords={=>,<-,<\%,<:,>:,\#,@},
+  sensitive=true,
+  morecomment=[l]{//},
+  morecomment=[n]{/*}{*/},
+  morestring=[b]",
+  morestring=[b]',
+  morestring=[b]"""
+}
+
+\lstset{language=Scala,
+	basicstyle=\ttfamily,
+	keywordstyle=\color{javapurple}\bfseries,
+	stringstyle=\color{javagreen},
+	commentstyle=\color{javagreen},
+	morecomment=[s][\color{javadocblue}]{/**}{*/},
+	numbers=left,
+	numberstyle=\tiny\color{black},
+	stepnumber=1,
+	numbersep=10pt,
+	tabsize=2,
+	showspaces=false,
+	showstringspaces=false}
+
+% beamer stuff 
+\renewcommand{\slidecaption}{AFL 01, King's College London, 26.~September 2012}
+
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}<1>[t]
+\frametitle{%
+  \begin{tabular}{@ {}c@ {}}
+  \\[-3mm]
+  \LARGE Automata and \\[-2mm] 
+  \LARGE Formal Languages (1)\\[-3mm] 
+  \end{tabular}}
+
+  \begin{center}
+  \includegraphics[scale=0.3]{pics/ante1.jpg}\hspace{5mm}
+  \includegraphics[scale=0.31]{pics/ante2.jpg}\\
+  \footnotesize\textcolor{gray}{Antikythera automaton, 100 BC (Archimedes?)}
+  \end{center}
+
+\normalsize
+  \begin{center}
+  \begin{tabular}{ll}
+  Email:  & christian.urban at kcl.ac.uk\\
+  Of$\!$fice: & S1.27 (1st floor Strand Building)\\
+  Slides: & KEATS
+  \end{tabular}
+  \end{center}
+
+
+\end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{textblock}{1}(2,5)
+\begin{tabular}{c}
+\includegraphics[scale=0.15]{pics/servers.png}\\[-2mm]
+\small Server
+\end{tabular}
+\end{textblock}
+
+\begin{textblock}{1}(5.6,4)
+  \begin{tikzpicture}[scale=1.1]
+  \draw[white] (0,1) node (X) {};
+  \draw[white] (2,1) node (Y) {};
+   \draw[white] (0,0) node (X1) {};
+  \draw[white] (2,0) node (Y1) {};
+   \draw[white] (0,-1) node (X2) {};
+  \draw[white] (2,-1) node (Y2) {};
+  \draw[red, <-, line width = 2mm] (X) -- (Y);
+  \node [inner sep=5pt,label=above:\textcolor{black}{GET request}] at ($ (X)!.5!(Y) $) {};
+  \draw[red, ->, line width = 2mm] (X1) -- (Y1);
+  \node [inner sep=5pt,label=above:\textcolor{black}{webpage}] at ($ (X1)!.5!(Y1) $) {};
+  \draw[red, <-, line width = 2mm] (X2) -- (Y2);
+  \node [inner sep=7pt,label=above:\textcolor{black}{POST data}] at ($ (X2)!.5!(Y2) $) {};
+  \end{tikzpicture}
+\end{textblock}
+
+
+\begin{textblock}{1}(9,5.5)
+\begin{tabular}{c}
+\includegraphics[scale=0.15]{pics/laptop.png}\\[-2mm]
+\small Browser
+\end{tabular}
+\end{textblock}
+  
+\only<2>{  
+\begin{textblock}{10}(2,13.5)
+\begin{itemize}
+\item programming languages, compilers
+\end{itemize}
+\end{textblock}}
+  
+  
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+transforming strings into structured data\\[10mm]
+
+{\LARGE\bf Lexing}\medskip\\
+\hspace{5mm}(recognising ``words'')\\[6mm]
+
+{\LARGE\bf Parsing}\medskip\\
+\hspace{5mm}(recognising ``sentences'')
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+The subject is quite old:
+
+\begin{itemize}
+\item Turing Machines, 1936
+\item first compiler for COBOL, 1957 (Grace Hopper)
+\item but surprisingly research papers are still published now
+\end{itemize}
+
+\begin{flushright}
+\includegraphics[scale=0.3]{pics/hopper.jpg}\\
+\footnotesize\textcolor{gray}{Grace Hopper}
+\end{flushright}
+
+{\footnotesize\textcolor{gray}{(she made it to David Letterman's Tonight Show, \url{http://www.youtube.com/watch?v=aZOxtURhfEU})}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}This Course\end{tabular}}
+
+\begin{itemize}
+\item the ultimate goal is to implement a small web-browser (really small one)\bigskip
+\end{itemize}
+
+Let's start with:
+
+\begin{itemize}
+\item a web-crawler
+\item an email harvester
+\item a web-scraper
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}A Web Crawler\end{tabular}}
+
+\mbox{}\\[10mm]
+
+\begin{enumerate}
+\item given an URL, read the corresponding webpage
+\item extract all links from it
+\item call the web-crawler again for all these links
+\end{enumerate}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}A Web Crawler\end{tabular}}
+
+\mbox{}\\[10mm]
+
+
+\begin{enumerate}
+\item given an URL, read the corresponding webpage
+\item if not possible print, out a problem
+\item if possible, extract all links from it
+\item call the web-crawler again for all these links
+\end{enumerate}\bigskip\pause
+
+\small (we need a bound for the number of recursive calls)
+
+\small (the purpose is to check all links on my own webpage)
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Scala\end{tabular}}
+
+\footnotesize a simple Scala function for reading webpages\\[-3mm]
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app0.scala}}}\pause
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinline{get_page("""http://www.inf.kcl.ac.uk/staff/urbanc/""")}}}\pause\bigskip
+
+
+\footnotesize slightly more complicated for handling errors properly:\\[-3mm]
+
+\footnotesize
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app1.scala}}}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}A Regular Expression\end{tabular}}
+
+\begin{itemize}
+\item \ldots{} is a pattern or template for specifying strings
+\end{itemize}\bigskip
+  
+\begin{center}  
+\only<1>{{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf
+\texttt{"https?://[$\hat{\hspace{2mm}}$"]*"}}}%
+\only<2>{{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf
+\texttt{"""\textbackslash{}"https?://[$\hat{\hspace{2mm}}$\textbackslash{}"]*\textbackslash{}"""".r}}}
+\end{center}\bigskip\bigskip
+
+matches for example\\  
+\;{\lstset{language=Scala}\fontsize{12}{14}\selectfont\bf
+\texttt{"http://www.foobar.com"}}\\
+\;{\lstset{language=Scala}\fontsize{12}{14}\selectfont\bf
+\texttt{"https://www.tls.org"}}\\
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf
+\texttt{rexp.findAllIn(string)}}\medskip
+  
+returns a list of all (sub)strings that match the regular expression\bigskip\bigskip  
+  
+{\lstset{language=Scala}\fontsize{18}{19}\selectfont\bf
+\texttt{rexp.findFirstIn(string)}}\medskip
+  
+returns either {\bf\texttt{None}} if no (sub)string matches 
+or {\bf\texttt{Some(s)}} with the first (sub)string
+  
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app2.scala}}}\medskip
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{crawl(some\_start\_URL, 2)}}\
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\footnotesize
+a version that only ``crawls'' links in my domain:
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app3.scala}}}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\footnotesize
+a little email ``harvester'':
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app4.scala}}}\bigskip
+
+\tiny
+\textcolor{gray}{\url{http://net.tutsplus.com/tutorials/other/8-regular-expressions-you-should-know/}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+\newcommand{\bl}[1]{\textcolor{blue}{#1}}       
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
+
+\begin{textblock}{6}(2,4)
+  \begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
+  \bl{r} & \bl{$::=$}  & \bl{$\varnothing$}  & null\\
+         & \bl{$\mid$} & \bl{$\epsilon$}        & empty string / "" / []\\
+         & \bl{$\mid$} & \bl{c}                         & character\\
+         & \bl{$\mid$} & \bl{r$_1$ $\cdot$ r$_2$} & sequence\\
+         & \bl{$\mid$} & \bl{r$_1$ + r$_2$}  & alternative / choice\\
+         & \bl{$\mid$} & \bl{r$^*$}                   & star (zero or more)\\
+  \end{tabular}
+  \end{textblock}
+  
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app51.scala}}}
+
+  
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}}
+
+\begin{textblock}{15}(1,4)
+ \begin{tabular}{@ {}rcl}
+ \bl{$L$($\varnothing$)}  & \bl{$\dn$} & \bl{$\varnothing$}\\
+ \bl{$L$($\epsilon$)}        & \bl{$\dn$} & \bl{$\{$""$\}$}\\
+ \bl{$L$(c)}                         & \bl{$\dn$} & \bl{$\{$"c"$\}$}\\
+ \bl{$L$(r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) $\cup$ $L$(r$_2$)}\\
+ \bl{$L$(r$_1$ $\cdot$ r$_2$)}  & \bl{$\dn$} & \bl{$\{$ s$_1$ @ s$_2$ $|$ s$_1$ $\in$ $L$(r$_1$) $\wedge$ s$_2$ $\in$ 
+     $L$(r$_2$) $\}$}\\
+ \bl{$L$(r$^*$)}                   & \bl{$\dn$} & \onslide<4->{\bl{$\bigcup_{n \ge 0}$ $L$(r)$^n$}}\\
+  \end{tabular}\bigskip
+  
+\onslide<2->{
+\hspace{5mm}\bl{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\
+\bl{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$}\hspace{9mm}\onslide<3->{\small\textcolor{gray}{(append on sets)}\\
+\small\hspace{5cm}\textcolor{gray}{$\{$ s$_1$ @ s$_2$ $|$ s$_1$ $\in$ $L$(r) $\wedge$ s$_2$ $\in$ 
+     $L$(r)$^n$ $\}$}}
+}  
+    \end{textblock}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}The Meaning of a Matching\end{tabular}}
+
+\large
+a regular expression \bl{r} matches a string \bl{s} is defined as
+
+\begin{center}
+\bl{s $\in$ $L$(r)}\\ 
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Nullability\end{tabular}}
+
+\small
+whether a regular expression matches the empty string:\medskip
+
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app5.scala}}}
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Derivative of a Rexp\end{tabular}}
+
+\large
+If \bl{r} matches the string \bl{c::s}, what is a regular expression that matches \bl{s}?\bigskip\bigskip\bigskip\bigskip
+
+\small
+\bl{der c r} gives the answer
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
+
+\begin{center}
+\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
+  \bl{der c ($\varnothing$)}            & \bl{$\dn$} & \bl{$\varnothing$} & \\
+  \bl{der c ($\epsilon$)}           & \bl{$\dn$} & \bl{$\varnothing$} & \\
+  \bl{der c (d)}           & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
+  \bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
+  \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{((der c r$_1$) $\cdot$ r$_2$) + } & \\
+       &          & \bl{\hspace{3mm}(if nullable r$_1$ then der c r$_2$ else $\varnothing$)}\\
+  \bl{der c (r$^*$)}          & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
+
+  \bl{ders [] r}     & \bl{$\dn$} & \bl{r} & \\
+  \bl{ders (c::s) r} & \bl{$\dn$} & \bl{ders s (der c r)} & \\
+  \end{tabular}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
+
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app6.scala}}}
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}The Rexp Matcher\end{tabular}}
+
+
+{\lstset{language=Scala}\fontsize{8}{10}\selectfont
+\texttt{\lstinputlisting{app7.scala}}}
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}This Course\end{tabular}}
+
+We will have a look at:
+
+\begin{itemize}
+\item regular expressions / regular expression matching
+\item automata
+\item the Myhill-Nerode theorem
+\item parsing
+\item grammars
+\item a small interpreter / web browser
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Exam\end{tabular}}
+
+\begin{itemize}
+\item The question ``Is this relevant for the exam?'' is not appreciated!\bigskip\\
+
+Whatever is in the homework sheets (and is not marked optional) is relevant for the
+exam.\\ No code needs to be written.
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}Maps in Scala\end{tabular}}
+
+\begin{itemize}
+\item {\bf\texttt{map}} takes a function, say f, and applies it to every element of the list:
+\end{itemize}
+
+\begin{textblock}{15}(2,7)
+\fontsize{13}{14}\selectfont
+\bf\texttt{List(1, 2, 3, 4, 5, 6, 7, 8, 9)}
+\end{textblock}
+
+\begin{textblock}{15}(2,10)
+\fontsize{13}{14}\selectfont
+\bf\texttt{List(1, 4, 9, 16, 25, 36, 49, 64, 81)}
+\end{textblock}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+\end{document}
+
+%%% Local Variables:  
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 
+