\documentclass[dvipsnames,14pt,t,xelatex]{beamer}
\usepackage{beamerthemeplaincu}
 \usepackage{fontenc,xltxtra,xunicode}
\defaultfontfeatures{Mapping=tex-text}
\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

\makeatletter
\lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}}
\@empty\z@\@empty
\makeatother

\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\\
  Office: & S1.27 (1st floor Strand Building)\\
  Slides: & KEATS
  \end{tabular}
  \end{center}


\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     

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\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 compiler (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{../progs/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{../progs/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{../progs/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{../progs/app3.scala}}}


\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]

\footnotesize
a little email ``harvester'':

{\lstset{language=Scala}\fontsize{8}{10}\selectfont
\texttt{\lstinputlisting{../progs/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}[t]
\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}

Their inductive definition:\medskip

\begin{textblock}{6}(2,5)
  \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}}

\small
In Scala:


{\lstset{language=Scala}\fontsize{8}{10}\selectfont
\texttt{\lstinputlisting{../progs/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 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}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 in the exam.
\end{itemize}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   


\end{document}

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