\documentclass[dvipsnames,14pt,t,xelatex]{beamer}
\usepackage{../slides}
\usepackage{../graphics}
\usepackage{../langs}
\usepackage{../data}

\hfuzz=220pt 

%\setmonofont[Scale=.88]{Consolas}
%\newfontfamily{\consolas}{Consolas}

\lstset{language=Scala,
        style=mystyle,
        numbersep=0pt,
        numbers=none,
        xleftmargin=0mm}

\newcommand{\bl}[1]{\textcolor{blue}{#1}}     

% beamer stuff 
\renewcommand{\slidecaption}{AFL 01, King's College London}


\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{The Goal of this Course}

\begin{center}
  \begin{tikzpicture}[scale=1,
                      node/.style={
                      rectangle,rounded corners=3mm,
                      very thick,draw=black!50,minimum height=18mm, minimum width=20mm,
                      top color=white,bottom color=black!20}]

  \node at (3.05, 1.8) {\Large\bf A Compiler};

  \node (0) at (-2.3,0) {}; 
  
  \node (A) at (0,0)  [node] {};
  \node [below right] at (A.north west) {lexer};

  \node (B) at (3,0)  [node] {};
  \node [below right=1mm] at (B.north west) {\mbox{}\hspace{-1mm}parser};

  \node (C) at (6,0)  [node] {};
  \node [below right] at (C.north west) {\mbox{}\hspace{-1mm}code gen};

  \node (1) at (8.4,0) {}; 

  \draw [->,line width=4mm] (0) -- (A); 
  \draw [->,line width=4mm] (A) -- (B); 
  \draw [->,line width=4mm] (B) -- (C); 
  \draw [->,line width=4mm] (C) -- (1); 
  \end{tikzpicture}
  \end{center}

\only<2,3>{
\begin{textblock}{1}(1,2)
\begin{bubble}[9.8cm]
\normalsize
lexer input: a string\smallskip\\
\hspace{5mm}\code{"read(n);"}\medskip\\
lexer output: a sequence of tokens\smallskip\\
\hspace{5mm}\code{key(read); lpar; id(n); rpar; semi}
\end{bubble}
\end{textblock}}

\only<3>{
\begin{textblock}{1}(6,7.8)
\begin{tabular}{c}
\includegraphics[scale=0.2]{../pics/rosetta.jpg}\\[-2mm]
\footnotesize lexing $\Rightarrow$ recognising words (Stone of Rosetta)
\end{tabular}
\end{textblock}}

\only<4>{
\begin{textblock}{1}(1,1.5)
\begin{bubble}[8.5cm]
\normalsize
parser input: a sequence of token\smallskip\\
parser output: an abstract syntax tree\smallskip\\
\footnotesize
\hspace{2cm}\begin{tikzpicture}
  \node {\code{read}}
    child {node {\code{lpar}}}
    child {node {\code{n}}}
    child {node {\code{rpar}}};
\end{tikzpicture}
\end{bubble}
\end{textblock}}

\only<5,6>{
\begin{textblock}{1}(1,1.5)
\begin{bubble}[4cm]
\normalsize
code generator:\smallskip\\
\hspace{5mm}\code{istore 2}\\ 
\hspace{5mm}\code{iload 2}\\ 
\hspace{5mm}\code{ldc 10}\\
\hspace{5mm}\code{isub}\\
\hspace{5mm}\code{ifeq Label2}\\ 
\hspace{5mm}\code{iload 2}\\
\hspace{5mm}\code{...}\\
\end{bubble}
\end{textblock}}

\only<6>{
\begin{textblock}{6}(8.4,7)
\begin{bubble}[5cm]
\mbox{\begin{tikzpicture}[scale=0.58,rounded corners=0mm]
\begin{axis}[axis x line=bottom, axis y line=left, ylabel=secs,
    xlabel=n,
    enlargelimits=0.05,
    ybar interval=0.7, legend style=small]
\addplot file {interpreted2.data};
\addplot file {compiled2.data};
%\legend{interpreted, compiled}
\end{axis}
\end{tikzpicture}}
\end{bubble}
\end{textblock}}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{The subject is quite old}

\begin{itemize}
\item Turing Machines, 1936
\item Regular Expressions, 1956\\
\item The first compiler for COBOL, 1957\\ (Grace Hopper)
\item But surprisingly research papers are still published nowadays
\end{itemize}

\begin{flushright}
\includegraphics[scale=0.3]{pics/hopper.jpg}\\
\footnotesize\textcolor{gray}{Grace Hopper}
\end{flushright}

\mbox{}\\[-10mm]
{\footnotesize\textcolor{gray}{(she made it to David Letterman's Tonight Show, \url{http://www.youtube.com/watch?v=aZOxtURhfEU})}}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Why Bother?}

\begin{columns}[b]
\begin{column}{.5\textwidth}
Ruby, Python\\ and Others\bigskip\\
\begin{tikzpicture}[y=.08cm, x=.10cm]
   %axis
   \draw (0,0) -- coordinate (x axis mid) (30,0);
   \draw (0,0) -- coordinate (y axis mid) (0,30);
   %ticks
   \foreach \x in {0,5,...,30}
     \draw (\x,1pt) -- (\x,-3pt) node[anchor=north] {\footnotesize\x};
   \foreach \y in {0,5,...,30}
     \draw (1pt,\y) -- (-3pt,\y) node[anchor=east] {\footnotesize\y}; 
	%labels      
	\node[below=0.6cm] at (x axis mid) {\footnotesize number of \texttt{a}s};
	\node[rotate=90,left=1cm] at (y axis mid) {\footnotesize time in secs};
	%plots
	\draw[color=blue] plot[mark=*] 
		file {re-python.data};
	\draw[color=brown] plot[mark=triangle*] 
		file {re-ruby.data};	 
   %legend
	\begin{scope}[shift={(4,20)}] 
	\draw[color=blue] (0,0) -- 
		plot[mark=*] (0.25,0) -- (0.5,0) 
		node[right]{\small Python};
	\draw[yshift=-\baselineskip, color=brown] (0,0) -- 
		plot[mark=triangle*] (0.25,0) -- (0.5,0)
		node[right]{\small Ruby};
	\end{scope}	
\end{tikzpicture}
\end{column}
\begin{column}{.5\textwidth}
Us (after this course)\\\mbox{}\bigskip\\
\begin{tikzpicture}[y=.08cm, x=.0003cm]
 	%axis
	\draw (0,0) -- coordinate (x axis mid) (12000,0);
   \draw (0,0) -- coordinate (y axis mid) (0,30);
   %ticks
   \foreach \x in {0,4000,...,12000}
     	\draw (\x,1pt) -- (\x,-3pt) node[anchor=north] {\footnotesize\x};
   \foreach \y in {0,5,...,30}
     	\draw (1pt,\y) -- (-3pt,\y) node[anchor=east] {\footnotesize\y}; 
	%labels      
	\node[below=0.6cm] at (x axis mid) {\footnotesize number of \texttt{a}s};
	\node[rotate=90, left=1cm] at (y axis mid) {\footnotesize time in secs};

	%plots
   \draw[color=green] plot[mark=square*, mark options={fill=white} ] 
		file {re2b.data};
	\draw[color=black] plot[mark=square*, mark options={fill=white} ] 
		file {re3.data};	 
\end{tikzpicture}
\end{column}
\end{columns}\bigskip\medskip

\hspace{2cm}matching \texttt{[a?]\{n\}[a]\{n\}} against 
$\underbrace{\texttt{a}...\texttt{a}}_n$
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Lectures 1 - 5}

transforming strings into structured data\\[10mm]

\alert<2>{\LARGE\bf Lexing} \onslide<2>{\hfill{}baseed on regular expressions}\medskip\\
\hspace{5mm}(recognising ``words'')\\[6mm]

{\LARGE\bf Parsing}\medskip\\
\hspace{5mm}(recognising ``sentences'')

\begin{textblock}{1}(10,9.1)
\begin{tabular}{c}
\includegraphics[scale=0.1]{../pics/rosetta.jpg}\\[-2mm]
\footnotesize Stone of Rosetta
\end{tabular}
\end{textblock}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Familiar Regular Expr.}
\small
\begin{center}
\texttt{[a-z0-9\_.-]+ @ [a-z0-9.-]+ . [a-z.]\{2,6\}}
\end{center}\smallskip

\begin{center}
\begin{tabular}{@{}lp{8.5cm}@{}}
\pcode{re*} & matches 0 or more times\\
\pcode{re+} & matches 1 or more times\\
\pcode{re?} & matches 0 or 1 times\\
\pcode{re\{n\}}	& matches exactly \pcode{n} number of times\\
\pcode{re\{n,m\}} & matches at least \pcode{n} and at most {\tt m} times\\
\pcode{[...]} & matches any single character inside the brackets\\
\pcode{[^...]} & matches any single character not inside the 
brackets\\
\pcode{a-zA-Z} & character ranges\\
\pcode{\\d} & matches digits; equivalent to \pcode{[0-9]}\\
\pcode{.} & matches every character except newline\\
\pcode{(re)}	& groups regular expressions and remembers 
the matched text
\end{tabular}
\end{center}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Today}

\begin{itemize}
\item the ultimate goal is to implement a small compiler 
(a really small one for the JVM)\bigskip
\end{itemize}

Let's start with:

\begin{itemize}
\item a web-crawler
\item an email harvester
\item \textcolor{gray}{a web-scraper}
\end{itemize}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{A Web-Crawler}

\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{A Web-Crawler}

\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   


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

  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Scala}

\small A simple Scala function for reading webpages:
\smallskip

\footnotesize
\lstinputlisting{../progs/app0.scala}
\medskip\pause

\lstinline{get_page("""http://www.inf.kcl.ac.uk/staff/urbanc/""")}
\bigskip\medskip\pause


\small A slightly more complicated version for handling errors properly:
\smallskip

\footnotesize
\lstinputlisting{../progs/app1.scala}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Why Scala?}

\begin{textblock}{6}(1,3)
\begin{tabular}{l}
\mbox{}\hspace{-1mm}\includegraphics[scale=0.36]{pics/twitter.png}\\[-1mm]
\includegraphics[scale=0.30]{pics/linked.png}\\
\includegraphics[scale=0.30]{pics/guardian.jpg}\\[-3mm]
\mbox{}\hspace{-2mm}\includegraphics[scale=0.38]{pics/morgan.png}\\[-3mm]
\includegraphics[scale=0.30]{pics/suisse.png}\\
\includegraphics[scale=0.20]{pics/edf.png}\\[-1mm]
\includegraphics[scale=0.08]{pics/novell.png}\\[-1mm]
\includegraphics[scale=0.30]{pics/foursquare.png}\\
\includegraphics[scale=0.30]{pics/hsbc.png}\\
{\large\bf ...}
\end{tabular}
\end{textblock}
 
\only<2->{  
\begin{textblock}{6}(6,3)
\includegraphics[scale=0.35]{pics/jobgraph.png}\\
\end{textblock}}  
  
\only<3->{  
\begin{textblock}{6}(7.3,9.2)
\begin{tabular}{l}
\footnotesize 2013: 1$\%$\\[-2mm]
\footnotesize 2014: 3$\%$\\[-2mm]
\footnotesize 2015: 9$\%$\\[-2mm]
\footnotesize 2016: 27$\%$\\[-2mm]
\footnotesize 2017: 81$\%$\\[-2mm]
\footnotesize 2018: 243$\%$ \raisebox{-1mm}{\includegraphics[scale=0.02]{pics/smiley.jpg}}
\end{tabular}
\end{textblock}} 
  
\only<3->{  
\begin{textblock}{6}(6,9.5)
\footnotesize 5 yrs $\begin{cases}\mbox{}\\[1.4cm]\end{cases}$
\end{textblock}}

\only<4->{  
\begin{textblock}{11}(5,14.1)
\textcolor{gray}{
\footnotesize {\bf in London today:} 1 Scala job for every 30 Java jobs;\\[-2mm]
Scala programmers seem to get up to 20\% better salary}
\end{textblock}}


\only<5->{
\begin{textblock}{1}(3,6)
\begin{bubble}[8.5cm]
\normalsize
Scala is a functional and object-oriented programming
language; compiles to the JVM; does not need null-pointer
exceptions; a course on Coursera\\
\mbox{}\hfill\url{http://www.scala-lang.org}
\end{bubble}
\end{textblock}}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{A Regular Expression}

\begin{itemize}
\item \ldots{} is a pattern or template for specifying strings
\end{itemize}\bigskip
  
\begin{center}  
\only<1>{\scode{"https?://[^"]*"}}%
\only<2>{\scode{""""https?://[^"]*"""".r}}
\end{center}\bigskip\bigskip

matches for example\smallskip\\  
\hspace{2mm}\code{"http://www.foobar.com"}\\
\hspace{2mm}\code{"https://www.tls.org"}\\

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Finding Operations}

{\bf\code{rexp.findAllIn(string)}}\medskip
  
returns a list of all (sub)strings that match the 
regular expression
\bigskip\bigskip  
  

{\bf\code{rexp.findFirstIn(string)}}\medskip
 
returns either 

\begin{itemize}
\item \code{None} if no (sub)string matches or 
\item \code{Some(s)} with the first (sub)string
\end{itemize}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]

\footnotesize
\lstinputlisting{../progs/app2.scala}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]

\small
A version that only crawls links in ``my'' domain:

\footnotesize
\lstinputlisting{../progs/app3.scala}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\lstset{xleftmargin=-4mm}
\small
A little email harvester:

\footnotesize
\lstinputlisting{../progs/app4.scala}\bigskip

\tiny
\url{http://net.tutsplus.com/tutorials/other/8-regular-expressions-you-should-know/}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 / \pcode{""} / \pcode{[]}\\
           & \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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Regular Expressions}

\small
In Scala:\bigskip

\footnotesize
\lstinputlisting{../progs/app51.scala}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Strings}

\ldots are lists of characters. For example \code{"hello"}

\begin{center}
\bl{$[h, e, l, l, o]$}
\end{center}

the empty string: $[]$ or \pcode{""}\bigskip\\

the concatenation of two strings:

\begin{center}
\bl{$s_1 \,@\, s_2$}
\end{center}

\textit{foo $@$ bar = foobar}, \textit{baz $@\, []$ = baz}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{The Meaning of Matching}

\begin{bubble}[10cm]
\large
A regular expression \bl{$r$} matches a string \bl{$s$} 
provided

\begin{center}
\bl{$s \in L(r)$}\\ 
\end{center}
\end{bubble}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Written Exam}

\begin{itemize}
\item Accounts for 75\%.\bigskip

\item You will understand the question ``Is this relevant for
      the exam?'' is very demotivating for the lecturer!\bigskip\\

\item Deal: Whatever is in the homework (and is not marked
      ``optional'') is relevant for the exam.
\end{itemize}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Coursework}

\begin{itemize}
\item Accounts for 25\%. Two strands. Choose \alert{\bf one}!\bigskip
\end{itemize}

\begin{columns}[t]
\begin{column}{.5\textwidth}
\underline{\bf Strand 1}\medskip
\begin{itemize}
\item four programming subtasks:
\begin{itemize}
\item matcher (5\%, 13.10.) 
\item lexer (5\%, 03.11.)
\item parser (5\%, 27.11.)
\item compiler (10\%, 12.12.)
\end{itemize}
\end{itemize}
\end{column}

\hspace{-45pt}\vrule{}\hspace{10pt}
\begin{column}{.5\textwidth}
\underline{\bf Strand 2}\smallskip\begin{itemize}
\item one task: prove the correctness of a regular expression matcher in 
the Isabelle theorem prover
\item 25\%, submission 12.12.
\end{itemize}
\end{column}
\end{columns}\medskip

\small
\begin{itemize}
\item Solving more than one strand will {\bf not} give you more 
marks.\\[-2mm]
\item The exam will contain in much, much smaller form 
elements from both (but will also be in lectures and HW).
\end{itemize}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{\begin{tabular}{c}\\[3cm]\alert{Questions?}\end{tabular}}

\mbox{}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
\end{document}

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