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

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\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{app4.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 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 expression / regular expression matching
\item a bit of sets (of strings)
\item automata
\item the Myhill-Nerode theorem
\item parsing
\item grammars
\item a small interpreter / webbrowser
\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 exams?'' 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}

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