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\usepackage{../langs}

\usepackage{../data}

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\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}}

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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}}

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\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}}

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\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 (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 a web-scraper

\end{itemize}

\begin{textblock}{6}(10,7)

\begin{tikzpicture}[scale=0.38]

\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{textblock}

\end{frame}}

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\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}}

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\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}}

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\mode<presentation>{

\begin{frame}[c]

\frametitle{\begin{tabular}{c}Scala\end{tabular}}

\small a simple Scala function for reading webpages\\[-3mm]

\footnotesize

{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/app0.scala}}}\pause

{\lstset{language=Scala}\texttt{\lstinline{get_page("""http://www.inf.kcl.ac.uk/staff/urbanc/""")}}}\pause\bigskip

\small slightly more complicated for handling errors properly:\\[-3mm]

\footnotesize

{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/app1.scala}}}

\end{frame}}

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\mode<presentation>{

\begin{frame}[c]

\frametitle{\begin{tabular}{c}Why Scala?\end{tabular}}

\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{tikzpicture}

\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 

{\normalsize\color{darkgray}

\begin{minipage}{8.5cm}\raggedright\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\textcolor{blue}{\url{http://www.scala-lang.org}}

\end{minipage}};

\end{tikzpicture}

\end{textblock}}

\end{frame}}

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\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}}

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\mode<presentation>{

\begin{frame}[c]

\small

{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/app2.scala}}}\medskip

{\lstset{language=Scala}\texttt{crawl(some\_start\_URL, 2)}}\

\end{frame}}

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\mode<presentation>{

\begin{frame}[c]

\footnotesize

a version that only ``crawls'' links in my domain:

\small

{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/app3.scala}}}

\end{frame}}

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\mode<presentation>{

\begin{frame}[c]

\footnotesize

a little email ``harvester'':

\small

{\lstset{language=Scala}\texttt{\lstinputlisting{../progs/app4.scala}}}\bigskip

\tiny

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

\end{frame}}

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

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\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}}

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\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}}

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\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions

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\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}}

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\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}}

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\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 derivatives 

\item automata