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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{beamerthemeplainculight}
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\usepackage[absolute,overlay]{textpos}
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\usepackage{ifthen}
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\usepackage{calc}
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\usepackage{courier}
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\renewcommand{\uline}[1]{#1}
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\usetikzlibrary{shadows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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\usepackage{graphicx}
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\definecolor{javared}{rgb}{0.6,0,0} % for strings
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\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
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\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
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\lstset{language=Java,
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basicstyle=\ttfamily,
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keywordstyle=\color{javapurple}\bfseries,
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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showspaces=false,
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showstringspaces=false}
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\lstdefinelanguage{scala}{
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morekeywords={abstract,case,catch,class,def,%
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do,else,extends,false,final,finally,%
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for,if,implicit,import,match,mixin,%
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new,null,object,override,package,%
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private,protected,requires,return,sealed,%
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super,this,throw,trait,true,try,%
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type,val,var,while,with,yield},
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otherkeywords={=>,<-,<\%,<:,>:,\#,@},
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sensitive=true,
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morecomment=[n]{/*}{*/},
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morestring=[b]",
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morestring=[b]',
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morestring=[b]"""
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}
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\lstset{language=Scala,
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basicstyle=\ttfamily,
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keywordstyle=\color{javapurple}\bfseries,
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stringstyle=\color{javagreen},
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morecomment=[s][\color{javadocblue}]{/**}{*/},
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tabsize=2,
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showstringspaces=false}
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% beamer stuff
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\renewcommand{\slidecaption}{AFL 02, King's College London, 3.~October 2012}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Automata and \\[-2mm]
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\LARGE Formal Languages (2)\\[-3mm]
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\end{tabular}}
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\begin{center}
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\includegraphics[scale=0.3]{pics/ante1.jpg}\hspace{5mm}
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\includegraphics[scale=0.31]{pics/ante2.jpg}\\
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\footnotesize\textcolor{gray}{Antikythera automaton, 100 BC (Archimedes?)}
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\end{center}
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Of$\!$fice: & S1.27 (1st floor Strand Building)\\
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Slides: & KEATS
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
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\begin{textblock}{6}(2,4)
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\begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
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\bl{r} & \bl{$::=$} & \bl{$\varnothing$} & null\\
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& \bl{$\mid$} & \bl{$\epsilon$} & empty string / "" / []\\
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& \bl{$\mid$} & \bl{c} & character\\
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& \bl{$\mid$} & \bl{r$_1$ $\cdot$ r$_2$} & sequence\\
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& \bl{$\mid$} & \bl{r$_1$ + r$_2$} & alternative / choice\\
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& \bl{$\mid$} & \bl{r$^*$} & star (zero or more)\\
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\end{tabular}
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\end{textblock}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}}
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\begin{textblock}{15}(1,4)
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\begin{tabular}{@ {}rcl}
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\bl{$L$($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$}\\
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\bl{$L$($\epsilon$)} & \bl{$\dn$} & \bl{$\{$""$\}$}\\
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\bl{$L$(c)} & \bl{$\dn$} & \bl{$\{$"c"$\}$}\\
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\bl{$L$(r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) $\cup$ $L$(r$_2$)}\\
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\bl{$L$(r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) @ $L$(r$_2$)}\\
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\bl{$L$(r$^*$)} & \bl{$\dn$} & \bl{$\bigcup_{n \ge 0}$ $L$(r)$^n$}\\
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\end{tabular}\bigskip
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\hspace{5mm}\textcolor{gray}{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\
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\textcolor{gray}{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$}
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\end{textblock}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\YES}{\textcolor{gray}{yes}}
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\newcommand{\NO}{\textcolor{gray}{no}}
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\newcommand{\FORALLR}{\textcolor{gray}{$\forall$ r.}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Reg Exp Equivalences\end{tabular}}
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7
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\begin{center}
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\begin{tabular}{lrcl@ {\hspace{7mm}}l}
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&\bl{(a + b) + c} & \bl{$\equiv^?$} & \bl{a + (b + c)} & \onslide<2->{\YES}\\
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&\bl{a + a} & \bl{$\equiv^?$} & \bl{a} & \onslide<3->{\YES}\\
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&\bl{(a $\cdot$ b) $\cdot$ c} & \bl{$\equiv^?$} & \bl{a $\cdot$ (b $\cdot$ c)} & \onslide<4->{\YES}\\
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&\bl{a $\cdot$ a} & \bl{$\equiv^?$} & \bl{a} & \onslide<5->{\NO}\\
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&\bl{$\epsilon^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$} & \onslide<6->{\YES}\\
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&\bl{$\varnothing^*$} & \bl{$\equiv^?$} & \bl{$\varnothing$} & \onslide<7->{\NO}\\
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\FORALLR &\bl{r $\cdot$ $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<8->{\YES}\\
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\FORALLR &\bl{r + $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<9->{\NO}\\
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\FORALLR &\bl{r + $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<10->{\YES}\\
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\FORALLR &\bl{r $\cdot$ $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<11->{\NO}\\
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&\bl{c $\cdot$ (a + b)} & \bl{$\equiv^?$} & \bl{(c $\cdot$ a) + (c $\cdot$ b)} & \onslide<12->{\YES}\\
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&\bl{a$^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$ + (a $\cdot$ a$^*$)} & \onslide<13->{\YES}
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}The Meaning of Matching\end{tabular}}
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\large
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a regular expression \bl{r} matches a string \bl{s} is defined as
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\begin{center}
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\bl{s $\in$ $L$(r)}\\
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\end{center}\bigskip\bigskip\pause
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\small
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if \bl{r$_1$ $\equiv$ r$_2$}, then \bl{$s$ $\in$ $L$(r$_1$)} iff \bl{$s$ $\in$ $L$(r$_2$)}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}}
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\begin{itemize}
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\item given a regular expression \bl{r} and a string \bl{s}, say yes or no for whether
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\begin{center}
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\bl{s $\in$ $L$(r)}
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\end{center}\bigskip\bigskip\pause
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\only<2>{\item foo}%
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\only<3>{\item bar}
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}An Matching Algorithm\end{tabular}}
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7
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\small
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whether a regular expression matches the empty string:\medskip
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{\lstset{language=Scala}\fontsize{8}{10}\selectfont
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\texttt{\lstinputlisting{app5.scala}}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Derivative of a Rexp\end{tabular}}
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\large
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If \bl{r} matches the string \bl{c::s}, what is a regular expression that matches \bl{s}?\bigskip\bigskip\bigskip\bigskip
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\small
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\bl{der c r} gives the answer
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
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\begin{center}
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\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
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\bl{der c ($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\
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\bl{der c ($\epsilon$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\
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\bl{der c (d)} & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
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\bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
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\bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{((der c r$_1$) $\cdot$ r$_2$) + } & \\
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& & \bl{\hspace{3mm}(if nullable r$_1$ then der c r$_2$ else $\varnothing$)}\\
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\bl{der c (r$^*$)} & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
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\bl{ders [] r} & \bl{$\dn$} & \bl{r} & \\
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\bl{ders (c::s) r} & \bl{$\dn$} & \bl{ders s (der c r)} & \\
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
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{\lstset{language=Scala}\fontsize{8}{10}\selectfont
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\texttt{\lstinputlisting{app6.scala}}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}The Rexp Matcher\end{tabular}}
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{\lstset{language=Scala}\fontsize{8}{10}\selectfont
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\texttt{\lstinputlisting{app7.scala}}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}This Course\end{tabular}}
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We will have a look at:
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\begin{itemize}
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\item regular expressions / regular expression matching
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\item automata
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\item the Myhill-Nerode theorem
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\item parsing
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\item grammars
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\item a small interpreter / web browser
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Exam\end{tabular}}
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\begin{itemize}
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\item The question ``Is this relevant for the exam?'' is not appreciated!\bigskip\\
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Whatever is in the homework sheets (and is not marked optional) is relevant for the
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exam.\\ No code needs to be written.
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\end{itemize}
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\end{frame}}
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\mode<presentation>{
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\begin{frame}[t]
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\frametitle{\begin{tabular}{c}Maps in Scala\end{tabular}}
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\begin{itemize}
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\item {\bf\texttt{map}} takes a function, say f, and applies it to every element of the list:
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\end{itemize}
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\begin{textblock}{15}(2,7)
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\fontsize{13}{14}\selectfont
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\bf\texttt{List(1, 2, 3, 4, 5, 6, 7, 8, 9)}
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\end{textblock}
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\begin{textblock}{15}(2,10)
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\fontsize{13}{14}\selectfont
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\bf\texttt{List(1, 4, 9, 16, 25, 36, 49, 64, 81)}
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\end{textblock}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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