
diff -r 6eff65f7e6cd -r 5353d405e4e6 slides02.tex
--- a/slides02.tex	Thu Sep 27 12:22:21 2012 +0100
+++ b/slides02.tex	Sat Sep 29 12:46:42 2012 +0100
@@ -71,8 +71,9 @@
 	showstringspaces=false}
 
 % beamer stuff 
-\renewcommand{\slidecaption}{AFL 01, King's College London, 26.~September 2012}
-
+\renewcommand{\slidecaption}{AFL 02, King's College London, 3.~October 2012}
+\newcommand{\bl}[1]{\textcolor{blue}{#1}}       
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
 
 \begin{document}
 
@@ -83,7 +84,7 @@
   \begin{tabular}{@ {}c@ {}}
   \\[-3mm]
   \LARGE Automata and \\[-2mm] 
-  \LARGE Formal Languages (1)\\[-3mm] 
+  \LARGE Formal Languages (2)\\[-3mm] 
   \end{tabular}}
 
   \begin{center}
@@ -108,258 +109,6 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \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 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}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\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)
@@ -378,19 +127,6 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
-
-{\lstset{language=Scala}\fontsize{8}{10}\selectfont
-\texttt{\lstinputlisting{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}}
 
@@ -400,32 +136,40 @@
  \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)$^n$}}\\
+ \bl{$L$(r$_1$ $\cdot$ r$_2$)}  & \bl{$\dn$} & \bl{$L$(r$_1$) @ $L$(r$_2$)}\\
+ \bl{$L$(r$^*$)}                   & \bl{$\dn$} & \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}
+\hspace{5mm}\textcolor{gray}{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\
+\textcolor{gray}{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$}  
+\end{textblock}
 
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+\newcommand{\YES}{\textcolor{gray}{yes}}
+\newcommand{\NO}{\textcolor{gray}{no}}
+\newcommand{\FORALLR}{\textcolor{gray}{$\forall$ r.}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \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
+\frametitle{\begin{tabular}{c}Reg Exp Equivalences\end{tabular}}
 
 \begin{center}
-\bl{s $\in$ $L$(r)}\\ 
+\begin{tabular}{lrcl@ {\hspace{7mm}}l}
+&\bl{(a + b)  + c} & \bl{$\equiv^?$} & \bl{a + (b + c)} & \onslide<2->{\YES}\\
+&\bl{a + a} & \bl{$\equiv^?$} & \bl{a} & \onslide<3->{\YES}\\
+&\bl{(a $\cdot$ b)  $\cdot$ c} & \bl{$\equiv^?$} & \bl{a $\cdot$ (b $\cdot$ c)} & \onslide<4->{\YES}\\
+&\bl{a $\cdot$ a} & \bl{$\equiv^?$} & \bl{a} & \onslide<5->{\NO}\\
+&\bl{$\epsilon^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$} & \onslide<6->{\YES}\\
+&\bl{$\varnothing^*$} & \bl{$\equiv^?$} & \bl{$\varnothing$} & \onslide<7->{\NO}\\
+\FORALLR &\bl{r $\cdot$ $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<8->{\YES}\\
+\FORALLR &\bl{r + $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<9->{\NO}\\
+\FORALLR &\bl{r + $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<10->{\YES}\\
+\FORALLR &\bl{r $\cdot$ $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<11->{\NO}\\
+&\bl{c $\cdot$ (a + b)} & \bl{$\equiv^?$} & \bl{(c $\cdot$ a) + (c $\cdot$ b)} & \onslide<12->{\YES}\\
+&\bl{a$^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$ + (a $\cdot$ a$^*$)} & \onslide<13->{\YES}
+\end{tabular}
 \end{center}
 
 \end{frame}}
@@ -434,7 +178,44 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Nullability\end{tabular}}
+\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}\bigskip\bigskip\pause
+
+\small
+if \bl{r$_1$ $\equiv$ r$_2$}, then \bl{$s$ $\in$ $L$(r$_1$)} iff \bl{$s$ $\in$ $L$(r$_2$)}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}}
+
+\begin{itemize}
+\item given a regular expression \bl{r} and a string \bl{s}, say yes or no for whether
+\begin{center}
+\bl{s $\in$ $L$(r)}
+\end{center}\bigskip\bigskip\pause
+\only<2>{\item foo}%
+\only<3>{\item bar}
+\end{itemize}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}An Matching Algorithm\end{tabular}}
 
 \small
 whether a regular expression matches the empty string:\medskip




