
diff -r 5988e44ea048 -r dff4b062a8a9 slides07.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/slides07.tex	Wed Nov 14 08:46:00 2012 +0000
@@ -0,0 +1,542 @@
+\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}
+\usetikzlibrary{plotmarks}
+\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 07, King's College London, 14.~November 2012}
+\newcommand{\bl}[1]{\textcolor{blue}{#1}}       
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+
+
+% The data files, written on the first run.
+\begin{filecontents}{re-python.data}
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+\end{filecontents}
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}<1>[t]
+\frametitle{%
+  \begin{tabular}{@ {}c@ {}}
+  \\[-3mm]
+  \LARGE Automata and \\[-2mm] 
+  \LARGE Formal Languages (7)\\[3mm] 
+  \end{tabular}}
+
+  \normalsize
+  \begin{center}
+  \begin{tabular}{ll}
+  Email:  & christian.urban at kcl.ac.uk\\
+  Of$\!$fice: & S1.27 (1st floor Strand Building)\\
+  Slides: & KEATS (also home work is there)\\
+  \end{tabular}
+  \end{center}
+
+
+\end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}\bl{$(a?\{n\})a\{n\}$}\end{tabular}}
+
+\mbox{}\\[-13mm]
+
+\begin{tikzpicture}[y=.2cm, x=.3cm]
+ 	%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] {\x};
+    	\foreach \y in {0,5,...,30}
+     		\draw (1pt,\y) -- (-3pt,\y) 
+     			node[anchor=east] {\y}; 
+	%labels      
+	\node[below=0.6cm] at (x axis mid) {\bl{a}s};
+	\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+	%plots
+	\draw[color=blue] plot[mark=*, mark options={fill=white}] 
+		file {re-python.data};
+	\draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 
+		file {re1.data};
+         \draw[color=green] plot[mark=square*, mark options={fill=white} ] 
+		file {re2.data};
+         \draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ] 
+		file {re-ruby.data};
+    
+	%legend
+	\begin{scope}[shift={(4,20)}] 
+	\draw[color=blue] (0,0) -- 
+		plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) 
+		node[right]{\small Python};
+	\draw[yshift=-\baselineskip, color=brown] (0,0) -- 
+		plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+		node[right]{\small Ruby (Daniel Baldwin)};
+         \draw[yshift=\baselineskip, color=red] (0,0) -- 
+		plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+		node[right]{\small Scala V1};	
+	 \draw[yshift=2\baselineskip, color=green] (0,0) -- 
+		plot[mark=square*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+		node[right]{\small Scala V2 with simplifications};
+	\end{scope}
+\end{tikzpicture}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+
+\begin{tikzpicture}[y=.7cm, x=.0009cm]
+ 	%axis
+	\draw (0,0) -- coordinate (x axis mid) (10000,0);
+    	\draw (0,0) -- coordinate (y axis mid) (0,6);
+    	%ticks
+    	\foreach \x in {0,2000,...,10000}
+     		\draw (\x,1pt) -- (\x,-3pt)
+			node[anchor=north] {\x};
+    	\foreach \y in {0,1,...,6}
+     		\draw (1pt,\y) -- (-3pt,\y) 
+     			node[anchor=east] {\y}; 
+	%labels      
+	\node[below=0.6cm] at (x axis mid) {\bl{a}s};
+	\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+	%plots
+	\draw[color=blue] plot[mark=*, mark options={fill=white}] 
+		file {re-internal.data};
+	\only<1->{	 
+         \draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 
+		file {re3.data};}
+    
+	%legend
+	\begin{scope}[shift={(2000,4)}] 
+	\draw[color=blue] (0,0) -- 
+		plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) 
+		node[right]{\small Scala Internal};
+        \only<1->{
+	\draw[yshift=\baselineskip, color=red] (0,0) -- 
+		plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+		node[right]{\small Scala V3 with explicit $\_\{\_\}$};}
+	\end{scope}
+\end{tikzpicture}
+
+\begin{center}
+\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
+  \\[-8mm]
+  \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$}  & \bl{if nullable r$_1$}\\
+  & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ 
+  & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\
+  \bl{der c (r$\{n\}$)} & \bl{$\dn$} & \bl{if $n = 0$ then $\varnothing$}\\
+  & & \bl{else (der c r) $\cdot$ r$\{n - 1\}$}
+  \end{tabular}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+
+\newcommand{\qq}{\mbox{\texttt{"}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CFG\end{tabular}}
+
+A \alert{context-free} grammar \bl{$G$} consists of
+
+\begin{itemize}
+\item a finite set of nonterminal symbols (upper case)
+\item a finite terminal symbols or tokens (lower case)
+\item a start symbol (which must be a nonterminal)
+\item a set of rules
+\begin{center}
+\bl{$A \rightarrow \text{rhs}$}
+\end{center}
+
+where \bl{rhs} are sequences involving terminals and nonterminals (can also be empty).\medskip\pause
+
+We can also allow rules
+\begin{center}
+\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
+\end{center}
+\end{itemize}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}A CFG Derivation\end{tabular}}
+
+\begin{enumerate}
+\item Begin with a string with only the start symbol \bl{$S$}\bigskip
+\item Replace any non-terminal \bl{$X$} in the string by the
right-hand side of some production \bl{$X \rightarrow \text{rhs}$}\bigskip
+\item Repeat 2 until there are no non-terminals
+\end{enumerate}
+
+\begin{center}
+\bl{$S \rightarrow \ldots \rightarrow \ldots  \rightarrow \ldots  \rightarrow \ldots $}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Language of a CFG\end{tabular}}
+
+Let \bl{$G$} be a context-free grammar with start symbol \bl{$S$}. 
+Then the language \bl{$L(G)$} is:
+
+\begin{center}
+\bl{$\{c_1\ldots c_n \;|\; \forall i.\; c_i \in T \wedge S \rightarrow^* c_1\ldots c_n \}$}
+\end{center}\pause
+
+\begin{itemize}
+\item Terminals are so-called because there are no rules for replacing them
+\item Once generated, terminals are ``permanent''
+\item Terminals ought to be tokens of the language (at least in this course)
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $num\_token$ \\
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ &  $( \cdot E \cdot )$ 
+\end{tabular}}
+\end{center}\pause\bigskip
+
+A CFG is \alert{left-recursive} if it has a nonterminal \bl{$E$} such
+that \bl{$E \rightarrow^+ E\cdot \ldots$}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Parse Trees\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $F \;|\; F \cdot * \cdot F$\\
+$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
+$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
+\end{tabular}}
+\end{center}
+
+\begin{center}
+\begin{tikzpicture}[level distance=8mm, blue]
+  \node {$E$}
+    child {node {$F$} 
+     child {node {$T$} 
+                 child {node {(\,$E$\,)}
+                            child {node{$F$ *{} $F$}
+                                  child {node {$T$} child {node {2}}}
+                                  child {node {$T$} child {node {3}}} 
+                               }
+                          }
+              }
+     child {node {+}}
+     child {node {$T$}
+       child {node {(\,$E$\,)} 
+       child {node {$F$}
+       child {node {$T$ +{} $T$}
+                    child {node {3}}
+                    child {node {4}} 
+                 }
+                 }}
+    }};
+\end{tikzpicture}
+\end{center}
+
+\begin{textblock}{5}(1, 6.5)
+\bl{\texttt{(2*3)+(3+4)}}
+\end{textblock}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
+
+A CFG is \alert{ambiguous} if there is a string that has at least parse trees.
+
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $num\_token$ \\
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ &  $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ &  $( \cdot E \cdot )$ 
+\end{tabular}}
+\end{center}
+
+\bl{\texttt{1 + 2 * 3 + 4}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Dangling Else\end{tabular}}
+
+Another ambiguous grammar:\bigskip
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  if $E$ then $E$\\
+ & $|$ &  if $E$ then $E$ else $E$ \\
+ & $|$ &  id 
+\end{tabular}}
+\end{center}\bigskip
+
+\bl{\texttt{if a then if x then y else c}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+\end{document}
+
+%%% Local Variables:  
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 
+




