--- a/slides07.tex Sat Jun 15 09:11:11 2013 -0400
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,542 +0,0 @@
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-\usepackage[T1]{fontenc}
-\usepackage[latin1]{inputenc}
-\usepackage{mathpartir}
-\usepackage[absolute,overlay]{textpos}
-\usepackage{ifthen}
-\usepackage{tikz}
-\usepackage{pgf}
-\usepackage{calc}
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-\usepackage{graphicx}
-
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-% beamer stuff
-\renewcommand{\slidecaption}{AFL 07, King's College London, 14.~November 2012}
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-\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
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- %labels
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- \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) --
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- 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};
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-\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);
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- \foreach \x in {0,2000,...,10000}
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- file {re-internal.data};
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- 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}CFGs\end{tabular}}
-
-A \alert{context-free} grammar (CFG) \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:
-