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\documentclass[dvipsnames,14pt,t]{beamer}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{beamerthemeplaincu}
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\usepackage[absolute,overlay]{textpos}
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\usepackage{ifthen}
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\usepackage{tikz}
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\usepackage{pgf}
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\usepackage{calc}
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\usepackage{ulem}
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\usepackage{courier}
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\usepackage{listings}
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\renewcommand{\uline}[1]{#1}
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\usetikzlibrary{arrows}
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\usetikzlibrary{automata}
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\usetikzlibrary{shapes}
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\usetikzlibrary{shadows}
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\usetikzlibrary{positioning}
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\usetikzlibrary{calc}
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\usetikzlibrary{plotmarks}
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\usepackage{graphicx}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../langs}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../data}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\makeatletter
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\@empty\z@\@empty
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\makeatother
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% beamer stuff
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\slidecaption}{AFL 06, King's College London, 30.~October 2013}
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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 (6)\\[3mm]
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\end{tabular}}
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Office: & S1.27 (1st floor Strand Building)\\
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Slides: & KEATS (also home work is there)\\
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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While regular expressions are very useful for lexing,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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there is no regular expression that can recognise the language \bl{$a^nb^n$}.\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bl{$(((()()))())$} \;\;vs.\;\; \bl{$(((()()))()))$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\qq}{\mbox{\texttt{"}}}
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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}Grammars\end{tabular}}
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A (context-free) grammar \bl{$G$} consists of
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\begin{itemize}
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\item a finite set of nonterminal symbols (upper case)
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\item a finite terminal symbols or tokens (lower case)
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\item a start symbol (which must be a nonterminal)
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\item a set of rules
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\begin{center}
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\bl{$A \rightarrow \text{rhs}$}
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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where \bl{rhs} are sequences involving terminals and nonterminals,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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including the empty sequence \bl{$\epsilon$}.\medskip\pause
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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We also allow rules
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\begin{center}
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\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
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\end{center}
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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}Palindromes\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$S$ & $\rightarrow$ & $\epsilon$ \\
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$S$ & $\rightarrow$ & $a\cdot S\cdot a$ \\
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$S$ & $\rightarrow$ & $b\cdot S\cdot b$ \\
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\end{tabular}}
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\end{center}\pause
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or
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
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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}Arithmetic Expressions\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{lcl}
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$E$ & $\rightarrow$ & $num\_token$ \\
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$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
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$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
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$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
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$E$ & $\rightarrow$ & $( \cdot E \cdot )$
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\end{tabular}}
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\end{center}\pause
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\bl{\texttt{1 + 2 * 3 + 4}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{\begin{tabular}{c}A CFG Derivation\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\begin{enumerate}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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\item Begin with a string containing only the start symbol, say \bl{$S$}\bigskip
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184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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\item Replace any nonterminal \bl{$X$} in the string by the
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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right-hand side of some production \bl{$X \rightarrow \text{rhs}$}\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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\item Repeat 2 until there are no nonterminals
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{enumerate}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\bl{$S \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots $}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\frametitle{\begin{tabular}{c}Example Derivation\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\bl{\begin{tabular}{lcl}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{center}\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{tabular}{lcl}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\bl{$S$} & \bl{$\rightarrow$} & \bl{$aSa$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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& \bl{$\rightarrow$} & \bl{$abSba$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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& \bl{$\rightarrow$} & \bl{$abaSaba$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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& \bl{$\rightarrow$} & \bl{$abaaba$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{tabular}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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200 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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203 |
\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\frametitle{\begin{tabular}{c}Example Derivation\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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205 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\bl{\begin{tabular}{lcl}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
$E$ & $\rightarrow$ & $num\_token$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
212 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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213 |
\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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215 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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218 |
\begin{tabular}{@{}c@{}c@{}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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220 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E*E$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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221 |
& \bl{$\rightarrow$} & \bl{$E+E*E$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
& \bl{$\rightarrow$} & \bl{$E+E*E+E$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
& \bl{$\rightarrow^+$} & \bl{$1+2*3+4$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
\end{tabular} &\pause
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E+E$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
& \bl{$\rightarrow$} & \bl{$E+E+E$}\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
& \bl{$\rightarrow$} & \bl{$E+E*E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
& \bl{$\rightarrow^+$} & \bl{$1+2*3+4$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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231 |
\end{tabular}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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232 |
\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
235 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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236 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
239 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
240 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
241 |
\frametitle{\begin{tabular}{c}Language of a CFG\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
242 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
243 |
Let \bl{$G$} be a context-free grammar with start symbol \bl{$S$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
244 |
Then the language \bl{$L(G)$} is:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
245 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
246 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
247 |
\bl{$\{c_1\ldots c_n \;|\; \forall i.\; c_i \in T \wedge S \rightarrow^* c_1\ldots c_n \}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
248 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
249 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
250 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
251 |
\item Terminals, because there are no rules for replacing them.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
252 |
\item Once generated, terminals are ``permanent''.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
\item Terminals ought to be tokens of the language\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
254 |
(but can also be strings).
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
255 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
256 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
257 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
258 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
259 |
|
|
49
|
260 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
261 |
\mode<presentation>{
|
|
|
262 |
\begin{frame}[c]
|
|
50
|
263 |
\frametitle{\begin{tabular}{c}Parse Trees\end{tabular}}
|
|
49
|
264 |
|
|
|
265 |
\begin{center}
|
|
|
266 |
\bl{\begin{tabular}{lcl}
|
|
53
|
267 |
$E$ & $\rightarrow$ & $F \;|\; F \cdot * \cdot F$\\
|
|
|
268 |
$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
|
|
|
269 |
$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
|
|
49
|
270 |
\end{tabular}}
|
|
|
271 |
\end{center}
|
|
|
272 |
|
|
|
273 |
\begin{center}
|
|
|
274 |
\begin{tikzpicture}[level distance=8mm, blue]
|
|
50
|
275 |
\node {$E$}
|
|
|
276 |
child {node {$F$}
|
|
|
277 |
child {node {$T$}
|
|
|
278 |
child {node {(\,$E$\,)}
|
|
|
279 |
child {node{$F$ *{} $F$}
|
|
|
280 |
child {node {$T$} child {node {2}}}
|
|
|
281 |
child {node {$T$} child {node {3}}}
|
|
49
|
282 |
}
|
|
|
283 |
}
|
|
|
284 |
}
|
|
50
|
285 |
child {node {+}}
|
|
|
286 |
child {node {$T$}
|
|
|
287 |
child {node {(\,$E$\,)}
|
|
|
288 |
child {node {$F$}
|
|
|
289 |
child {node {$T$ +{} $T$}
|
|
49
|
290 |
child {node {3}}
|
|
|
291 |
child {node {4}}
|
|
|
292 |
}
|
|
|
293 |
}}
|
|
|
294 |
}};
|
|
|
295 |
\end{tikzpicture}
|
|
|
296 |
\end{center}
|
|
|
297 |
|
|
50
|
298 |
\begin{textblock}{5}(1, 6.5)
|
|
49
|
299 |
\bl{\texttt{(2*3)+(3+4)}}
|
|
|
300 |
\end{textblock}
|
|
|
301 |
|
|
|
302 |
\end{frame}}
|
|
|
303 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
306 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
307 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
\end{center}\pause\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
320 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
A CFG is \alert{left-recursive} if it has a nonterminal \bl{$E$} such
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
that \bl{$E \rightarrow^+ E\cdot \ldots$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
323 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
325 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
|
|
50
|
328 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
329 |
\mode<presentation>{
|
|
|
330 |
\begin{frame}[c]
|
|
|
331 |
\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
|
|
|
332 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
A grammar is \alert{ambiguous} if there is a string that has at least two different parse trees.
|
|
50
|
334 |
|
|
|
335 |
|
|
|
336 |
\begin{center}
|
|
|
337 |
\bl{\begin{tabular}{lcl}
|
|
|
338 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
|
53
|
339 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
|
|
340 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
|
|
341 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
|
|
342 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
|
50
|
343 |
\end{tabular}}
|
|
|
344 |
\end{center}
|
|
|
345 |
|
|
|
346 |
\bl{\texttt{1 + 2 * 3 + 4}}
|
|
|
347 |
|
|
|
348 |
\end{frame}}
|
|
|
349 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
350 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\frametitle{\begin{tabular}{c}Dangling Else\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
Another ambiguous grammar:\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
358 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
360 |
$E$ & $\rightarrow$ & if $E$ then $E$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
& $|$ & if $E$ then $E$ else $E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
& $|$ & \ldots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
366 |
\bl{\texttt{if a then if x then y else c}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
372 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
\frametitle{\begin{tabular}{c}Parser Combinators\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
Parser combinators: \bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
378 |
\begin{minipage}{1.1\textwidth}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
380 |
\mbox{}\hspace{-12mm}\mbox{}$\underbrace{\text{list of tokens}}_{\text{input}}$ \bl{$\Rightarrow$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
381 |
$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
\end{minipage}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
\item sequencing
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
\item alternative
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
\item semantic action
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
Alternative parser (code \bl{$p\;||\;q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
399 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
\item apply \bl{$p$} and also \bl{$q$}; then combine the outputs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
408 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
\item apply first \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\item then apply \bl{$q$} to the unparsed parts
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
\item then combine the results:\\ \mbox{}\;\;((output$_1$, output$_2$), unparsed part)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
Function parser (code \bl{$p \Rightarrow f$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
\item apply \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
\item then apply the function \bl{$f$} to each first component
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
\end{center}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
\bl{$f$} is the semantic action (``what to do with the parsed input'')
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
Addition
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
\bl{$T \sim + \sim E \Rightarrow \underbrace{f((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
Multiplication
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
\bl{$F \sim * \sim T \Rightarrow f((x,y), z) \Rightarrow x * z$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
Parenthesis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\bl{$\text{(} \sim E \sim \text{)} \Rightarrow f((x,y), z) \Rightarrow y$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
482 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
\frametitle{\begin{tabular}{c}Types of Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
then \bl{$p \sim q$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\bl{$T \times S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
and \bl{$p \;||\; q$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\bl{$T$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
\bl{$T$} to \bl{$S$}, then
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\bl{$p \Rightarrow f$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\bl{$S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\frametitle{\begin{tabular}{c}Input Types of Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
\item input: \alert{string}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\item output: set of (output\_type, \alert{string})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
\end{itemize}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
actually it can be any input type as long as it is a kind of sequence
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
(for example a string)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
534 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
\frametitle{\begin{tabular}{c}Scannerless Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
\item input: \alert{string}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
\item output: set of (output\_type, \alert{string})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
but lexers are better when whitespaces or comments need to be filtered out;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
then input is a sequence of tokens
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
552 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
\frametitle{\begin{tabular}{c}Successful Parses\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
\item input: string
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\item output: \alert{set of} (output\_type, string)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
a parse is successful whenever the input has been
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
fully ``consumed'' (that is the second component is empty)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
\begin{frame}[c]
|
170
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
\frametitle{Abstract Parser Class}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
\mbox{\lstset{language=Scala}\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
\texttt{\lstinputlisting{../progs/app7.scala}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
{\lstset{language=Scala}\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\texttt{\lstinputlisting{../progs/app8.scala}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
586 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
587 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
588 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
589 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\frametitle{\begin{tabular}{c}Two Grammars\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
Which languages are recognised by the following two grammars?
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
$S$ & $\rightarrow$ & $1 \cdot S \cdot S$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
& $|$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
$U$ & $\rightarrow$ & $1 \cdot U$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
& $|$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
\mbox{}\\[-25mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
619 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
\begin{tikzpicture}[y=.2cm, x=.009cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
%axis
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
\draw (0,0) -- coordinate (x axis mid) (1000,0);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
\draw (0,0) -- coordinate (y axis mid) (0,30);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
%ticks
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
\foreach \x in {0, 20, 100, 200,...,1000}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
\draw (\x,1pt) -- (\x,-3pt)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
node[anchor=north] {\small \x};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
\foreach \y in {0,5,...,30}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
\draw (1pt,\y) -- (-3pt,\y)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
node[anchor=east] {\small\y};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
%labels
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\node[below=0.6cm] at (x axis mid) {\bl{1}s};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\node[rotate=90, left=1.2cm] at (y axis mid) {secs};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
%plots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
\draw[color=blue] plot[mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
file {s-grammar1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
\only<2->{\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
file {s-grammar2.data};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
%legend
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
\begin{scope}[shift={(400,20)}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
\draw[color=blue] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
node[right]{\small unambiguous};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
\only<2->{\draw[yshift=\baselineskip, color=red] (0,0) --
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
node[right]{\small ambiguous};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
\end{scope}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
\frametitle{\begin{tabular}{c}While-Language\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
$Stmt$ & $\rightarrow$ & $\text{skip}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
& $|$ & $Id := AExp$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
& $|$ & $\text{if}\; B\!Exp \;\text{then}\; Block \;\text{else}\; Block$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
& $|$ & $\text{while}\; B\!Exp \;\text{do}\; Block$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
$Stmts$ & $\rightarrow$ & $Stmt \;\text{;}\; Stmts$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
& $|$ & $Stmt$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
$Block$ & $\rightarrow$ & $\{ Stmts \}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
& $|$ & $Stmt$\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
$AExp$ & $\rightarrow$ & \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
$BExp$ & $\rightarrow$ & \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
676 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
681 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
682 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\bl{\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
$\{$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
\;\;$x := 5 \text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
\;\;$y := x * 3\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
\;\;$y := x * 4\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
693 |
\;\;$x := u * 3$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
694 |
$\}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
695 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
696 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
700 |
\item \bl{\text{eval}(stmt, env)}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
701 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
702 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
705 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
706 |
|
|
50
|
707 |
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
|
|
53
|
709 |
|
|
51
|
710 |
|
|
49
|
711 |
\end{document}
|
|
|
712 |
|
|
|
713 |
%%% Local Variables:
|
|
|
714 |
%%% mode: latex
|
|
|
715 |
%%% TeX-master: t
|
|
|
716 |
%%% End:
|
|
|
717 |
|