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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{../slides}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{../graphics}
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% beamer stuff
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\renewcommand{\slidecaption}{CFL 07, King's College London}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Compilers and \\[-2mm]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\LARGE Formal Languages (7)\\[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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Office: & N7.07 (North Wing, Bush House)\\
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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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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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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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\newcommand{\qq}{\mbox{\texttt{"}}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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{CFGs}
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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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A \alert{context-free} grammar (CFG) \bl{$G$} consists of:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{itemize}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\item a finite set of nonterminal symbols (upper case)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\item a finite terminal symbols or tokens (lower case)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\item a start symbol (which must be a nonterminal)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\item a set of rules
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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{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
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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{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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where \bl{rhs} are sequences involving terminals and nonterminals (can also be empty).\medskip\pause
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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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\end{itemize}
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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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\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>
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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}Hierarchy of 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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Recall that languages are sets of strings.
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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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changeset
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\begin{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
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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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\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\draw (0,-1.4) node [rect] {regular languages};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{tikzpicture}
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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{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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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>
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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}Arithmetic Expressions\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>
diff
changeset
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A grammar for arithmetic expressions and numbers:
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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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\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
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$E$ & $\rightarrow$ & $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1 \;|\: \ldots \;|\; 9$
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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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96 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Unfortunately it is left-recursive (and ambiguous).\medskip\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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A problem for \alert{recursive descent parsers} (e.g.~parser combinators).
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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\bigskip\pause
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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100 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
102 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
103 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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106 |
\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
\begin{frame}[t]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
\frametitle{\begin{tabular}{c}Numbers\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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110 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
111 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
\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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114 |
$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
A non-left-recursive, non-ambiguous grammar for numbers:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
$N$ & $\rightarrow$ & $0 \cdot N \;|\;1 \cdot N \;|\;\ldots\;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
125 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
126 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
127 |
\end{frame}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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129 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
130 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
131 |
\mode<presentation>{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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133 |
\frametitle{\begin{tabular}{c}Operator Precedences\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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134 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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135 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
To disambiguate
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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137 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
139 |
\bl{\begin{tabular}{lcl}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
141 |
\end{tabular}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
144 |
Decide on how many precedence levels, say\medskip\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
145 |
\hspace{5mm}highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
146 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
147 |
\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
\bl{\begin{tabular}{lcl}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
149 |
$E_{low}$ & $\rightarrow$ & $E_{med} \cdot + \cdot E_{low} \;|\; E_{med}$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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150 |
$E_{med}$ & $\rightarrow$ & $E_{hi} \cdot * \cdot E_{med} \;|\; E_{hi}$\\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
$E_{hi}$ & $\rightarrow$ & $( \cdot E_{low} \cdot ) \;|\;N$ \\
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
152 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
153 |
\end{center}\pause
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
\small What happens with \bl{$1 + 3 + 4$}?
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
160 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
\frametitle{\begin{tabular}{c}Removing Left-Recursion\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
The rule for numbers is directly left-recursive:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
Translate
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
\begin{tabular}{ccc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
$N$ & $\rightarrow$ & $N \cdot \alpha$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
& $\;|\;$ & $\beta$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
& {\Large$\Rightarrow$} &
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
$N$ & $\rightarrow$ & $\beta \cdot N'$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
$N'$ & $\rightarrow$ & $\alpha \cdot N'$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
& $\;|\;$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
Which means
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1 \cdot N'$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
$N'$ & $\rightarrow$ & $N \cdot N' \;|\; \epsilon$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
198 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
\frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
All rules must be of the form
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
\bl{$A \rightarrow a$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
212 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
213 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
214 |
or
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
215 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
216 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
\bl{$A \rightarrow B\cdot C$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
218 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
219 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
220 |
No rule can contain \bl{$\epsilon$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
221 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
231 |
\item If \bl{$A\rightarrow \alpha \cdot B \cdot \beta$} and \bl{$B \rightarrow \epsilon$} are in the grammar,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
232 |
then add \bl{$A\rightarrow \alpha \cdot \beta$} (iterate if necessary).
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
\item Throw out all \bl{$B \rightarrow \epsilon$}.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
\end{enumerate}
|
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
|
236 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
\begin{tabular}{ccc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
239 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
240 |
$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
241 |
$N'$ & $\rightarrow$ & $N \cdot N'\;|\;\epsilon$\\
|
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 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
244 |
\\
|
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 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
247 |
\end{tabular}} &
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
248 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
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 |
$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
251 |
$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
252 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
254 |
$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
255 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
256 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
257 |
\end{center}
|
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 |
\pause\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
260 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
261 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
262 |
$N$ & $\rightarrow$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
263 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
264 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
265 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
266 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
267 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
268 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
269 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
270 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
271 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
273 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
If grammar is in Chomsky normalform \ldots
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\bl{\begin{tabular}{@ {}lcl@ {}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
$S$ & $\rightarrow$ & $N\cdot P$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
$P$ & $\rightarrow$ & $V\cdot N$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
$N$ & $\rightarrow$ & $N\cdot N$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
$N$ & $\rightarrow$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
$V$ & $\rightarrow$ & $\texttt{trains}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
\bl{\texttt{Jeff trains geometry students}}
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
293 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
296 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
297 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
298 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
\item fastest possible algorithm for recognition problem
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
\item runtime is \bl{$O(n^3)$}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
\item grammars need to be transferred into CNF
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
\end{frame}}
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
Recall that languages are sets of strings.
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
317 |
[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
320 |
\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
321 |
\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
323 |
\draw (0,-1.4) node [rect] {regular languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\end{tikzpicture}
|
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 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
\end{frame}}
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
329 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
334 |
\frametitle{\begin{tabular}{c}Context Sensitive Grms\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
335 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
336 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
337 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
338 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
339 |
$S$ & $\Rightarrow$ & $bSAA\;|\; \epsilon$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
340 |
$A$ & $\Rightarrow$ & $a$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
341 |
$bA$ & $\Rightarrow$ & $Ab$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
343 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\bl{$S \Rightarrow\ldots\Rightarrow^? "ababaa"$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\begin{frame}[c]
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
\begin{center}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
\bl{\begin{tabular}{@{}lcl@{}}
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
358 |
\textit{Stmt} & $\rightarrow$ & $\texttt{skip}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
& $|$ & \textit{Id}\;\texttt{:=}\;\textit{AExp}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
360 |
& $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Block} \;\texttt{else}\; \textit{Block}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
& $|$ & \texttt{while}\; \textit{BExp} \;\texttt{do}\; \textit{Block}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
& $|$ & \texttt{read}\;\textit{Id}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
& $|$ & \texttt{write}\;\textit{Id}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
& $|$ & \texttt{write}\;\textit{String}\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
\textit{Stmts} & $\rightarrow$ & \textit{Stmt} \;\texttt{;}\; \textit{Stmts}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
366 |
& $|$ & \textit{Stmt}\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
367 |
\textit{Block} & $\rightarrow$ & \texttt{\{}\,\textit{Stmts}\,\texttt{\}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
& $|$ & \textit{Stmt}\medskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
\textit{AExp} & $\rightarrow$ & \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
\textit{BExp} & $\rightarrow$ & \ldots\\
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
\end{tabular}}
|
187
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
372 |
\end{center}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
|
369
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
\mode<presentation>{
|
369
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
378 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
380 |
\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
|
369
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
381 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
\end{frame}}
|
369
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
\mode<presentation>{
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
\begin{frame}[c]
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}}
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
\bl{\begin{tabular}{l}
|
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 |
\;\;$x := 5 \text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\;\;$y := x * 3\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
\;\;$y := x * 4\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
\;\;$x := u * 3$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
$\}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
399 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
\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
|
404 |
\item \bl{\text{eval}(stmt, env)}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
|
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 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
|
63
|
416 |
\begin{center}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
$\text{eval}(n, E)$ & $\dn$ & $n$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
\end{tabular}}
|
63
|
427 |
\end{center}
|
|
428 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
\end{frame}}
|
63
|
430 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
431 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
\mode<presentation>{
|
63
|
433 |
\begin{frame}[c]
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}
|
63
|
435 |
|
|
436 |
\begin{center}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
\text{eval}(cs_1,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
448 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
|
63
|
450 |
\end{tabular}}
|
|
451 |
\end{center}
|
|
452 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\end{frame}}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\mode<presentation>{
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\begin{frame}[c]
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\frametitle{\begin{tabular}{c}Test Program\end{tabular}}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\mbox{}\\[-18mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
{\lstset{language=While}%%\fontsize{10}{12}\selectfont
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\texttt{\lstinputlisting{../progs/loops.while}}}
|
63
|
466 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
\end{frame}}
|
63
|
468 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
469 |
|
|
470 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
471 |
\mode<presentation>{
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
\begin{frame}[t]
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
|
63
|
474 |
|
|
475 |
\begin{center}
|
188
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
477 |
\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
478 |
\addplot+[smooth] file {interpreted.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
479 |
\end{axis}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
480 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\end{center}
|
63
|
482 |
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
483 |
\end{frame}}
|
63
|
484 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
485 |
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
487 |
\mode<presentation>{
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
\begin{frame}[c]
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}}
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
490 |
|
188
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 introduced in 1995
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
493 |
\item is a stack-based VM (like Postscript, CLR of .Net)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
494 |
\item contains a JIT compiler
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
\item many languages take advantage of JVM's infrastructure (JRE)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\item is garbage collected $\Rightarrow$ no buffer overflows
|
387
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\item some languages compile to the JVM: Scala, Clojure\ldots
|
369
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
\end{frame}}
|
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 |
|
184
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
|
63
|
504 |
\end{document}
|
|
505 |
|
|
506 |
%%% Local Variables:
|
|
507 |
%%% mode: latex
|
|
508 |
%%% TeX-master: t
|
|
509 |
%%% End:
|
|
510 |
|