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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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\usepackage{../grammar}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\hfuzz=220pt
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\pgfplotsset{compat=1.11}
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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{\bl}[1]{\textcolor{blue}{#1}}
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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}
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\begin{document}
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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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\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 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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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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{Regular Languages}
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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, there is
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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no regular expression that can recognise the language
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\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}\bigskip\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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\small
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\noindent So we cannot find out with regular expressions
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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whether parentheses are matched or unmatched.
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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{Hierarchy of Languages}
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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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\begin{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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[rect/.style={draw=black!50,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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top color=white,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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bottom color=black!20,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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rectangle,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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very thick,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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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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changeset
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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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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>
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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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
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{Grammars}
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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>
diff
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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>
diff
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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>
diff
changeset
|
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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>
diff
changeset
|
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\frametitle{Palindromes}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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A grammar for palindromes over the alphabet~\bl{$\{a,b\}$}:
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49
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118 |
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119 |
\begin{center}
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50
|
120 |
\bl{\begin{tabular}{lcl}
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$S$ & $\rightarrow$ & $\epsilon$ \\
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53
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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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|
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\end{tabular}}
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\end{center}\pause
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or
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128 |
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\begin{center}
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\bl{\begin{tabular}{lcl}
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53
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$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
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50
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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}\pause\bigskip
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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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\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
Can you find the grammar rules for matched parentheses?
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49
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137 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
\end{frame}
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
140 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
142 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\frametitle{Arithmetic Expressions}
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49
|
144 |
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|
145 |
\begin{center}
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|
146 |
\bl{\begin{tabular}{lcl}
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50
|
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$E$ & $\rightarrow$ & $num\_token$ \\
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53
|
148 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
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|
149 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
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|
150 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
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|
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$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
49
|
152 |
\end{tabular}}
|
50
|
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\end{center}\pause
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49
|
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\bl{\texttt{1 + 2 * 3 + 4}}
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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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\end{frame}
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|
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\frametitle{A CFG Derivation}
|
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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 |
\begin{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
\item Begin with a string containing only the start symbol, say \bl{$S$}\bigskip
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
\item Replace any nonterminal \bl{$X$} in the string by the
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
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
changeset
|
168 |
\item Repeat 2 until there are no nonterminals
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
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\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
\bl{$S \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots \rightarrow \ldots $}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
\frametitle{Example Derivation}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
\bl{$S$} & \bl{$\rightarrow$} & \bl{$aSa$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
& \bl{$\rightarrow$} & \bl{$abSba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
& \bl{$\rightarrow$} & \bl{$abaSaba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
& \bl{$\rightarrow$} & \bl{$abaaba$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
|
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 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
\frametitle{Example Derivation}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
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
|
213 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
214 |
\end{center}\bigskip
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
218 |
\begin{tabular}{@{}c@{}c@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
219 |
\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
220 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E*E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
221 |
& \bl{$\rightarrow$} & \bl{$E+E*E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
& \bl{$\rightarrow$} & \bl{$E+E*E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
& \bl{$\rightarrow^+$} & \bl{$1+2*3+4$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
\end{tabular} &\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
\begin{tabular}{l@{\hspace{1mm}}l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
\bl{$E$} & \bl{$\rightarrow$} & \bl{$E+E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
& \bl{$\rightarrow$} & \bl{$E+E+E$}\\
|
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
|
231 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
232 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
\end{frame}
|
169
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
239 |
\frametitle{Language of a CFG}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
240 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
241 |
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
|
242 |
Then the language \bl{$L(G)$} is:
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
245 |
\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
|
246 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
247 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
248 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
249 |
\item Terminals, because there are no rules for replacing them.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
250 |
\item Once generated, terminals are ``permanent''.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
251 |
\item Terminals ought to be tokens of the language\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
252 |
(but can also be strings).
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
254 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
255 |
\end{frame}
|
169
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 |
|
49
|
258 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
259 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
260 |
\frametitle{Parse Trees}
|
49
|
261 |
|
|
262 |
\begin{center}
|
|
263 |
\bl{\begin{tabular}{lcl}
|
53
|
264 |
$E$ & $\rightarrow$ & $F \;|\; F \cdot * \cdot F$\\
|
|
265 |
$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
|
|
266 |
$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
|
49
|
267 |
\end{tabular}}
|
|
268 |
\end{center}
|
|
269 |
|
|
270 |
\begin{center}
|
|
271 |
\begin{tikzpicture}[level distance=8mm, blue]
|
50
|
272 |
\node {$E$}
|
|
273 |
child {node {$F$}
|
|
274 |
child {node {$T$}
|
|
275 |
child {node {(\,$E$\,)}
|
|
276 |
child {node{$F$ *{} $F$}
|
|
277 |
child {node {$T$} child {node {2}}}
|
|
278 |
child {node {$T$} child {node {3}}}
|
49
|
279 |
}
|
|
280 |
}
|
|
281 |
}
|
50
|
282 |
child {node {+}}
|
|
283 |
child {node {$T$}
|
|
284 |
child {node {(\,$E$\,)}
|
|
285 |
child {node {$F$}
|
|
286 |
child {node {$T$ +{} $T$}
|
49
|
287 |
child {node {3}}
|
|
288 |
child {node {4}}
|
|
289 |
}
|
|
290 |
}}
|
|
291 |
}};
|
|
292 |
\end{tikzpicture}
|
|
293 |
\end{center}
|
|
294 |
|
50
|
295 |
\begin{textblock}{5}(1, 6.5)
|
49
|
296 |
\bl{\texttt{(2*3)+(3+4)}}
|
|
297 |
\end{textblock}
|
|
298 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
299 |
\end{frame}
|
49
|
300 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
301 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
302 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
304 |
\frametitle{Arithmetic Expressions}
|
169
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
307 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
309 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
\end{center}\pause\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
315 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
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
|
317 |
that \bl{$E \rightarrow^+ E\cdot \ldots$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
318 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
319 |
\end{frame}
|
169
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 |
|
50
|
322 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
323 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
324 |
\frametitle{Ambiguous Grammars}
|
50
|
325 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
326 |
A grammar is \alert{ambiguous} if there is a string that has
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
327 |
at least two different parse trees.
|
50
|
328 |
|
|
329 |
|
|
330 |
\begin{center}
|
|
331 |
\bl{\begin{tabular}{lcl}
|
|
332 |
$E$ & $\rightarrow$ & $num\_token$ \\
|
53
|
333 |
$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
|
|
334 |
$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
|
|
335 |
$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
|
|
336 |
$E$ & $\rightarrow$ & $( \cdot E \cdot )$
|
50
|
337 |
\end{tabular}}
|
|
338 |
\end{center}
|
|
339 |
|
|
340 |
\bl{\texttt{1 + 2 * 3 + 4}}
|
|
341 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
\end{frame}
|
50
|
343 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
344 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\frametitle{Dangling Else}
|
169
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 |
Another ambiguous grammar:\bigskip
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
$E$ & $\rightarrow$ & if $E$ then $E$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
& $|$ & if $E$ then $E$ else $E$ \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
355 |
& $|$ & \ldots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
356 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
358 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
\bl{\texttt{if a then if x then y else c}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
360 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
366 |
\frametitle{Parser Combinators}
|
169
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 |
Parser combinators: \bigskip
|
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 |
\begin{minipage}{1.1\textwidth}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
372 |
\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
|
373 |
$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
\end{minipage}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
376 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
377 |
\begin{itemize}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
378 |
\item atomic parsers
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
\item sequencing
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
380 |
\item alternative
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
381 |
\item semantic action
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
386 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
387 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
Atomic parsers, for example, number tokens
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
\bl{$\texttt{Num(123)}::rest \;\Rightarrow\; \{(\texttt{Num(123)}, rest)\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
\item you consume one or more token from the\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
input (stream)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
399 |
\item also works for characters and strings
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
\begin{frame}[c]
|
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 |
Alternative parser (code \bl{$p\;||\;q$})\bigskip
|
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 |
\begin{itemize}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
\item apply \bl{$p$} and also \bl{$q$}; then combine
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
the outputs
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\item apply first \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
\item then apply \bl{$q$} to the unparsed parts
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
\item then combine the results:\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
((output$_1$, output$_2$), unparsed part)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
\end{center}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
\end{itemize}
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
\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
|
440 |
\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
|
441 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
449 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
Function parser (code \bl{$p \Rightarrow f$})\bigskip
|
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 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
\item apply \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
\item then apply the function \bl{$f$} to each first component
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\end{itemize}
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
\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
|
463 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\end{center}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
\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
|
467 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
|
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 |
Addition
|
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{$T \sim + \sim E \Rightarrow \underbrace{f((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\end{center}\pause
|
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 |
Multiplication
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
\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
|
487 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
489 |
Parenthesis
|
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{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
492 |
\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
|
493 |
\end{center}
|
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 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
|
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 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
\frametitle{\begin{tabular}{c}Types of Parsers\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
\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
|
505 |
then \bl{$p \sim q$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\bl{$T \times S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
\end{center}\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
\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
|
512 |
and \bl{$p \;||\; q$} returns results of type
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
\bl{$T$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
\end{center}\pause
|
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 |
\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
|
519 |
\bl{$T$} to \bl{$S$}, then
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
\bl{$p \Rightarrow f$} returns results of type
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
\bl{$S$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
|
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 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
\frametitle{Input Types of Parsers}
|
169
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 |
\begin{itemize}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
\item input: \alert{token list}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\item output: set of (output\_type, \alert{token list})
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
\end{itemize}\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
actually it can be any input type as long as it is a kind of
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
sequence (for example a string)
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
\frametitle{Scannerless Parsers}
|
169
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 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
552 |
\item input: \alert{string}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\item output: set of (output\_type, \alert{string})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
but lexers are better when whitespaces or comments need to be
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
filtered out; then input is a sequence of tokens
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
\frametitle{Successful Parses}
|
169
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 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
\item input: string
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
\item output: \alert{set of} (output\_type, string)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
\end{itemize}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
a parse is successful whenever the input has been fully
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
``consumed'' (that is the second component is empty)
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
|
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 |
\begin{frame}[c]
|
170
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
\frametitle{Abstract Parser Class}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
\lstinputlisting[language=Scala,xleftmargin=1mm]{../progs/app7.scala}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
\begin{frame}[c]
|
295
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 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\lstinputlisting[language=Scala,xleftmargin=1mm]{../progs/app8.scala}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\frametitle{Two Grammars}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
Which languages are recognised by the following two grammars?
|
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 |
$S$ & $\rightarrow$ & $1 \cdot S \cdot S$\\
|
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}\bigskip
|
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 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
\bl{\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
$U$ & $\rightarrow$ & $1 \cdot U$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
& $|$ & $\epsilon$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\end{frame}
|
169
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 |
|
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{frame}[t]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
621 |
\frametitle{Ambiguous Grammars}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
\begin{center}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
\begin{axis}[xlabel={\pcode{1}s},ylabel={time in secs},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
enlargelimits=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
xtick={0,100,...,1000},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
xmax=1050,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
ymax=33,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
ytick={0,5,...,30},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
scaled ticks=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
axis lines=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
width=11cm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
height=7cm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
legend entries={unambiguous,ambiguous},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
legend pos=north east,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
legend cell align=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
x tick label style={font=\small,/pgf/number format/1000 sep={}}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
\addplot[blue,mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
table {s-grammar1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
\only<2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
table {s-grammar2.data};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
\end{axis}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
\begin{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
\frametitle{While-Language}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
\mbox{}\\[-23mm]\mbox{}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
\bl{\begin{plstx}[rhs style=,one per line]
: \meta{Stmt} ::= skip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
| \meta{Id} := \meta{AExp}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
| if \meta{BExp} then \meta{Block} else \meta{Block}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
| while \meta{BExp} do \meta{Block}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
: \meta{Stmts} ::= \meta{Stmt} ; \meta{Stmts}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
| \meta{Stmt}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
: \meta{Block} ::= \{ \meta{Stmts} \}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
| \meta{Stmt}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
: \meta{AExp} ::= \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
: \meta{BExp} ::= \ldots\\
\end{plstx}}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\begin{frame}[c]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
\frametitle{An Interpreter}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\bl{\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
676 |
$\{$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
\;\;$x := 5 \text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
\;\;$y := x * 3\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\;\;$y := x * 4\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
\;\;$x := u * 3$\\
|
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 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\item \bl{\texttt{eval(stmt, env)}}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
|
50
|
693 |
|
49
|
694 |
\end{document}
|
|
695 |
|
|
696 |
%%% Local Variables:
|
|
697 |
%%% mode: latex
|
|
698 |
%%% TeX-master: t
|
|
699 |
%%% End:
|
|
700 |
|