| author | Christian Urban <urbanc@in.tum.de> |
| Tue, 06 Nov 2018 00:48:53 +0000 | |
| changeset 597 | ce8419e3915c |
| parent 531 | f6e937ed0332 |
| child 598 | e3ad67cd5123 |
| permissions | -rw-r--r-- |
| 49 | 1 |
\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{../slides}
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\usepackage{../graphics}
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\usepackage{../langs}
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\usepackage{../data}
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\usepackage{../grammar}
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% beamer stuff |
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\renewcommand{\slidecaption}{CFL 06, King's College London}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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%\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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\newcommand{\qq}{\mbox{\texttt{"}}}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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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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\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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Office: & N\liningnums{7.07} (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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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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||
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% \begin{frame}[c]
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% \small |
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% \mbox{}\\[5mm]
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% %\begin{textblock}{10}(3,5)
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% \begin{tikzpicture}[scale=1.5,
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% node distance=1cm, |
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% every node/.style={minimum size=7mm}]
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% \node (r1) {\bl{$r_1$}};
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% \node (r2) [right=of r1] {\bl{$r_2$}};
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% \draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
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% \node (r3) [right=of r2] {\bl{$r_3$}};
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% \draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
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% \node (r4) [right=of r3] {\bl{$r_4$}};
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% \draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
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% \draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
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% \node (v4) [below=of r4] {\bl{$v_4$}};
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% \draw[->,line width=1mm] (r4) -- (v4); |
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% \node (v3) [left=of v4] {\bl{$v_3$}};
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% \draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
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% \node (v2) [left=of v3] {\bl{$v_2$}};
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% \draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
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% \node (v1) [left=of v2] {\bl{$v_1$}};
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% \draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
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% \draw[->,line width=0.5mm] (r3) -- (v3); |
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% \draw[->,line width=0.5mm] (r2) -- (v2); |
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% \draw[->,line width=0.5mm] (r1) -- (v1); |
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% \draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
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% \end{tikzpicture}
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% %\end{textblock}
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% \begin{center}
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% \begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
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% \\[-10mm] |
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% \bl{$inj\,(c)\,c\,Empty$} & \bl{$\dn$} & \bl{$Char\,c$}\\
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% \bl{$inj\,(r_1 + r_2)\,c\,Left(v)$} & \bl{$\dn$} & \bl{$Left(inj\,r_1\,c\,v)$}\\
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% \bl{$inj\,(r_1 + r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Right(inj\,r_2\,c\,v)$}\\
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% \bl{$inj\,(r_1 \cdot r_2)\,c\,Seq(v_1,v_2)$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
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% \bl{$inj\,(r_1 \cdot r_2)\,c\,Left(Seq(v_1,v_2))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
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% \bl{$inj\,(r_1 \cdot r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),inj\,r_2\,c\,v)$}\\
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% \bl{$inj\,(r^*)\,c\,Seq(v,vs)$} & \bl{$\dn$} & \bl{$inj\,r\,c\,v\,::\,vs$}\\
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% \end{tabular}
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% \end{center}
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% \end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{frame}[c]
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parents:
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\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}}
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parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Recall that languages are sets of strings. |
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parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{tikzpicture}
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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>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
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\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
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\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
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\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
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\draw (0,-1.4) node [rect] {regular languages};
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\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\end{frame}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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| 531 | 109 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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113 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Atomic parsers, for example |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\bl{$1::rest \;\Rightarrow\; \{(1, rest)\}$}
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parents:
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\end{center}\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{itemize}
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\item you consume one or more tokens from the\\ |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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input (stream) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\item also works for characters and strings |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\end{itemize}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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\end{frame}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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127 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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129 |
\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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130 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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131 |
Alternative parser (code \bl{$p\;||\;q$})\bigskip
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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132 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\begin{itemize}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\item apply \bl{$p$} and also \bl{$q$}; then combine
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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the outputs |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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\end{itemize}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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137 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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138 |
\begin{center}
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5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\large \bl{$p(\text{input}) \cup q(\text{input})$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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\end{center}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
|
141 |
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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|
142 |
\end{frame}
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|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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|
143 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
144 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
145 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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|
146 |
\begin{frame}[c]
|
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5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
147 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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|
148 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
149 |
|
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
150 |
\begin{itemize}
|
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
151 |
\item apply first \bl{$p$} producing a set of pairs
|
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5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
152 |
\item then apply \bl{$q$} to the unparsed parts
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
153 |
\item then combine the results:\medskip |
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
154 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
155 |
((output$_1$, output$_2$), unparsed part) |
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
156 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
157 |
\end{itemize}
|
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updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
158 |
|
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updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
159 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
160 |
\begin{tabular}{l}
|
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
161 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
162 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
163 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
|
5a83336a9690
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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|
164 |
\end{tabular}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
165 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
166 |
|
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5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
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changeset
|
167 |
|
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5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
168 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
169 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
170 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
171 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
172 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
173 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
174 |
Function parser (code \bl{$p \Rightarrow f\;$})\bigskip
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
175 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
176 |
\begin{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
177 |
\item apply \bl{$p$} producing a set of pairs
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
178 |
\item then apply the function \bl{$f$} to each first component
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
179 |
\end{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
180 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
181 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
182 |
\begin{tabular}{l}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
183 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
184 |
\end{tabular}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
185 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
186 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
187 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
188 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
189 |
|
| 531 | 190 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
191 |
\begin{frame}[c]
|
|
192 |
\frametitle{Types of Parsers}
|
|
193 |
||
194 |
\begin{itemize}
|
|
195 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
|
196 |
then \bl{$p \sim q$} returns results of type
|
|
197 |
||
198 |
\begin{center}
|
|
199 |
\bl{$T \times S$}
|
|
200 |
\end{center}\pause
|
|
201 |
||
202 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
|
203 |
and \bl{$p \;||\; q$} returns results of type
|
|
204 |
||
205 |
\begin{center}
|
|
206 |
\bl{$T$}
|
|
207 |
\end{center}\pause
|
|
208 |
||
209 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
|
210 |
\bl{$T$} to \bl{$S$}, then
|
|
211 |
\bl{$p \Rightarrow f$} returns results of type
|
|
212 |
||
213 |
\begin{center}
|
|
214 |
\bl{$S$}
|
|
215 |
\end{center}
|
|
216 |
||
217 |
\end{itemize}
|
|
218 |
||
219 |
\end{frame}
|
|
220 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
221 |
||
222 |
||
223 |
||
224 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
225 |
\begin{frame}[c]
|
|
226 |
\frametitle{Two Grammars}
|
|
227 |
||
228 |
Which languages are recognised by the following two grammars? |
|
229 |
||
| 597 | 230 |
\bl{\begin{plstx}[margin=3cm]
|
231 |
: \meta{S} ::= \liningnums{1}\cdot\meta{S}\cdot \meta{S} | \epsilon\\
|
|
232 |
\end{plstx}}
|
|
| 531 | 233 |
|
| 597 | 234 |
\bl{\begin{plstx}[margin=3cm]
|
235 |
: \meta{U} ::= \liningnums{1}\cdot\meta{U} | \epsilon\\
|
|
236 |
\end{plstx}}
|
|
| 531 | 237 |
|
238 |
\end{frame}
|
|
239 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
240 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
241 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
242 |
\begin{frame}[t]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
243 |
\frametitle{Ambiguous Grammars}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
244 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
245 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
246 |
\begin{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
247 |
\begin{axis}[xlabel={\pcode{1}s},ylabel={time in secs},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
248 |
enlargelimits=false, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
249 |
xtick={0,100,...,1000},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
250 |
xmax=1050, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
251 |
ymax=33, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
252 |
ytick={0,5,...,30},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
253 |
scaled ticks=false, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
254 |
axis lines=left, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
255 |
width=11cm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
256 |
height=7cm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
257 |
legend entries={unambiguous,ambiguous},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
258 |
legend pos=north east, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
259 |
legend cell align=left, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
260 |
x tick label style={font=\small,/pgf/number format/1000 sep={}}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
261 |
\addplot[blue,mark=*, mark options={fill=white}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
262 |
table {s-grammar1.data};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
263 |
\only<2>{
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
264 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
265 |
table {s-grammar2.data};}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
266 |
\end{axis}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
267 |
\end{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
268 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
269 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
270 |
\end{frame}
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
271 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
272 |
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
273 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
274 |
\begin{frame}[c]
|
| 597 | 275 |
\frametitle{Arithmetic Expressions}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
276 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
277 |
A grammar for arithmetic expressions and numbers: |
| 50 | 278 |
|
| 597 | 279 |
\bl{\begin{plstx}[margin=1cm]
|
280 |
: \meta{E} ::= \meta{E} \cdot + \cdot \meta{E}
|
|
281 |
| \meta{E} \cdot * \cdot \meta{E}
|
|
282 |
| ( \cdot \meta{E} \cdot ) | \meta{N}\\
|
|
283 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
284 |
0 | 1 | \ldots | 9\\ |
|
285 |
\end{plstx}}
|
|
| 49 | 286 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
287 |
Unfortunately it is left-recursive (and ambiguous).\medskip\\ |
| 597 | 288 |
A problem for \alert{recursive descent parsers} (e.g.~parser
|
289 |
combinators). \bigskip\pause |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
290 |
|
| 597 | 291 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
292 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
293 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
294 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
295 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
296 |
\begin{frame}[t]
|
| 597 | 297 |
\frametitle{Numbers}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
298 |
|
| 597 | 299 |
\bl{\begin{plstx}[margin=1cm]
|
300 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
301 |
0 | 1 | \ldots | 9\\ |
|
302 |
\end{plstx}}
|
|
| 49 | 303 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
304 |
A non-left-recursive, non-ambiguous grammar for numbers: |
| 49 | 305 |
|
| 597 | 306 |
\bl{\begin{plstx}[margin=1cm]
|
307 |
: \meta{N} ::= 0 \cdot \meta{N} | 1 \cdot \meta{N} | \ldots |
|
|
308 |
0 | 1 | \ldots | 9\\ |
|
309 |
\end{plstx}}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
310 |
|
| 597 | 311 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
312 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
313 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
314 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
315 |
\begin{frame}[c]
|
| 597 | 316 |
\frametitle{Removing Left-Recursion}
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
317 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
318 |
The rule for numbers is directly left-recursive: |
| 49 | 319 |
|
320 |
\begin{center}
|
|
| 50 | 321 |
\bl{\begin{tabular}{lcl}
|
| 597 | 322 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \meta{N} \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
323 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
324 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
325 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
326 |
Translate |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
327 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
328 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
329 |
\begin{tabular}{ccc}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
330 |
\bl{\begin{tabular}{lcl}
|
| 597 | 331 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \alpha$\\
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
332 |
& $\;|\;$ & $\beta$\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
333 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
334 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
335 |
& {\Large$\Rightarrow$} &
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
336 |
\bl{\begin{tabular}{lcl}
|
| 597 | 337 |
$\meta{N}$ & $::=$ & $\beta \cdot \meta{N}'$\\
|
338 |
$\meta{N}'$ & $::=$ & $\alpha \cdot \meta{N}'$\\
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
339 |
& $\;|\;$ & $\epsilon$ |
| 50 | 340 |
\end{tabular}}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
341 |
\end{tabular}
|
| 50 | 342 |
\end{center}\pause
|
343 |
||
| 597 | 344 |
Which means in this case: |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
345 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
346 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
347 |
\bl{\begin{tabular}{lcl}
|
| 597 | 348 |
$\meta{N}$ & $\rightarrow$ & $0 \cdot \meta{N}' \;|\; 1 \cdot \meta{N}'$\\
|
349 |
$\meta{N}'$ & $\rightarrow$ & $\meta{N} \cdot \meta{N}' \;|\; \epsilon$\\
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
350 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
351 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
352 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
353 |
|
| 597 | 354 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
355 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
356 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
357 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
358 |
\begin{frame}[c]
|
| 597 | 359 |
\frametitle{Operator Precedences}
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
360 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
361 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
362 |
To disambiguate |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
363 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
364 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
365 |
\bl{\begin{tabular}{lcl}
|
| 597 | 366 |
$\meta{E}$ & $::=$ & $\meta{E} \cdot + \cdot \meta{E} \;|\;\meta{E} \cdot * \cdot \meta{E} \;|\;( \cdot \meta{E} \cdot ) \;|\;\meta{N}$ \\
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
367 |
\end{tabular}}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
368 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
369 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
370 |
Decide on how many precedence levels, say\medskip\\ |
| 597 | 371 |
highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+}
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
372 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
373 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
374 |
\bl{\begin{tabular}{lcl}
|
| 597 | 375 |
$\meta{E}_{low}$ & $::=$ & $\meta{E}_{med} \cdot + \cdot \meta{E}_{low} \;|\; \meta{E}_{med}$ \\
|
376 |
$\meta{E}_{med}$ & $::=$ & $\meta{E}_{hi} \cdot * \cdot \meta{E}_{med} \;|\; \meta{E}_{hi}$\\
|
|
377 |
$\meta{E}_{hi}$ & $::=$ & $( \cdot \meta{E}_{low} \cdot ) \;|\;\meta{N}$ \\
|
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
378 |
\end{tabular}}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
379 |
\end{center}\pause
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
380 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
381 |
\small What happens with \bl{$1 + 3 + 4$}?
|
| 597 | 382 |
\end{frame}
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
383 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
384 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
385 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
386 |
\begin{frame}[c]
|
| 597 | 387 |
\frametitle{Chomsky Normal Form}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
388 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
389 |
All rules must be of the form |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
390 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
391 |
\begin{center}
|
| 597 | 392 |
\bl{$\meta{A} ::= a$}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
393 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
394 |
|
| 50 | 395 |
or |
396 |
||
397 |
\begin{center}
|
|
| 597 | 398 |
\bl{$\meta{A} ::= \meta{B}\cdot \meta{C}$}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
399 |
\end{center}
|
| 49 | 400 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
401 |
No rule can contain \bl{$\epsilon$}.
|
| 49 | 402 |
|
| 597 | 403 |
\end{frame}
|
| 49 | 404 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
405 |
||
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
406 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
407 |
\begin{frame}[c]
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
408 |
\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
409 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
410 |
\begin{enumerate}
|
| 597 | 411 |
\item If \bl{$A::= \alpha \cdot B \cdot \beta$} and \bl{$B ::= \epsilon$} are in the grammar,
|
412 |
then add \bl{$A::= \alpha \cdot \beta$} (iterate if necessary).
|
|
413 |
\item Throw out all \bl{$B ::= \epsilon$}.
|
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
414 |
\end{enumerate}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
415 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
416 |
\small |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
417 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
418 |
\begin{tabular}{ccc}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
419 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
| 597 | 420 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'$\\ |
421 |
$N'$ & $::=$ & $N \cdot N'\;|\;\epsilon$\\ |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
422 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
423 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
424 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
425 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
426 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
427 |
\end{tabular}} &
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
428 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
429 |
\\ |
| 597 | 430 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ |
431 |
$N'$ & $::=$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\ |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
432 |
\\ |
| 597 | 433 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ |
434 |
$N'$ & $::=$ & $N \cdot N'\;|\;N$\\ |
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
435 |
\end{tabular}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
436 |
\end{tabular}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
437 |
\end{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
438 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
439 |
\pause\normalsize |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
440 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
441 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
| 597 | 442 |
$N$ & $::=$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\ |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
443 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
444 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
445 |
\end{center}
|
|
368
a9911966c0df
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
366
diff
changeset
|
446 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
447 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
448 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
449 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
450 |
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
451 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
452 |
\begin{frame}[c]
|
| 597 | 453 |
\frametitle{CYK Algorithm}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
454 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
455 |
If grammar is in Chomsky normalform \ldots |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
456 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
457 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
458 |
\bl{\begin{tabular}{@ {}lcl@ {}}
|
| 597 | 459 |
$\meta{S}$ & $::=$ & $\meta{N}\cdot \meta{P}$ \\
|
460 |
$\meta{P}$ & $::=$ & $\meta{V}\cdot \meta{N}$ \\
|
|
461 |
$\meta{N}$ & $::=$ & $\meta{N}\cdot \meta{N}$ \\
|
|
462 |
$\meta{N}$ & $::=$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
|
|
463 |
$\meta{V}$ & $::=$ & $\texttt{trains}$
|
|
| 49 | 464 |
\end{tabular}}
|
465 |
\end{center}
|
|
466 |
||
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
467 |
\bl{\texttt{Jeff trains geometry students}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
468 |
|
| 597 | 469 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
470 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 597 | 471 |
|
472 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
473 |
\begin{frame}[c]
|
| 597 | 474 |
\frametitle{CYK Algorithm}
|
| 49 | 475 |
|
476 |
||
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
477 |
\begin{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
478 |
\item fastest possible algorithm for recognition problem |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
479 |
\item runtime is \bl{$O(n^3)$}\bigskip
|
| 597 | 480 |
\item grammars need to be transformed into CNF |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
481 |
\end{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
482 |
|
| 597 | 483 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
484 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
485 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
486 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
487 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
488 |
\frametitle{The Goal of this Course}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
489 |
\mbox{}\\[-26mm]\mbox{}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
490 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
491 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
492 |
\begin{tikzpicture}[scale=1,
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
493 |
node/.style={
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
494 |
rectangle,rounded corners=3mm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
495 |
very thick,draw=black!50, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
496 |
minimum height=18mm, minimum width=20mm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
497 |
top color=white,bottom color=black!20}] |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
498 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
499 |
\node at (3.05, 1.8) {\Large\bf Write a Compiler};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
500 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
501 |
\node (0) at (-2.3,0) {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
502 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
503 |
\node (A) at (0,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
504 |
\node [below right] at (A.north west) {lexer};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
505 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
506 |
\node (B) at (3,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
507 |
\node [below right=1mm] at (B.north west) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
508 |
{\mbox{}\hspace{-1mm}parser};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
509 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
510 |
\node (C) at (6,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
511 |
\node [below right] at (C.north west) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
512 |
{\mbox{}\hspace{-1mm}code gen};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
513 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
514 |
\node (1) at (8.4,0) {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
515 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
516 |
\draw [->,line width=4mm] (0) -- (A); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
517 |
\draw [->,line width=4mm] (A) -- (B); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
518 |
\draw [->,line width=4mm] (B) -- (C); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
519 |
\draw [->,line width=4mm] (C) -- (1); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
520 |
\end{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
521 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
522 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
523 |
We have lexer and parser. |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
524 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
525 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
526 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
527 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
528 |
\begin{frame}[c]
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
529 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
530 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
531 |
\bl{\begin{tabular}{@{}lcl@{}}
|
| 597 | 532 |
\textit{Stmt} & $::=$ & $\texttt{skip}$\\
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
533 |
& $|$ & \textit{Id}\;\texttt{:=}\;\textit{AExp}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
534 |
& $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Block} \;\texttt{else}\; \textit{Block}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
535 |
& $|$ & \texttt{while}\; \textit{BExp} \;\texttt{do}\; \textit{Block}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
536 |
& $|$ & \texttt{read}\;\textit{Id}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
537 |
& $|$ & \texttt{write}\;\textit{Id}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
538 |
& $|$ & \texttt{write}\;\textit{String}\medskip\\
|
| 597 | 539 |
\textit{Stmts} & $::=$ & \textit{Stmt} \;\texttt{;}\; \textit{Stmts}\\
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
540 |
& $|$ & \textit{Stmt}\medskip\\
|
| 597 | 541 |
\textit{Block} & $::=$ & \texttt{\{}\,\textit{Stmts}\,\texttt{\}}\\
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
542 |
& $|$ & \textit{Stmt}\medskip\\
|
| 597 | 543 |
\textit{AExp} & $::=$ & \ldots\\
|
544 |
\textit{BExp} & $::=$ & \ldots\\
|
|
| 50 | 545 |
\end{tabular}}
|
546 |
\end{center}
|
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
547 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
548 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
549 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
550 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
551 |
\mode<presentation>{
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
552 |
\begin{frame}[c]
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
553 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
554 |
\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
555 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
556 |
\end{frame}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
557 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
558 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
559 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
560 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
561 |
\mode<presentation>{
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
562 |
\begin{frame}[c]
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
563 |
\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
564 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
565 |
\begin{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
566 |
\bl{\begin{tabular}{l}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
567 |
$\{$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
568 |
\;\;$x := 5 \text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
569 |
\;\;$y := x * 3\text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
570 |
\;\;$y := x * 4\text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
571 |
\;\;$x := u * 3$\\ |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
572 |
$\}$ |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
573 |
\end{tabular}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
574 |
\end{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
575 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
576 |
\begin{itemize}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
577 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
578 |
\item \bl{\text{eval}(stmt, env)}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
579 |
\end{itemize}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
580 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
581 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
582 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
583 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
584 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
585 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
586 |
\mode<presentation>{
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
587 |
\begin{frame}[c]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
588 |
\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
589 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
590 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
591 |
\bl{\begin{tabular}{@{}lcl@{}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
592 |
$\text{eval}(n, E)$ & $\dn$ & $n$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
593 |
$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
594 |
$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
595 |
$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
596 |
$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
597 |
$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
598 |
$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
599 |
$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
600 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
601 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
602 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
603 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
604 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
605 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
606 |
\mode<presentation>{
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
607 |
\begin{frame}[c]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
608 |
\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
609 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
610 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
611 |
\bl{\begin{tabular}{@{}lcl@{}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
612 |
$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
613 |
$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
614 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
615 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
616 |
\text{eval}(cs_1,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
617 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
618 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
619 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
620 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
621 |
\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
622 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
623 |
$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
624 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
625 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
626 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
627 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
628 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
629 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
630 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
631 |
\begin{frame}[c]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
632 |
\frametitle{\begin{tabular}{c}Test Program\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
633 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
634 |
\mbox{}\\[-18mm]\mbox{}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
635 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
636 |
{\lstset{language=While}%%\fontsize{10}{12}\selectfont
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
637 |
\texttt{\lstinputlisting{../progs/loops.while}}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
638 |
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
639 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
640 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
641 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
642 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
643 |
\mode<presentation>{
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
644 |
\begin{frame}[t]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
645 |
\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
646 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
647 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
648 |
\begin{tikzpicture}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
649 |
\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
650 |
\addplot+[smooth] file {interpreted.data};
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
651 |
\end{axis}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
652 |
\end{tikzpicture}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
653 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
654 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
655 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
656 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
657 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
658 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
659 |
\mode<presentation>{
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
660 |
\begin{frame}[c]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
661 |
\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
662 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
663 |
\begin{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
664 |
\item introduced in 1995 |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
665 |
\item is a stack-based VM (like Postscript, CLR of .Net) |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
666 |
\item contains a JIT compiler |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
667 |
\item many languages take advantage of JVM's infrastructure (JRE) |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
668 |
\item is garbage collected $\Rightarrow$ no buffer overflows |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
669 |
\item some languages compile to the JVM: Scala, Clojure\ldots |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
670 |
\end{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
671 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
672 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
673 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
674 |
|
| 50 | 675 |
|
| 49 | 676 |
\end{document}
|
677 |
||
678 |
%%% Local Variables: |
|
679 |
%%% mode: latex |
|
680 |
%%% TeX-master: t |
|
681 |
%%% End: |
|
682 |