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% !TEX program = xelatex
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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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\hfuzz=220pt
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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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\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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\renewcommand{\slidecaption}{CFL 04, King's College London}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Compilers and \\[-2mm]
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\LARGE Formal Languages (4)\\[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 Hours: & Thursdays 12 -- 14\\
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Location: & N7.07 (North Wing, Bush House)\\
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Slides \& Progs: & KEATS (also homework 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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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\begin{center}
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\begin{tikzpicture}[scale=2,>=stealth',very thick,
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every state/.style={minimum size=0pt,draw=blue!50,very thick,fill=blue!20},]
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\only<-7>{\node[state, initial] (q0) at ( 0,1) {$\mbox{Q}_0$};}
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\only<8->{\node[state, initial,accepting] (q0) at ( 0,1) {$\mbox{Q}_0$};}
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\only<-7>{\node[state] (q1) at ( 1,1) {$\mbox{Q}_1$};}
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\only<8->{\node[state,accepting] (q1) at ( 1,1) {$\mbox{Q}_1$};}
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\node[state] (q2) at ( 2,1) {$\mbox{Q}_2$};
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\path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
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(q1) edge[bend left] node[above] {\alert{$b$}} (q0)
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(q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
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(q1) edge node[above] {\alert{$a$}} (q2)
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(q2) edge [loop right] node {\alert{$a$}} ()
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(q0) edge [loop below] node {\alert{$b$}} ()
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;
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\end{tikzpicture}
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\end{center}\bigskip
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\begin{center}
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\begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l}
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,b + \mbox{Q}_1\,b + \mbox{Q}_2\,b$}\\
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\bl{$\mbox{Q}_1$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a$}\\
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\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_1\,a + \mbox{Q}_2\,a$}\\
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\end{tabular}
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\end{center}
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Arden's Lemma:
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\begin{center}
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If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
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\end{center}
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\only<2-6>{\small
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\begin{textblock}{6}(1,0.8)
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\begin{bubble}[6.7cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{substitute \bl{$\mbox{Q}_1$} into \bl{$\mbox{Q}_0$} \& \bl{$\mbox{Q}_2$}:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,b + \mbox{Q}_0\,a\,b + \mbox{Q}_2\,b$}\\
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\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a + \mbox{Q}_2\,a$}
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\only<3-6>{\small
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\begin{textblock}{6}(2,4.15)
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\begin{bubble}[6.7cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{simplifying \bl{$\mbox{Q}_0$}:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b) + \mbox{Q}_2\,b$}\\
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\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a + \mbox{Q}_2\,a$}
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\only<4-6>{\small
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\begin{textblock}{6}(3,7.55)
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\begin{bubble}[6.7cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{Arden for \bl{$\mbox{Q}_2$}:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b) + \mbox{Q}_2\,b$}\\
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\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a\,(a^*)$}
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\only<5-6>{\small
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\begin{textblock}{6}(4,10.9)
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\begin{bubble}[7.5cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{Substitute \bl{$\mbox{Q}_2$} and simplify:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b + a\,a\,(a^*)\,b)$}\\
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\only<6>{\small
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\begin{textblock}{6}(5,13.4)
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\begin{bubble}[7.5cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{Arden again for \bl{$\mbox{Q}_0$}:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*$}\\
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\only<7->{\small
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\begin{textblock}{6}(6,11.5)
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\begin{bubble}[6.7cm]
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\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
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\multicolumn{3}{@{}l}{Finally:}\\
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\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*$}\\
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\bl{$\mbox{Q}_1$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*\,a$}\\
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\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*\,a\,a\,(a^*)$}\\
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\end{tabular}
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\end{bubble}
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\end{textblock}}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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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\frametitle{Coursework}
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\begin{itemize}
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\item \bl{$\der\,c\,(r^+) \dn \der\,c (r\cdot r^*)$}\quad given
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that \bl{$r^+ \dn r\cdot r^*$}
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\end{itemize}\bigskip\pause
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\begin{center}
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\begin{tabular}{lcl}
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\bl{$\der\,c\,(r\cdot r^*)$} & \bl{$\dn$} &
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\only<2-4>{if \bl{$nullable\,r$}}%
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\only<5>{\bl{$(\der\,c\,r)\cdot r^*$}}\\
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& &
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\only<2>{then \bl{$(\der\,c\,r)\cdot r^* \,+\, \der\,c\,(r^*)$}}%
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\only<3>{then \bl{$(\der\,c\,r)\cdot r^* \,+\, (\der\,c\,r)\cdot r^*$}}%
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\only<4>{then \bl{$(\der\,c\,r)\cdot r^*$}}\\
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& & \only<2-4>{else \bl{$(\der\,c\,r)\cdot r^*$}}
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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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\begin{frame}[c]
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\frametitle{Coursework (2)}
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\begin{itemize}
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\item \bl{\texttt{CFUN(f: Char => Boolean)}}
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\end{itemize}\medskip
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\begin{center}
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\begin{tabular}{l}
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\bl{\texttt{CHAR(c: Char)}} \bl{$\dn$}\\
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\quad\bl{\texttt{CFUN(\_ == c)}}\medskip\\
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\bl{\texttt{RANGE(cs: Set[Char])}} \bl{$\dn$}\\
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\quad\bl{\texttt{CFUN(cs.contains(\_))}}\medskip\\
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\bl{\texttt{ALL}} \bl{$\dn$}\\
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\quad\bl{\texttt{CFUN((c: Char) => true)}}\\
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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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\begin{frame}[c]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\frametitle{Regexps and Automata}
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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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\node (rexp) {\bl{\bf Regexps}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\node (nfa) [right=of rexp] {\bl{\bf NFAs}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\node (dfa) [right=of nfa] {\bl{\bf DFAs}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\node (mdfa) [right=of dfa] {\bl{\bf \begin{tabular}{c}minimal\\ DFAs\end{tabular}}};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\path[->,red, line width=2mm] (rexp) edge node [above=4mm, black]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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{\begin{tabular}{c@{\hspace{9mm}}}Thompson's\\[-1mm] construction\end{tabular}} (nfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\path[->,red, line width=2mm] (nfa) edge node [above=4mm, black]
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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{\begin{tabular}{c}subset\\[-1mm] construction\end{tabular}}(dfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\path[->, red, line width=2mm] (dfa) edge node [below=5mm, black] {minimisation} (mdfa);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%\path[->, red, line width=2mm] (dfa) edge [bend left=45] (rexp);
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\path[->, red, line width=2mm] (dfa) edge [bend left=45] node [below, black] {\begin{tabular}{l}Brzozowski's\\ method\end{tabular}} (rexp);
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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{tikzpicture}\\
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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>
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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{\bl{$a^{?\{n\}} \cdot a^{\{n\}}$}}
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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{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{axis}[xlabel={\pcode{a}s},ylabel={time in secs},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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enlargelimits=false,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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xtick={0,5,...,30},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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xmax=30,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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ymax=35,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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ytick={0,5,...,30},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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scaled ticks=false,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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axis lines=left,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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width=10cm,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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height=7cm,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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legend entries={Python,Ruby,my NFA},
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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legend pos=north west,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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legend cell align=left]
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\addplot[blue,mark=*, mark options={fill=white}] table {re-python.data};
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\addplot[brown,mark=pentagon*, mark options={fill=white}] table {re-ruby.data};
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\addplot[red,mark=triangle*, mark options={fill=white}] table {nfasearch.data};
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{axis}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{tikzpicture}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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579
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The punchline is that many existing libraries do depth-first search
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in NFAs (backtracking).
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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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% \begin{frame}[c]
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% \frametitle{DFA to Rexp}
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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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252 |
% \begin{tikzpicture}[scale=2,>=stealth',very thick,
|
|
|
253 |
% every state/.style={minimum size=0pt,
|
|
|
254 |
% draw=blue!50,very thick,fill=blue!20},]
|
|
|
255 |
% \node[state, initial] (q0) at ( 0,1) {$q_0$};
|
|
|
256 |
% \node[state] (q1) at ( 1,1) {$q_1$};
|
|
|
257 |
% \node[state, accepting] (q2) at ( 2,1) {$q_2$};
|
|
|
258 |
% \path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
|
|
|
259 |
% (q1) edge[bend left] node[above] {\alert{$b$}} (q0)
|
|
|
260 |
% (q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
|
|
|
261 |
% (q1) edge node[above] {\alert{$a$}} (q2)
|
|
|
262 |
% (q2) edge [loop right] node {\alert{$a$}} ()
|
|
|
263 |
% (q0) edge [loop below] node {\alert{$b$}} ();
|
|
|
264 |
% \end{tikzpicture}
|
|
|
265 |
% \end{center}\bigskip
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
266 |
|
|
520
|
267 |
% \begin{center}
|
|
|
268 |
% \begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l@{\hspace{7mm}}l}
|
|
|
269 |
% \bl{$q_0$} & \bl{$=$} & \bl{$\ONE + q_0\,b + q_1\,b + q_2\,b$} & (start state)\\
|
|
|
270 |
% \bl{$q_1$} & \bl{$=$} & \bl{$q_0\,a$}\\
|
|
|
271 |
% \bl{$q_2$} & \bl{$=$} & \bl{$q_1\,a + q_2\,a$}\\
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
|
|
520
|
273 |
% \end{tabular}
|
|
|
274 |
% \end{center}
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
|
|
520
|
276 |
% Arden's Lemma:
|
|
|
277 |
% \begin{center}
|
|
|
278 |
% If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
|
|
|
279 |
% \end{center}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
|
|
520
|
282 |
% \end{frame}
|
|
|
283 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
|
|
520
|
285 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
286 |
% \begin{frame}[c]
|
|
|
287 |
% \frametitle{DFA Minimisation}
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
|
|
520
|
289 |
% \begin{enumerate}
|
|
|
290 |
% \item Take all pairs \bl{$(q, p)$} with \bl{$q \not= p$}
|
|
|
291 |
% \item Mark all pairs that accepting and non-accepting states
|
|
|
292 |
% \item For all unmarked pairs \bl{$(q, p)$} and all characters \bl{$c$} test whether
|
|
|
293 |
% \begin{center}
|
|
|
294 |
% \bl{$(\delta(q, c), \delta(p,c))$}
|
|
|
295 |
% \end{center}
|
|
|
296 |
% are marked. If yes, then also mark \bl{$(q, p)$}.
|
|
|
297 |
% \item Repeat last step until no change.
|
|
|
298 |
% \item All unmarked pairs can be merged.
|
|
|
299 |
% \end{enumerate}
|
145
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
300 |
|
|
520
|
301 |
% \end{frame}
|
|
|
302 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
270
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
303 |
|
|
520
|
304 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
305 |
% \begin{frame}[c]
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
306 |
|
|
520
|
307 |
% \begin{center}
|
|
|
308 |
% \begin{tabular}{@{\hspace{-8mm}}cc@{}}
|
|
|
309 |
% \begin{tikzpicture}[>=stealth',very thick,auto,
|
|
|
310 |
% every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
|
|
|
311 |
% \node[state,initial] (q_0) {$q_0$};
|
|
|
312 |
% \node[state] (q_1) [right=of q_0] {$q_1$};
|
|
|
313 |
% \node[state] (q_2) [below right=of q_0] {$q_2$};
|
|
|
314 |
% \node[state] (q_3) [right=of q_2] {$q_3$};
|
|
|
315 |
% \node[state, accepting] (q_4) [right=of q_1] {$q_4$};
|
|
|
316 |
% \path[->] (q_0) edge node [above] {\alert{$a$}} (q_1);
|
|
|
317 |
% \path[->] (q_1) edge node [above] {\alert{$a$}} (q_4);
|
|
|
318 |
% \path[->] (q_4) edge [loop right] node {\alert{$a, b$}} ();
|
|
|
319 |
% \path[->] (q_3) edge node [right] {\alert{$a$}} (q_4);
|
|
|
320 |
% \path[->] (q_2) edge node [above] {\alert{$a$}} (q_3);
|
|
|
321 |
% \path[->] (q_1) edge node [right] {\alert{$b$}} (q_2);
|
|
|
322 |
% \path[->] (q_0) edge node [above] {\alert{$b$}} (q_2);
|
|
|
323 |
% \path[->] (q_2) edge [loop left] node {\alert{$b$}} ();
|
|
|
324 |
% \path[->] (q_3) edge [bend left=95, looseness=1.3] node [below] {\alert{$b$}} (q_0);
|
|
|
325 |
% \end{tikzpicture}
|
|
|
326 |
% &
|
|
|
327 |
% \raisebox{9mm}{\begin{tikzpicture}[scale=0.6,line width=0.8mm]
|
|
|
328 |
% \draw (0,0) -- (4,0);
|
|
|
329 |
% \draw (0,1) -- (4,1);
|
|
|
330 |
% \draw (0,2) -- (3,2);
|
|
|
331 |
% \draw (0,3) -- (2,3);
|
|
|
332 |
% \draw (0,4) -- (1,4);
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
|
|
520
|
334 |
% \draw (0,0) -- (0, 4);
|
|
|
335 |
% \draw (1,0) -- (1, 4);
|
|
|
336 |
% \draw (2,0) -- (2, 3);
|
|
|
337 |
% \draw (3,0) -- (3, 2);
|
|
|
338 |
% \draw (4,0) -- (4, 1);
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
339 |
|
|
520
|
340 |
% \draw (0.5,-0.5) node {$q_0$};
|
|
|
341 |
% \draw (1.5,-0.5) node {$q_1$};
|
|
|
342 |
% \draw (2.5,-0.5) node {$q_2$};
|
|
|
343 |
% \draw (3.5,-0.5) node {$q_3$};
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
|
|
520
|
345 |
% \draw (-0.5, 3.5) node {$q_1$};
|
|
|
346 |
% \draw (-0.5, 2.5) node {$q_2$};
|
|
|
347 |
% \draw (-0.5, 1.5) node {$q_3$};
|
|
|
348 |
% \draw (-0.5, 0.5) node {$q_4$};
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
349 |
|
|
520
|
350 |
% \draw (0.5,0.5) node {\large$\star$};
|
|
|
351 |
% \draw (1.5,0.5) node {\large$\star$};
|
|
|
352 |
% \draw (2.5,0.5) node {\large$\star$};
|
|
|
353 |
% \draw (3.5,0.5) node {\large$\star$};
|
|
|
354 |
% \draw (0.5,1.5) node {\large$\star$};
|
|
|
355 |
% \draw (2.5,1.5) node {\large$\star$};
|
|
|
356 |
% \draw (0.5,3.5) node {\large$\star$};
|
|
|
357 |
% \draw (1.5,2.5) node {\large$\star$};
|
|
|
358 |
% \end{tikzpicture}}
|
|
|
359 |
% \end{tabular}
|
|
|
360 |
% \end{center}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
361 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
362 |
|
|
520
|
363 |
% \mbox{}\\[-20mm]\mbox{}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
|
|
520
|
365 |
% \begin{center}
|
|
|
366 |
% \begin{tikzpicture}[>=stealth',very thick,auto,
|
|
|
367 |
% every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
|
|
|
368 |
% \node[state,initial] (q_02) {$q_{0, 2}$};
|
|
|
369 |
% \node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
|
|
|
370 |
% \node[state, accepting] (q_4) [right=of q_13] {$q_{4\phantom{,0}}$};
|
|
|
371 |
% \path[->] (q_02) edge [bend left] node [above] {\alert{$a$}} (q_13);
|
|
|
372 |
% \path[->] (q_13) edge [bend left] node [below] {\alert{$b$}} (q_02);
|
|
|
373 |
% \path[->] (q_02) edge [loop below] node {\alert{$b$}} ();
|
|
|
374 |
% \path[->] (q_13) edge node [above] {\alert{$a$}} (q_4);
|
|
|
375 |
% \path[->] (q_4) edge [loop above] node {\alert{$a, b$}} ();
|
|
|
376 |
% \end{tikzpicture}\\
|
|
|
377 |
% minimal automaton
|
|
|
378 |
% \end{center}
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
379 |
|
|
520
|
380 |
% \end{frame}
|
|
|
381 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
265
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
382 |
|
144
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
383 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
384 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
385 |
\frametitle{Regular Languages}
|
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 |
Two equivalent definitions:\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
388 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
389 |
\begin{quote}\rm A language is \alert{regular} iff there exists a
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
390 |
regular expression that recognises all its strings.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
391 |
\end{quote}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
392 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
393 |
\begin{quote}\rm A language is \alert{regular} iff there exists an
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
394 |
automaton that recognises all its strings.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
395 |
\end{quote}\bigskip\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
396 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
397 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
398 |
\small
|
|
445
|
399 |
for example \bl{$a^nb^n$} is not regular
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
400 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
|
|
578
|
403 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
405 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
\frametitle{Negation}
|
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 |
Regular languages are closed under negation:\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
410 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
\begin{center}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
\begin{tikzpicture}[scale=2,>=stealth',very thick,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
413 |
every state/.style={minimum size=0pt,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
414 |
draw=blue!50,very thick,fill=blue!20}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
415 |
\only<1>{\node[state,initial] (q0) at ( 0,1) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
416 |
\only<2>{\node[state,initial,accepting] (q0) at ( 0,1) {$q_0$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
\only<1>{\node[state] (q1) at ( 1,1) {$q_1$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
418 |
\only<2>{\node[state,accepting] (q1) at ( 1,1) {$q_1$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
\only<1>{\node[state, accepting] (q2) at ( 2,1) {$q_2$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
420 |
\only<2>{\node[state] (q2) at ( 2,1) {$q_2$};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
421 |
\path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
422 |
(q1) edge[bend left] node[above] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
423 |
(q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
(q1) edge node[above] {\alert{$a$}} (q2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
(q2) edge [loop right] node {\alert{$a$}} ()
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
(q0) edge [loop below] node {\alert{$b$}} ();
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\end{center}\bigskip\bigskip
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
429 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
430 |
But requires that the automaton is \alert{completed}!
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
431 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
\begin{frame}[c]
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\frametitle{The Goal of this Course}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
438 |
\mbox{}\\[-26mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
439 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
\begin{tikzpicture}[scale=1,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
node/.style={
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
rectangle,rounded corners=3mm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
very thick,draw=black!50,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
minimum height=18mm, minimum width=20mm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
top color=white,bottom color=black!20}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
|
|
578
|
448 |
\node at (3.05, 1.8) {\Large\bf Write a compiler};
|
352
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 |
\node (0) at (-2.3,0) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
451 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
452 |
\node (A) at (0,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\node [below right] at (A.north west) {lexer};
|
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 |
\node (B) at (3,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
\node [below right=1mm] at (B.north west)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
{\mbox{}\hspace{-1mm}parser};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\node (C) at (6,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
460 |
\node [below right] at (C.north west)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
{\mbox{}\hspace{-1mm}code gen};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\node (1) at (8.4,0) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
\draw [->,line width=4mm] (0) -- (A);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
\draw [->,line width=4mm] (A) -- (B);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
\draw [->,line width=4mm] (B) -- (C);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
\draw [->,line width=4mm] (C) -- (1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
\end{center}
|
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 |
Today a lexer.
|
|
579
|
473 |
|
|
|
474 |
\only<2>{
|
|
|
475 |
\begin{textblock}{1}(6,9.8)
|
|
|
476 |
\begin{tabular}{c}
|
|
|
477 |
\includegraphics[scale=0.13]{../pics/rosetta.jpg}\\[-2mm]
|
|
|
478 |
\footnotesize lexing $\Rightarrow$ recognising words (Stone of Rosetta)
|
|
|
479 |
\end{tabular}
|
|
|
480 |
\end{textblock}}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
481 |
\end{frame}
|
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 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
484 |
\begin{frame}[c]
|
|
578
|
485 |
\frametitle{Regular Expressions}
|
|
|
486 |
|
|
|
487 |
In programming languages they are often used to recognise:\medskip
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
|
|
578
|
489 |
\begin{itemize}
|
|
662
|
490 |
\item operands, digits
|
|
578
|
491 |
\item identifiers
|
|
|
492 |
\item numbers (non-leading zeros)
|
|
|
493 |
\item keywords
|
|
|
494 |
\item comments
|
|
|
495 |
\end{itemize}\bigskip
|
|
|
496 |
|
|
|
497 |
\mbox{}\hfill\bl{\url{http://www.regexper.com}}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
498 |
\end{frame}
|
|
578
|
499 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
501 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
\begin{frame}[c]
|
|
521
|
504 |
\frametitle{Lexing: Test Case}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
\mbox{\lstinputlisting[language=While]{../progs/fib.while}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
|
|
578
|
511 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
512 |
%\begin{frame}[c]
|
|
|
513 |
%\frametitle{?? Test Case}
|
|
|
514 |
%
|
|
|
515 |
%\mbox{\lstinputlisting[language=While]{../progs/collatz.while}}
|
|
|
516 |
%
|
|
|
517 |
%\end{frame}
|
139
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
|
|
35
|
520 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
\begin{center}\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
\code{"if true then then 42 else +"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
\end{center}
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
KEYWORD: \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
\hspace{5mm}{if}, {then}, {else},\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
WHITESPACE:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
\hspace{5mm}{" "}, {$\backslash$n},\\
|
|
521
|
534 |
IDENTIFIER:\\
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
\hspace{5mm}LETTER $\cdot$ (LETTER + DIGIT + {\_})$^*$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {0}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
OP:\\
|
|
521
|
539 |
\hspace{5mm}+, -, *, \%, <, <=\\
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
COMMENT:\\
|
277
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
541 |
\hspace{5mm}{$\slash$*} $\cdot$ $\sim$(ALL$^*$ $\cdot$ (*$\slash$) $\cdot$ ALL$^*$) $\cdot$ {*$\slash$}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
\end{frame}
|
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}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
550 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
551 |
\begin{center}\large
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
552 |
\code{"if true then then 42 else +"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
553 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
\only<1>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
557 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
558 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
559 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
560 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
561 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
562 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
563 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
564 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
WHITESPACE,\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
\only<2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
\small\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
KEYWORD(if),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
IDENT(true),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
KEYWORD(then),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
NUM(42),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
KEYWORD(else),\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
580 |
OP(+)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\end{frame}
|
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]
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
There is one small problem with the tokenizer. How should we
|
|
578
|
591 |
tokenize\ldots?
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
\large\code{"x-3"}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
\end{center}
|
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 |
\tt
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
\begin{tabular}{@{}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
599 |
ID: \ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
OP:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
\hspace{5mm}\texttt{"+"}, \texttt{"-"}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
NUM:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\hspace{5mm}(NONZERODIGIT $\cdot$ DIGIT$^*$) + {''0''}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
604 |
NUMBER:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
\hspace{5mm}NUM + (\texttt{"-"} $\cdot$ NUM)\\
|
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 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
The same problem with\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
\[
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\bl{(ab + a) \cdot (c + bc)}
|
353
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
\]\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
|
|
662
|
619 |
and the string $\bl{abc}$.\pause\bigskip
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
|
|
662
|
621 |
Or, keywords are \code{if} etc and identifiers are
|
353
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
622 |
letters followed by ``letters + numbers + \_''$^*$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
624 |
\[
|
|
578
|
625 |
\bl{if}\qquad\bl{iffoo}
|
353
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
\]
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\frametitle{POSIX: Two Rules}
|
|
33
|
634 |
|
|
38
|
635 |
\begin{itemize}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
\item Longest match rule (``maximal munch rule''): The
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
longest initial substring matched by any regular expression is taken
|
278
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
as the next token.\bigskip
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
\item Rule priority:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
For a particular longest initial substring, the first regular
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
expression that can match determines the token.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
643 |
\end{itemize}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
\hfill most posix matchers are buggy\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
\footnotesize
|
353
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\hfill
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
\url{http://www.haskell.org/haskellwiki/Regex_Posix}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
\smallskip\pause
|
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 |
\hfill \small traditional lexers are fast, but hairy
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
%\url{http://www.technologyreview.com/tr10/?year=2011}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
%finite deterministic automata/ nondeterministic automaton
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
%\item problem with infix operations, for example i-12
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
\begin{frame}[c]
|
|
581
|
663 |
\frametitle{Sulzmann \& Lu Matcher}
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
We want to match the string \bl{$abc$} using \bl{$r_1$}:
|
|
38
|
666 |
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};\pause
|
|
521
|
676 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable?$}}};\pause
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
\draw[->,line width=1mm] (r4) -- (v4);\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
681 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
682 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
683 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
684 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
685 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
272
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
690 |
\end{center}
|
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 |
\end{frame}
|
|
33
|
693 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
694 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
695 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
696 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
697 |
\frametitle{Regexes and Values}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
698 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
699 |
Regular expressions and their corresponding values:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
700 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
701 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
702 |
\begin{columns}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
703 |
\begin{column}{3cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
704 |
\begin{tabular}{@{}rrl@{}}
|
|
445
|
705 |
\bl{$r$} & \bl{$::=$} & \bl{$\ZERO$}\\
|
|
|
706 |
& \bl{$\mid$} & \bl{$\ONE$} \\
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
707 |
& \bl{$\mid$} & \bl{$c$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
708 |
& \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
709 |
& \bl{$\mid$} & \bl{$r_1 + r_2$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
710 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
711 |
& \bl{$\mid$} & \bl{$r^*$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
712 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
713 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
714 |
\end{column}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
715 |
\begin{column}{3cm}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
716 |
\begin{tabular}{@{\hspace{-7mm}}rrl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
717 |
\bl{$v$} & \bl{$::=$} & \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
718 |
& & \bl{$Empty$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
719 |
& \bl{$\mid$} & \bl{$Char(c)$} \\
|
279
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
720 |
& \bl{$\mid$} & \bl{$Seq(v_1,v_2)$}\\
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
721 |
& \bl{$\mid$} & \bl{$Left(v)$} \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
722 |
& \bl{$\mid$} & \bl{$Right(v)$} \\
|
|
578
|
723 |
& \bl{$\mid$} & \bl{$Stars\,[]$} \\
|
|
|
724 |
& \bl{$\mid$} & \bl{$Stars\,[v_1,\ldots\,v_n]$} \\
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
725 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
726 |
\end{column}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
727 |
\end{columns}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
728 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
729 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
730 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
731 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
732 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
733 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
734 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
735 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
736 |
{\small\lstinputlisting[language=Scala,numbers=none,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
737 |
xleftmargin=-5mm] {../progs/app01.scala}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
738 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
739 |
{\small\lstinputlisting[language=Scala,numbers=none,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
740 |
xleftmargin=-5mm] {../progs/app02.scala}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
741 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
742 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
743 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
744 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
745 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
746 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
747 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
748 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
749 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
750 |
\begin{textblock}{10}(3,5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
751 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
752 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
753 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
754 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
755 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
756 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
757 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
758 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
759 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
760 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
761 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
762 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
763 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
764 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
765 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
766 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
767 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
768 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
769 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
770 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
771 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
772 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
773 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
774 |
|
|
662
|
775 |
\only<1->{
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
776 |
\begin{textblock}{6}(1,0.8)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
777 |
\begin{bubble}[6cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
778 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
779 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
780 |
\bl{$r_1$}: & \bl{$a \cdot (b \cdot c)$}\\
|
|
445
|
781 |
\bl{$r_2$}: & \bl{$\ONE \cdot (b \cdot c)$}\\
|
|
|
782 |
\bl{$r_3$}: & \bl{$(\ZERO \cdot (b \cdot c)) + (\ONE \cdot c)$}\\
|
|
|
783 |
\bl{$r_4$}: & \bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}\\
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
784 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
785 |
\end{bubble}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
786 |
\end{textblock}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
787 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
788 |
\only<2->{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
789 |
\begin{textblock}{6}(5,11.4)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
790 |
\begin{bubble}[7.6cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
791 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
792 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
793 |
\bl{$v_1$}: & \bl{$Seq(Char(a), Seq(Char(b), Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
794 |
\bl{$v_2$}: & \bl{$Seq(Empty, Seq(Char(b), Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
795 |
\bl{$v_3$}: & \bl{$Right(Seq(Empty, Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
796 |
\bl{$v_4$}: & \bl{$Right(Right(Empty))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
797 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
798 |
\end{bubble}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
799 |
\end{textblock}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
800 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
801 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
802 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
803 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
804 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
805 |
\frametitle{Flatten}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
806 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
807 |
Obtaining the string underlying a value:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
808 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
809 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
810 |
\begin{tabular}{lcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
811 |
\bl{$|Empty|$} & \bl{$\dn$} & \bl{$[]$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
812 |
\bl{$|Char(c)|$} & \bl{$\dn$} & \bl{$[c]$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
813 |
\bl{$|Left(v)|$} & \bl{$\dn$} & \bl{$|v|$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
814 |
\bl{$|Right(v)|$} & \bl{$\dn$} & \bl{$|v|$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
815 |
\bl{$|Seq(v_1,v_2)|$}& \bl{$\dn$} & \bl{$|v_1| \,@\, |v_2|$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
816 |
\bl{$|[v_1,\ldots ,v_n]|$} & \bl{$\dn$} & \bl{$|v_1| \,@\ldots @\, |v_n|$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
817 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
818 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
819 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
820 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
821 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
822 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
823 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
824 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
825 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
826 |
\begin{textblock}{10}(3,5)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
827 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
828 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
829 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
830 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
831 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
832 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
833 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
834 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
835 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
836 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
837 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
838 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
839 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
840 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
841 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
842 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
843 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
844 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
845 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
846 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
847 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
848 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
849 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
850 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
851 |
\begin{textblock}{6}(1,0.8)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
852 |
\begin{bubble}[6cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
853 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
854 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
855 |
\bl{$r_1$}: & \bl{$a \cdot (b \cdot c)$}\\
|
|
445
|
856 |
\bl{$r_2$}: & \bl{$\ONE \cdot (b \cdot c)$}\\
|
|
|
857 |
\bl{$r_3$}: & \bl{$(\ZERO \cdot (b \cdot c)) + (\ONE \cdot c)$}\\
|
|
|
858 |
\bl{$r_4$}: & \bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}\\
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
859 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
860 |
\end{bubble}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
861 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
862 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
863 |
\begin{textblock}{6}(1,11.4)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
864 |
\begin{bubble}[7.6cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
865 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
866 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
867 |
\bl{$v_1$}: & \bl{$Seq(Char(a), Seq(Char(b), Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
868 |
\bl{$v_2$}: & \bl{$Seq(Empty, Seq(Char(b), Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
869 |
\bl{$v_3$}: & \bl{$Right(Seq(Empty, Char(c)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
870 |
\bl{$v_4$}: & \bl{$Right(Right(Empty))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
871 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
872 |
\end{bubble}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
873 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
874 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
875 |
\begin{textblock}{6}(12,11.4)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
876 |
\begin{bubble}[2cm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
877 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
878 |
\begin{tabular}{ll}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
879 |
\bl{$|v_1|$}: & \bl{$abc$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
880 |
\bl{$|v_2|$}: & \bl{$bc$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
881 |
\bl{$|v_3|$}: & \bl{$c$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
882 |
\bl{$|v_4|$}: & \bl{$[]$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
883 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
884 |
\end{bubble}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
885 |
\end{textblock}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
886 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
887 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
888 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
889 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
890 |
|
|
662
|
891 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
892 |
\begin{frame}[c]
|
|
|
893 |
\frametitle{Mkeps}
|
|
|
894 |
|
|
|
895 |
Finding a (posix) value for recognising the empty string:
|
|
|
896 |
|
|
|
897 |
\begin{center}
|
|
|
898 |
\begin{tabular}{lcl}
|
|
|
899 |
\bl{$mkeps\,(\ONE)$} & \bl{$\dn$} & \bl{$Empty$}\\
|
|
|
900 |
\bl{$mkeps\,(r_1 + r_2)$} & \bl{$\dn$} & \bl{if $nullable(r_1)$} \\
|
|
|
901 |
& & \bl{then $Left(mkeps(r_1))$}\\
|
|
|
902 |
& & \bl{else $Right(mkeps(r_2))$}\\
|
|
|
903 |
\bl{$mkeps\,(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),mkeps(r_2))$}\\
|
|
|
904 |
\bl{$mkeps\,(r^*)$} & \bl{$\dn$} & \bl{$Stars\,[]$} \\
|
|
|
905 |
\end{tabular}
|
|
|
906 |
\end{center}
|
|
|
907 |
|
|
|
908 |
\end{frame}
|
|
|
909 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
910 |
|
|
|
911 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
912 |
\begin{frame}[c]
|
|
|
913 |
\frametitle{Inject}
|
|
|
914 |
|
|
|
915 |
Injecting (``Adding'') a character to a value\\[-12mm]\mbox{}
|
|
|
916 |
|
|
|
917 |
\begin{center}
|
|
|
918 |
\begin{tabular}{@{\hspace{-3mm}}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
|
|
|
919 |
\bl{$inj\,(c)\,c\,(Empty)$} & \bl{$\dn$} & \bl{$Char\,c$}\\
|
|
|
920 |
\bl{$inj\,(r_1 + r_2)\,c\,(Left(v))$} & \bl{$\dn$} & \bl{$Left(inj\,r_1\,c\,v)$}\\
|
|
|
921 |
\bl{$inj\,(r_1 + r_2)\,c\,(Right(v))$} & \bl{$\dn$} & \bl{$Right(inj\,r_2\,c\,v)$}\\
|
|
|
922 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,(Seq(v_1,v_2))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
|
923 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,(Left(Seq(v_1,v_2)))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
|
924 |
\bl{$inj\,(r_1 \cdot r_2)\,c\,(Right(v))$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),inj\,r_2\,c\,v)$}\\
|
|
|
925 |
\bl{$inj\,(r^*)\,c\,(Seq(v,Stars\,vs))$} & \bl{$\dn$} & \bl{$Stars\,(inj\,r\,c\,v\,::\,vs)$}\\
|
|
|
926 |
\end{tabular}
|
|
|
927 |
\end{center}\bigskip
|
|
|
928 |
|
|
|
929 |
\footnotesize
|
|
|
930 |
\begin{tabular}{l@{\hspace{2mm}}l}
|
|
|
931 |
\bl{$inj$}: & 1st arg $\mapsto$ a rexp; 2nd arg $\mapsto$ a character;
|
|
|
932 |
3rd arg $\mapsto$ a value\\
|
|
|
933 |
& result $\mapsto$ a value
|
|
|
934 |
\end{tabular}
|
|
|
935 |
\end{frame}
|
|
|
936 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
937 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
938 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
939 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
940 |
\frametitle{Lexing}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
941 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
942 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
943 |
\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
944 |
\bl{$lex\,r\,[]$} & \bl{$\dn$} & \bl{if $nullable(r)$ then $mkeps(r)$ else $error$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
945 |
\bl{$lex\,r\,c::s$} & \bl{$\dn$} & \bl{$inj\,r\,c\,lex(der(c,r), s)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
946 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
947 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
948 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
949 |
\footnotesize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
950 |
\bl{$lex$}: returns a value
|
280
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
951 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
952 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
953 |
\begin{tikzpicture}[scale=2,node distance=1.0cm,every node/.style={minimum size=6mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
954 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
955 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
956 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
957 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
958 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
959 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
960 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
961 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
962 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
963 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
964 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
965 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
966 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
967 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
968 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
969 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
970 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
971 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
972 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
973 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
974 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
975 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
976 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
977 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
978 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
979 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
980 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
981 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
982 |
\frametitle{Records}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
983 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
984 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
985 |
\item new regex: \bl{$(x:r)$}\hspace{7mm}new value: \bl{$Rec(x,v)$}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
986 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
987 |
\item \bl{$nullable(x:r) \dn nullable(r)$}
|
|
671
|
988 |
\item \bl{$der\,c\,(x:r) \dn der\,c\,r$}
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
989 |
\item \bl{$mkeps(x:r) \dn Rec(x, mkeps(r))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
990 |
\item \bl{$inj\,(x:r)\,c\,v \dn Rec(x, inj\,r\,c\,v)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
991 |
\end{itemize}\bigskip\bigskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
992 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
993 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
994 |
for extracting subpatterns \bl{$(z: ((x:ab) + (y:ba))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
995 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
996 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
997 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
998 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
999 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1000 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1001 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1002 |
\begin{itemize}
|
|
445
|
1003 |
\item A regular expression for email addresses
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1004 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1005 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1006 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1007 |
(name: \bl{$[a\mbox{-}z0\mbox{-}9\_\!\_\,.-]^+$})\bl{$\cdot @\cdot$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1008 |
\qquad(domain: \bl{$[a\mbox{-}z0\mbox{-}9\,.-]^+$}) \bl{$\cdot .\cdot$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1009 |
\qquad\qquad(top\_level: \bl{$[a\mbox{-}z\,.]^{\{2,6\}}$})
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1010 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1011 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1012 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1013 |
\bl{\[
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1014 |
\texttt{christian.urban@kcl.ac.uk}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1015 |
\]}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1016 |
|
|
445
|
1017 |
\item the result environment:
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1018 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1019 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1020 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1021 |
\bl{$[(name:\texttt{christian.urban}),$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1022 |
\bl{$\phantom{[}(domain:\texttt{kcl}),$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1023 |
\bl{$\phantom{[}(top\_level:\texttt{ac.uk})]$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1024 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1025 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1026 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1027 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1028 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1029 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1030 |
|
273
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1031 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1032 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1033 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1034 |
\frametitle{While Tokens}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1035 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1036 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1037 |
\begin{tabular}{rcl}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1038 |
\pcode{WHILE\_REGS} & $\dn$ & \raisebox{-1mm}{\large(}\pcode{("k" : KEYWORD)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1039 |
& & \phantom{(}\pcode{("i" : ID)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1040 |
& & \phantom{(}\pcode{("o" : OP)} + \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1041 |
& & \phantom{(}\pcode{("n" : NUM)} + \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1042 |
& & \phantom{(}\pcode{("s" : SEMI)} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1043 |
& & \phantom{(}\pcode{("p" : (LPAREN + RPAREN))} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1044 |
& & \phantom{(}\pcode{("b" : (BEGIN + END))} +\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1045 |
& & \phantom{(}\pcode{("w" : WHITESPACE)}\raisebox{-1mm}{\large)$^*$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1046 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1047 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1048 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1049 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1050 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1051 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1052 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1053 |
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1054 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1055 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1056 |
\frametitle{Simplification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1057 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1058 |
\begin{itemize}
|
|
522
|
1059 |
\item If we simplify after the derivative, then we are building the
|
|
578
|
1060 |
value for the simplified regular expression, but \alert{\textbf{not}} for the original
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1061 |
regular expression.
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1062 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1063 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1064 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1065 |
\begin{tikzpicture}[scale=2,node distance=1.3cm,every node/.style={minimum size=8mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1066 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1067 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1068 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1069 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1070 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1071 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1072 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1073 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1074 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1075 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1076 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1077 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1078 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1079 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1080 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1081 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1082 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1083 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1084 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1085 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1086 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1087 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1088 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1089 |
\small
|
|
445
|
1090 |
\hspace{4.5cm}\bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1091 |
$\mapsto$
|
|
445
|
1092 |
\bl{$\ONE$}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1093 |
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1094 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1095 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1096 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1097 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1098 |
\begin{frame}[c]
|
447
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1099 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1100 |
Normally we would have
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1101 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1102 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1103 |
\bl{$(\ZERO \cdot (b \cdot c)) + ((\ZERO \cdot c) + \ONE)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1104 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1105 |
|
452
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1106 |
and answer how this regular expression matches the empty string
|
|
578
|
1107 |
with the value
|
447
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1108 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1109 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1110 |
\bl{$Right(Right(Empty))$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1111 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1112 |
|
|
578
|
1113 |
But now we simplify this to \bl{$\ONE$} and would produce \bl{$Empty$} (see \textit{mkeps}).
|
447
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1114 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1115 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1116 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1117 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1118 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1119 |
\begin{frame}[c]
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1120 |
\frametitle{Rectification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1121 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1122 |
\def\arraystretch{1.05}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1123 |
\begin{center}
|
|
445
|
1124 |
\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l@{\hspace{8mm}}l}
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1125 |
& & & \hspace{5mm}rectification \\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1126 |
& & & \hspace{5mm}functions:\\
|
|
445
|
1127 |
\bl{$r \cdot \ZERO$} & $\mapsto$ & \bl{$\ZERO$} & \\
|
|
|
1128 |
\bl{$\ZERO \cdot r$} & $\mapsto$ & \bl{$\ZERO$} & \\
|
|
|
1129 |
\bl{$r \cdot \ONE$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Seq(f_1\,v, f_2\,Empty)$}\\
|
|
|
1130 |
\bl{$\ONE \cdot r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Seq(f_1\,Empty, f_2\,v)$}\\
|
|
|
1131 |
\bl{$r + \ZERO$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Left(f_1\,v)$}\\
|
|
|
1132 |
\bl{$\ZERO + r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Right(f_2\,v)$}\\
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1133 |
\bl{$r + r$} & $\mapsto$ & \bl{$r$} & \bl{$\lambda f_1\,f_2\,v.\, Left(f_1\,v)$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1134 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1135 |
\end{center}\medskip\pause
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1136 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1137 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1138 |
old \bl{$simp$} returns a rexp;\\
|
|
445
|
1139 |
new \bl{$simp$} returns a rexp and a rectification~function.
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1140 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1141 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1142 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1143 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1144 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1145 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1146 |
\frametitle{Rectification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1147 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1148 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1149 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1150 |
\bl{$simp(r)$}:\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1151 |
\quad case \bl{$r = r_1 + r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1152 |
\qquad let \bl{$(r_{1s}, f_{1s}) = simp(r_1)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1153 |
\qquad \phantom{let} \bl{$(r_{2s}, f_{2s}) = simp(r_2)$}\smallskip\\
|
|
445
|
1154 |
\qquad case \bl{$r_{1s} = \ZERO$}:
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1155 |
return \bl{$(r_{2s}, \lambda v. \,Right(f_{2s}(v)))$}\\
|
|
445
|
1156 |
\qquad case \bl{$r_{2s} = \ZERO$}:
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1157 |
return \bl{$(r_{1s}, \lambda v. \,Left(f_{1s}(v)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1158 |
\qquad case \bl{$r_{1s} = r_{2s}$}:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1159 |
return \bl{$(r_{1s}, \lambda v. \,Left(f_{1s}(v)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1160 |
\qquad otherwise:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1161 |
return \bl{$(r_{1s} + r_{2s}, f_{alt}(f_{1s}, f_{2s}))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1162 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1163 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1164 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1165 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1166 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1167 |
\begin{tabular}{l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1168 |
\bl{$f_{alt}(f_1, f_2) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1169 |
\qquad \bl{$\lambda v.\,$} case \bl{$v = Left(v')$}:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1170 |
& return \bl{$Left(f_1(v'))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1171 |
\qquad \phantom{$\lambda v.\,$} case \bl{$v = Right(v')$}:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1172 |
& return \bl{$Right(f_2(v'))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1173 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1174 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1175 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1176 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1177 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1178 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1179 |
|
|
445
|
1180 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1181 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1182 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1183 |
{\footnotesize\lstinputlisting[language=Scala,numbers=none,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1184 |
xleftmargin=-5mm] {../progs/app05.scala}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1185 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1186 |
\end{frame}
|
|
445
|
1187 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1188 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1189 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1190 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1191 |
\frametitle{Rectification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1192 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1193 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1194 |
\begin{tabular}{@{\hspace{-3mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1195 |
\bl{$simp(r)$}:\ldots\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1196 |
\quad case \bl{$r = r_1 \cdot r_2$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1197 |
\qquad let \bl{$(r_{1s}, f_{1s}) = simp(r_1)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1198 |
\qquad \phantom{let} \bl{$(r_{2s}, f_{2s}) = simp(r_2)$}\smallskip\\
|
|
445
|
1199 |
\qquad case \bl{$r_{1s} = \ZERO$}:
|
|
|
1200 |
return \bl{$(\ZERO, f_{error})$}\\
|
|
|
1201 |
\qquad case \bl{$r_{2s} = \ZERO$}:
|
|
|
1202 |
return \bl{$(\ZERO, f_{error})$}\\
|
|
|
1203 |
\qquad case \bl{$r_{1s} = \ONE$}:
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1204 |
return \bl{$(r_{2s}, \lambda v. \,Seq(f_{1s}(Empty), f_{2s}(v)))$}\\
|
|
445
|
1205 |
\qquad case \bl{$r_{2s} = \ONE$}:
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1206 |
return \bl{$(r_{1s}, \lambda v. \,Seq(f_{1s}(v), f_{2s}(Empty)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1207 |
\qquad otherwise:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1208 |
return \bl{$(r_{1s} \cdot r_{2s}, f_{seq}(f_{1s}, f_{2s}))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1209 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1210 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1211 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1212 |
\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1213 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1214 |
\begin{tabular}{l@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1215 |
\bl{$f_{seq}(f_1, f_2) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1216 |
\qquad \bl{$\lambda v.\,$ case $v = Seq(v_1, v_2)$}:
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1217 |
& return \bl{$Seq(f_1(v_1), f_2(v_2))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1218 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1219 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1220 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1221 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1222 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1223 |
|
|
451
|
1224 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1225 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1226 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1227 |
{\footnotesize\lstinputlisting[language=Scala,numbers=none,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1228 |
xleftmargin=-5mm] {../progs/app06.scala}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1229 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1230 |
\end{frame}
|
|
451
|
1231 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1232 |
|
|
|
1233 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1234 |
\begin{frame}[t]
|
|
|
1235 |
\frametitle{Rectification Example}
|
|
|
1236 |
|
|
|
1237 |
\begin{center}
|
|
|
1238 |
\bl{$\only<1>{(b \cdot c)}%
|
|
|
1239 |
\only<2-3>{(\underline{b \cdot c})}%
|
|
|
1240 |
\only<1-3>{+}%
|
|
|
1241 |
\only<1>{(\ZERO + \ONE)}%
|
|
|
1242 |
\only<2-3>{(\underline{\ZERO + \ONE})}$}%
|
|
|
1243 |
\only<4->{%
|
|
|
1244 |
\bl{$\underline{(b \cdot c) + (\ZERO + \ONE)}$}%
|
|
|
1245 |
}
|
|
|
1246 |
$\mapsto$
|
|
|
1247 |
\bl{$(b \cdot c) + \ONE$}
|
|
|
1248 |
\end{center}\bigskip
|
|
|
1249 |
|
|
|
1250 |
\onslide<3->{%
|
|
|
1251 |
\begin{center}
|
|
|
1252 |
\begin{tabular}{lcl}
|
|
|
1253 |
\bl{$f_{s1}$} & \bl{$=$} & \bl{$\lambda v.v$}\\
|
|
|
1254 |
\bl{$f_{s2}$} & \bl{$=$} & \bl{$\lambda v. \textit{Right}(v)$}
|
|
|
1255 |
\end{tabular}
|
|
|
1256 |
\end{center}}
|
|
|
1257 |
|
|
|
1258 |
\only<4>{%
|
|
|
1259 |
\begin{center}
|
|
|
1260 |
\begin{tabular}{@{}l@{\hspace{1mm}}l@{}}
|
|
|
1261 |
\bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}\\
|
|
|
1262 |
\quad \bl{$\lambda v.\,$}
|
|
|
1263 |
case \bl{$v = Left(v')$}:
|
|
|
1264 |
& return \bl{$Left(f_{s1}(v'))$}\\
|
|
|
1265 |
\quad \phantom{$\lambda v.\,$}
|
|
|
1266 |
case \bl{$v = Right(v')$}:
|
|
|
1267 |
& return \bl{$Right(f_{s2}(v'))$}\\
|
|
|
1268 |
\end{tabular}
|
|
|
1269 |
\end{center}}%
|
|
|
1270 |
\only<5->{%
|
|
|
1271 |
\begin{center}
|
|
|
1272 |
\begin{tabular}{@{}l@{\hspace{1mm}}l@{}}
|
|
|
1273 |
\only<5->{\phantom{\bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}}}\\
|
|
|
1274 |
\quad \bl{$\lambda v.\,$}
|
|
|
1275 |
case \bl{$v = Left(v')$}:
|
|
|
1276 |
& return \bl{$Left(v')$}\\
|
|
|
1277 |
\quad \phantom{$\lambda v.\,$}
|
|
|
1278 |
case \bl{$v = Right(v')$}:
|
|
|
1279 |
& return \bl{$Right(Right(v'))$}\\
|
|
|
1280 |
\end{tabular}
|
|
|
1281 |
\end{center}}%
|
|
|
1282 |
|
|
|
1283 |
\only<6->{%
|
|
|
1284 |
\begin{center}
|
|
|
1285 |
\begin{tabular}{@{}l@{\hspace{4mm}}l@{}}
|
|
|
1286 |
\bl{$\textit{mkeps}$} simplified case: &
|
|
|
1287 |
\bl{$\textit{Right}(\textit{Empty})$}\\
|
|
|
1288 |
rectified case: &
|
|
|
1289 |
\bl{$\textit{Right}(\textit{Right}(\textit{Empty}))$}
|
|
|
1290 |
\end{tabular}
|
|
|
1291 |
\end{center}}%
|
|
|
1292 |
|
|
|
1293 |
\end{frame}
|
|
|
1294 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1295 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1296 |
|
274
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1297 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1298 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1299 |
\frametitle{Lexing with Simplification}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1300 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1301 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1302 |
\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1303 |
\bl{$lex\,r\,[]$} & \bl{$\dn$} & \bl{if $nullable(r)$ then $mkeps(r)$ else $error$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1304 |
\bl{$lex\,r\,c::s$} & \bl{$\dn$} & \bl{let $(r', frect) = simp(der(c, r))$}\smallskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1305 |
& & \bl{$inj\,r\,c\,(frect(lex(r', s)))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1306 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1307 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1308 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1309 |
\begin{center}\small
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1310 |
\begin{tikzpicture}[node distance=1.1cm,every node/.style={minimum size=7mm}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1311 |
\node (r1) {\bl{$r_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1312 |
\node (r2) [right=of r1] {\bl{$r_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1313 |
\draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1314 |
\node (r3) [right=of r2] {\bl{$r_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1315 |
\draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1316 |
\node (r4) [right=of r3] {\bl{$r_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1317 |
\draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1318 |
\draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1319 |
\node (v4) [below=of r4] {\bl{$v_4$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1320 |
\draw[->,line width=1mm] (r4) -- (v4);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1321 |
\node (v3) [left=of v4] {\bl{$v_3$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1322 |
\draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1323 |
\node (v2) [left=of v3] {\bl{$v_2$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1324 |
\draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1325 |
\node (v1) [left=of v2] {\bl{$v_1$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1326 |
\draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1327 |
\draw[->,line width=0.5mm] (r3) -- (v3);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1328 |
\draw[->,line width=0.5mm] (r2) -- (v2);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1329 |
\draw[->,line width=0.5mm] (r1) -- (v1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1330 |
\draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1331 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1332 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1333 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1334 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1335 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1336 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1337 |
|
|
451
|
1338 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1339 |
\begin{frame}[c]
|
|
|
1340 |
\frametitle{Environments}
|
|
|
1341 |
|
|
|
1342 |
Obtaining the ``recorded'' parts of a value:
|
|
|
1343 |
|
|
|
1344 |
\begin{center}
|
|
|
1345 |
\begin{tabular}{lcl}
|
|
|
1346 |
\bl{$env(Empty)$} & \bl{$\dn$} & \bl{$[]$}\\
|
|
|
1347 |
\bl{$env(Char(c))$} & \bl{$\dn$} & \bl{$[]$}\\
|
|
|
1348 |
\bl{$env(Left(v))$} & \bl{$\dn$} & \bl{$env(v)$}\\
|
|
|
1349 |
\bl{$env(Right(v))$} & \bl{$\dn$} & \bl{$env(v)$}\\
|
|
|
1350 |
\bl{$env(Seq(v_1,v_2))$}& \bl{$\dn$} & \bl{$env(v_1) \,@\, env(v_2)$}\\
|
|
578
|
1351 |
\bl{$env(Stars\,[v_1,\ldots ,v_n])$} & \bl{$\dn$} &
|
|
451
|
1352 |
\bl{$env(v_1) \,@\ldots @\, env(v_n)$}\\
|
|
|
1353 |
\bl{$env(Rec(x:v))$} & \bl{$\dn$} & \bl{$(x:|v|) :: env(v)$}\\
|
|
|
1354 |
\end{tabular}
|
|
|
1355 |
\end{center}
|
|
|
1356 |
|
|
|
1357 |
\end{frame}
|
|
|
1358 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1359 |
|
|
|
1360 |
|
|
|
1361 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1362 |
\begin{frame}[c]
|
|
|
1363 |
\frametitle{While Tokens}
|
|
|
1364 |
|
|
|
1365 |
\begin{center}
|
|
|
1366 |
\begin{tabular}{@{}r@{\hspace{2mm}}c@{\hspace{2mm}}l@{}}
|
|
|
1367 |
\pcode{WHILE\_REGS} & $\dn$ & \raisebox{-1mm}{\large(}\pcode{("k" : KEYWORD)} +\\
|
|
|
1368 |
& & \phantom{(}\pcode{("i" : ID)} +\\
|
|
|
1369 |
& & \phantom{(}\pcode{("o" : OP)} + \\
|
|
|
1370 |
& & \phantom{(}\pcode{("n" : NUM)} + \\
|
|
|
1371 |
& & \phantom{(}\pcode{("s" : SEMI)} +\\
|
|
|
1372 |
& & \phantom{(}\pcode{("p" : (LPAREN + RPAREN))} +\\
|
|
|
1373 |
& & \phantom{(}\pcode{("b" : (BEGIN + END))} +\\
|
|
|
1374 |
& & \phantom{(}\pcode{("w" : WHITESPACE)}\raisebox{-1mm}{\large)$^*$}
|
|
|
1375 |
\end{tabular}
|
|
|
1376 |
\end{center}
|
|
|
1377 |
|
|
|
1378 |
\end{frame}
|
|
|
1379 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1380 |
|
|
|
1381 |
|
|
|
1382 |
|
|
|
1383 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1384 |
\begin{frame}[t]
|
|
|
1385 |
|
|
|
1386 |
\consolas
|
|
|
1387 |
\begin{center}
|
|
|
1388 |
\code{"if true then then 42 else +"}
|
|
|
1389 |
\end{center}
|
|
|
1390 |
|
|
|
1391 |
\only<1>{
|
|
|
1392 |
\small\begin{tabular}{l}
|
|
|
1393 |
KEYWORD(if),\\
|
|
|
1394 |
WHITESPACE,\\
|
|
|
1395 |
IDENT(true),\\
|
|
|
1396 |
WHITESPACE,\\
|
|
|
1397 |
KEYWORD(then),\\
|
|
|
1398 |
WHITESPACE,\\
|
|
|
1399 |
KEYWORD(then),\\
|
|
|
1400 |
WHITESPACE,\\
|
|
|
1401 |
NUM(42),\\
|
|
|
1402 |
WHITESPACE,\\
|
|
|
1403 |
KEYWORD(else),\\
|
|
|
1404 |
WHITESPACE,\\
|
|
|
1405 |
OP(+)
|
|
|
1406 |
\end{tabular}}
|
|
|
1407 |
|
|
|
1408 |
\only<2>{
|
|
|
1409 |
\small\begin{tabular}{l}
|
|
|
1410 |
KEYWORD(if),\\
|
|
|
1411 |
IDENT(true),\\
|
|
|
1412 |
KEYWORD(then),\\
|
|
|
1413 |
KEYWORD(then),\\
|
|
|
1414 |
NUM(42),\\
|
|
|
1415 |
KEYWORD(else),\\
|
|
|
1416 |
OP(+)
|
|
|
1417 |
\end{tabular}}
|
|
|
1418 |
|
|
|
1419 |
\end{frame}
|
|
|
1420 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1421 |
|
|
|
1422 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1423 |
\begin{frame}[c]
|
|
521
|
1424 |
\frametitle{Lexer: Two Rules}
|
|
451
|
1425 |
|
|
|
1426 |
\begin{itemize}
|
|
|
1427 |
\item Longest match rule (``maximal munch rule''): The
|
|
|
1428 |
longest initial substring matched by any regular expression is taken
|
|
|
1429 |
as next token.\bigskip
|
|
|
1430 |
|
|
|
1431 |
\item Rule priority:
|
|
|
1432 |
For a particular longest initial substring, the first regular
|
|
|
1433 |
expression that can match determines the token.
|
|
|
1434 |
|
|
|
1435 |
\end{itemize}
|
|
|
1436 |
|
|
|
1437 |
%\url{http://www.technologyreview.com/tr10/?year=2011}
|
|
|
1438 |
|
|
|
1439 |
%finite deterministic automata/ nondeterministic automaton
|
|
|
1440 |
|
|
|
1441 |
%\item problem with infix operations, for example i-12
|
|
|
1442 |
|
|
|
1443 |
|
|
|
1444 |
\end{frame}
|
|
|
1445 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1446 |
|
|
|
1447 |
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1448 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1449 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1450 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1451 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1452 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
|
578
|
1453 |
\bl{$zeroable(\ZERO)$} & \bl{$\dn$} & \bl{$true$}\\
|
|
|
1454 |
\bl{$zeroable(\ONE)$} & \bl{$\dn$} & \bl{$\textit{false}$}\\
|
|
445
|
1455 |
\bl{$zeroable(c)$} & \bl{$\dn$} & \bl{$\textit{false}$}\\
|
|
|
1456 |
\bl{$zeroable(r_1 + r_2)$} & \bl{$\dn$} & \bl{$zeroable(r_1) \wedge zeroable(r_2)$}\\
|
|
|
1457 |
\bl{$zeroable(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$zeroable(r_1) \vee zeroable(r_2)$}\\
|
|
|
1458 |
\bl{$zeroable(r^*)$} & \bl{$\dn$} & \bl{$\textit{false}$}\\
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1459 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1460 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1461 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1462 |
\begin{center}
|
|
445
|
1463 |
\bl{$zeroable(r)$} if and only if \bl{$L(r) = \{\}$}
|
352
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1464 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1465 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1466 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1467 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1468 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1469 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1470 |
|
|
33
|
1471 |
\end{document}
|
|
|
1472 |
|
|
|
1473 |
%%% Local Variables:
|
|
|
1474 |
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|
|
|
1475 |
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|
|
|
1476 |
%%% End:
|
|
|
1477 |
|