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(*<*)
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theory Slides4
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imports "LaTeXsugar" "Nominal"
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begin
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notation (latex output)
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set ("_") and
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Cons ("_::/_" [66,65] 65)
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(*>*)
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text_raw {*
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\renewcommand{\slidecaption}{Nanjing, 31.~August 2010}
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\newcommand{\abst}[2]{#1.#2}% atom-abstraction
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\newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing
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\newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions
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\newcommand{\unit}{\langle\rangle}% unit
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\newcommand{\app}[2]{#1\,#2}% application
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\newcommand{\eqprob}{\mathrel{{\approx}?}}
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\newcommand{\freshprob}{\mathrel{\#?}}
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\newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction
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\newcommand{\id}{\varepsilon}% identity substitution
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\newcommand{\gr}[1]{\textcolor{gray}{#1}}
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\newcommand{\rd}[1]{\textcolor{red}{#1}}
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\newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}}
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\newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}}
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\newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}}
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\renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont}
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\newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont}
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\newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont}
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\newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont}
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\newcommand{\LL}{$\mathbb{L}\,$}
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\pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}%
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{rgb(0mm)=(0,0,0.9);
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rgb(0.9mm)=(0,0,0.7);
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rgb(1.3mm)=(0,0,0.5);
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rgb(1.4mm)=(1,1,1)}
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\def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex}
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\usebeamercolor[fg]{subitem projected}
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{\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}}
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\pgftext{%
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\usebeamerfont*{subitem projected}}
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\end{pgfpicture}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[t]
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\frametitle{%
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\begin{tabular}{@ {\hspace{-3mm}}c@ {}}
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\\
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\huge Error-Free Programming\\[-1mm]
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\huge with Theorem Provers\\[5mm]
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\end{tabular}}
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\begin{center}
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Christian Urban
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\end{center}
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\begin{center}
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\small Technical University of Munich, Germany\\[7mm]
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\small in Nanjing on the kind invitation of\\ Professor Xingyuan Zhang
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and his group
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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\mode<presentation>{
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\begin{frame}<1->[c]
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\frametitle{My Background}
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\begin{itemize}
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\item researcher in Theoretical Computer Science\medskip
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\item programmer on a \alert<2->{software system} with 800 kloc (though I am
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responsible only for 35 kloc)
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\end{itemize}
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\only<2->{
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\begin{textblock}{6}(2,11)
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\begin{tikzpicture}
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\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
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{\color{darkgray}
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\begin{minipage}{4cm}\raggedright
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A theorem prover called {\bf Isabelle}.
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\end{minipage}};
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\end{tikzpicture}
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\end{textblock}}
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\only<3>{
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\begin{textblock}{6}(9,11)
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\begin{tikzpicture}
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\draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
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{\color{darkgray}
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\begin{minipage}{4cm}\raggedright
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Like every other code, this code is very hard to
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get correct.
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\end{minipage}};
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\end{tikzpicture}
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\end{textblock}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1->[t]
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\frametitle{Regular Expressions}
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An example many (should) know about:\\
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\rd{\bf Regular Expressions:}
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\only<2>{
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\begin{center}
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\bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$ r$_1$$|$r$_2$ $\;\;\;|\;\;\;$
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r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$}
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\end{center}}
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\only<3->{
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\begin{center}
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\begin{tabular}{@ {}rrll@ {}}
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\bl{r} & \bl{$::=$} & \bl{NULL} & \gr{(matches no string)}\\
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& \bl{$\mid$} & \bl{EMPTY} & \gr{(matches the empty string, [])}\\
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& \bl{$\mid$} & \bl{CHR c} & \gr{(matches the character c)}\\
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& \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\
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& \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\
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& \bl{$\mid$} & \bl{STAR r} & \gr{(repeat, r$^*$)}\\
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\end{tabular}
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\end{center}\medskip}
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\small
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\begin{textblock}{14.5}(1,12.5)
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\only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\}
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\only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm}
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\{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
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\end{textblock}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[c]
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\frametitle{RegExp Matcher}
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Let's implement a regular expression matcher:\bigskip
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\begin{center}
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\begin{tikzpicture}
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%%\draw[help lines, black] (-3,0) grid (6,3);
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\draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3);
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\node[anchor=base] at (2,1)
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{\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\
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\Large\bf Expression \\
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\Large\bf Matcher\end{tabular}};
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\coordinate (m1) at (0,1.5);
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\draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}};
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\path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1);
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\coordinate (s1) at (0,0.5);
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\draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}};
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\path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1);
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\coordinate (r1) at (4,1.2);
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\draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}};
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\path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2);
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\end{tikzpicture}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1->[t]
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\frametitle{RegExp Matcher}
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\small
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{\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false
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\only<2->{
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\begin{center}
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\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
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\bl{match [] []} & \bl{$=$} & \bl{true}\\
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\bl{match [] \_} & \bl{$=$} & \bl{false}\\
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\bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\
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\bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
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\bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\
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\bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\
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\bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
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& & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
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\bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
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\bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
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& & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
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\end{tabular}
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\end{center}}
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\onslide<3->{we start the program with\\
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\hspace{6mm}\bl{matches r s $=$ match [r] s}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1>[c]
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\frametitle{Program in Scala}
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\bl{\footnotesize
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\begin{tabular}{l}
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sealed abstract class Rexp\\
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sealed case class Null extends Rexp\\
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sealed case class Empty extends Rexp\\
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sealed case class Chr(c: Char) extends Rexp\\
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sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\
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sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\
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sealed case class Star(r : Rexp) extends Rexp\medskip\\
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def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\
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\hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\
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\hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\
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\hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\
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\hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\
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\hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\
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\hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\
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\hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\
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\hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\
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\hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\
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\}
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\end{tabular}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1->[c]
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\frametitle{Testing}
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\small
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Every good programmer should do thourough tests:
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\begin{center}
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\begin{tabular}{@ {\hspace{-20mm}}lcl}
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\bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\
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\bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\
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\bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\
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\bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\
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\bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
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\onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}}\\
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\onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}}\\
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\onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}}
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\end{tabular}
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\end{center}
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\onslide<3->
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{looks OK \ldots let's ship it to customers\hspace{5mm}
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\raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1->[t]
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\frametitle{Testing}
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\begin{itemize}
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\item While testing is an important part in the process of programming development\pause
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\item we can only test a {\bf finite} amount of examples\bigskip\pause
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\begin{center}
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\colorbox{cream}
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{\gr{\begin{minipage}{10cm}
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``Testing can only show the presence of errors, never their
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absence'' (Edsger W.~Dijkstra)
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\end{minipage}}}
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\end{center}\bigskip\pause
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\item In a theorem prover we can establish properties that apply to
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{\bf all} input and {\bf all} output.\pause
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\item For example we can establish that the matcher terminates
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on all input.
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}<1->[t]
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\frametitle{RegExp Matcher}
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\small
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We need to find a measure that gets smaller in each recursive call.\bigskip
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\onslide<1->{
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\begin{center}
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\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}}
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\bl{match [] []} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
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\bl{match [] \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
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\bl{match (NULL::rs) s} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
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\bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\
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\bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\
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\bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
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\bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\
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& & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
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\bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s} & \onslide<6->{\ok}\\
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\bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\
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& & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
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\end{tabular}
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\end{center}}
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\begin{textblock}{5}(4,4)
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\begin{tikzpicture}
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%%\draw[help lines, black] (-3,0) grid (6,3);
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\coordinate (m1) at (-2,0);
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\coordinate (m2) at ( 2,0);
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\path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2);
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\draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}};
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\end{tikzpicture}
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\end{textblock}
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\end{frame}}
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*}
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text_raw {*
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\mode<presentation>{
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\begin{frame}<1->[c]
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\frametitle{Bug Hunting}
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367 |
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\only<1>{Several hours later\ldots}\pause
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369 |
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\begin{center}
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\begin{tabular}{@ {\hspace{-20mm}}lcl}
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\bl{matches (STAR (EMPTY)) s} & \bl{$\mapsto$} & loops\\
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\onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s} & \bl{$\mapsto$} & loops\\}
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\end{tabular}
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\end{center}
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\small
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\onslide<3->{
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\begin{center}
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\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
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\ldots\\
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\bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
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\ldots\\
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\bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
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& & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
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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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text_raw {*
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\mode<presentation>{
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\begin{frame}<1->[c]
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399 |
\frametitle{RegExp Matcher}
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400 |
\small
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401 |
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\begin{center}
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403 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
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\bl{match [] []} & \bl{$=$} & \bl{true}\\
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\bl{match [] \_} & \bl{$=$} & \bl{false}\\
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406 |
\bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\
|
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407 |
\bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
|
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408 |
\bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\
|
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409 |
\bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\
|
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410 |
\bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
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|
411 |
& & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
|
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|
412 |
\bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
|
|
|
413 |
\bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
|
|
|
414 |
& & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
|
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415 |
\end{tabular}
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\end{center}
|
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|
417 |
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418 |
\only<1>{
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\begin{textblock}{5}(4,4)
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\largenotok
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\end{textblock}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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426 |
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text_raw {*
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431 |
\mode<presentation>{
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432 |
\begin{frame}<1->[t]
|
|
|
433 |
\frametitle{Second Attempt}
|
|
|
434 |
|
|
|
435 |
Can a regular expression match the empty string?
|
|
|
436 |
|
|
|
437 |
\small
|
|
|
438 |
\begin{center}
|
|
|
439 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
|
|
|
440 |
\bl{nullable (NULL)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
|
|
|
441 |
\bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
|
|
|
442 |
\bl{nullable (CHR c)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
|
|
|
443 |
\bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)}
|
|
|
444 |
& \onslide<2->{\ok}\\
|
|
|
445 |
\bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)}
|
|
|
446 |
& \onslide<2->{\ok}\\
|
|
|
447 |
\bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
|
|
|
448 |
\end{tabular}
|
|
|
449 |
\end{center}
|
|
|
450 |
|
|
|
451 |
\end{frame}}
|
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452 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
|
453 |
*}
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454 |
|
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455 |
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456 |
text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
458 |
\mode<presentation>{
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|
459 |
\begin{frame}<1->[t]
|
|
|
460 |
\frametitle{RegExp Matcher 2}
|
|
|
461 |
|
|
|
462 |
If \bl{r} matches \bl{c::s}, which regular expression can match the string \bl{s}?
|
|
|
463 |
|
|
|
464 |
\small
|
|
|
465 |
\begin{center}
|
|
|
466 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
|
|
|
467 |
\bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
|
|
|
468 |
\bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
|
|
|
469 |
\bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \onslide<3->{\ok}\\
|
|
|
470 |
\bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \onslide<3->{\ok}\\
|
|
|
471 |
\bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \onslide<3->{\ok}\\
|
|
|
472 |
& & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
|
|
|
473 |
\bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} & \onslide<3->{\ok}\medskip\\
|
|
|
474 |
\pause
|
|
|
475 |
|
|
|
476 |
\bl{derivative r []} & \bl{$=$} & \bl{r} & \onslide<3->{\ok}\\
|
|
|
477 |
\bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \onslide<3->{\ok}\\
|
|
|
478 |
\end{tabular}
|
|
|
479 |
\end{center}
|
|
|
480 |
|
|
|
481 |
we call the program with\\
|
|
|
482 |
\bl{matches r s $=$ nullable (derivative r s)}
|
|
|
483 |
|
|
|
484 |
|
|
|
485 |
\end{frame}}
|
|
|
486 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
487 |
*}
|
|
|
488 |
|
|
|
489 |
text_raw {*
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490 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
491 |
\mode<presentation>{
|
|
|
492 |
\begin{frame}<1->[c]
|
|
|
493 |
\frametitle{But Now What?}
|
|
|
494 |
|
|
|
495 |
\begin{center}
|
|
|
496 |
{\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}}
|
|
|
497 |
\end{center}
|
|
|
498 |
|
|
|
499 |
\end{frame}}
|
|
|
500 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
501 |
*}
|
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|
502 |
|
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|
503 |
text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
505 |
\mode<presentation>{
|
|
|
506 |
\begin{frame}<1->[c]
|
|
|
507 |
\frametitle{Testing}
|
|
|
508 |
|
|
|
509 |
\small
|
|
|
510 |
|
|
|
511 |
\begin{center}
|
|
|
512 |
\begin{tabular}{@ {\hspace{-20mm}}lcl}
|
|
|
513 |
\bl{matches []$^*$ []} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
514 |
\bl{matches ([]$|$a)$^*$ a} & \bl{$\mapsto$} & \bl{true}\medskip\\
|
|
|
515 |
|
|
|
516 |
\bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
517 |
\bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
518 |
\bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\
|
|
|
519 |
\bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
520 |
\bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
|
|
|
521 |
|
|
|
522 |
\bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
523 |
\bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}\\
|
|
|
524 |
\bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}
|
|
|
525 |
\end{tabular}
|
|
|
526 |
\end{center}
|
|
|
527 |
|
|
|
528 |
|
|
|
529 |
\end{frame}}
|
|
|
530 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
531 |
*}
|
|
|
532 |
|
|
|
533 |
text_raw {*
|
|
|
534 |
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|
|
|
535 |
\mode<presentation>{
|
|
|
536 |
\begin{frame}<1->[t]
|
|
|
537 |
\frametitle{Specification}
|
|
|
538 |
|
|
|
539 |
We have to specify what it means for a regular expression to match
|
|
|
540 |
a string.
|
|
|
541 |
%
|
|
|
542 |
\only<2>{
|
|
|
543 |
\mbox{}\\[8mm]
|
|
|
544 |
\bl{(a$\cdot$b)$^*$}\\
|
|
|
545 |
\hspace{7mm}\bl{$\mapsto$\hspace{3mm}\{[], ab, abab, ababab, \ldots\}}\bigskip\\
|
|
|
546 |
\bl{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9 )$^*$}\\
|
|
|
547 |
\hspace{7mm}\bl{$\mapsto$\hspace{3mm}
|
|
|
548 |
\{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
|
|
|
549 |
%
|
|
|
550 |
\only<3->{
|
|
|
551 |
\begin{center}
|
|
|
552 |
\begin{tabular}{rcl}
|
|
|
553 |
\bl{\LL (NULL)} & \bl{$\dn$} & \bl{\{\}}\\
|
|
|
554 |
\bl{\LL (EMPTY)} & \bl{$\dn$} & \bl{\{[]\}}\\
|
|
|
555 |
\bl{\LL (CHR c)} & \bl{$\dn$} & \bl{\{c\}}\\
|
|
|
556 |
\bl{\LL (ALT r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<4->{\bl{\LL (r$_1$) $\cup$ \LL (r$_2$)}}\\
|
|
|
557 |
\bl{\LL (SEQ r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<6->{\bl{\LL (r$_1$) ; \LL (r$_2$)}}\\
|
|
|
558 |
\bl{\LL (STAR r)} & \bl{$\dn$} & \onslide<8->{\bl{(\LL (r))$^\star$}}\\
|
|
|
559 |
\end{tabular}
|
|
|
560 |
\end{center}}
|
|
|
561 |
|
|
|
562 |
\only<5-6>{
|
|
|
563 |
\begin{textblock}{6}(2.9,13.3)
|
|
|
564 |
\colorbox{cream}{\bl{S$_1$ ; S$_2$ $\;\dn\;$ \{ s$_1$@s$_2$ $|$ s$_1$$\in$S$_1$ $\wedge$
|
|
|
565 |
s$_2$$\in$S$_2$ \}}}
|
|
|
566 |
\end{textblock}}
|
|
|
567 |
|
|
|
568 |
\only<7->{
|
|
|
569 |
\begin{textblock}{9}(4,13)
|
|
|
570 |
\colorbox{cream}{\bl{$\infer{\mbox{[]} \in \mbox{S}^\star}{}$}}\hspace{3mm}
|
|
|
571 |
\colorbox{cream}{\bl{$\infer{\mbox{s}_1\mbox{@}\mbox{s}_2 \in \mbox{S}^\star}
|
|
|
572 |
{\mbox{s}_1 \in \mbox{S} & \mbox{s}_2 \in \mbox{S}^\star}$}}
|
|
|
573 |
\end{textblock}}
|
|
|
574 |
|
|
|
575 |
\end{frame}}
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|
576 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
577 |
*}
|
|
|
578 |
|
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|
579 |
text_raw {*
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|
580 |
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|
|
|
581 |
\mode<presentation>{
|
|
|
582 |
\begin{frame}<1->[t]
|
|
|
583 |
\frametitle{Is the Matcher Error-Free?}
|
|
|
584 |
|
|
|
585 |
We expect that
|
|
|
586 |
|
|
|
587 |
\begin{center}
|
|
|
588 |
\begin{tabular}{lcl}
|
|
|
589 |
\bl{matches r s = true} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}%
|
|
|
590 |
\only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\in$ \LL(r)}\\
|
|
|
591 |
\bl{matches r s = false} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}%
|
|
|
592 |
\only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\notin$ \LL(r)}\\
|
|
|
593 |
\end{tabular}
|
|
|
594 |
\end{center}
|
|
|
595 |
\pause\pause\bigskip
|
|
|
596 |
By \alert<4->{induction}, we can {\bf prove} these properties.\bigskip
|
|
|
597 |
|
|
|
598 |
\begin{tabular}{lrcl}
|
|
|
599 |
Lemmas: & \bl{nullable (r)} & \bl{$\Longleftrightarrow$} & \bl{[] $\in$ \LL (r)}\\
|
|
|
600 |
& \bl{s $\in$ \LL (der c r)} & \bl{$\Longleftrightarrow$} & \bl{(c::s) $\in$ \LL (r)}\\
|
|
|
601 |
\end{tabular}
|
|
|
602 |
|
|
|
603 |
\only<4->{
|
|
|
604 |
\begin{textblock}{3}(0.9,4.5)
|
|
|
605 |
\rd{\huge$\forall$\large{}r s.}
|
|
|
606 |
\end{textblock}}
|
|
|
607 |
\end{frame}}
|
|
|
608 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
609 |
*}
|
|
|
610 |
|
|
|
611 |
text_raw {*
|
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|
612 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
613 |
\mode<presentation>{
|
|
|
614 |
\begin{frame}<1->[t]
|
|
|
615 |
|
|
|
616 |
\mbox{}\\[-2mm]
|
|
|
617 |
|
|
|
618 |
\small
|
|
|
619 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
|
|
|
620 |
\bl{nullable (NULL)} & \bl{$=$} & \bl{false} &\\
|
|
|
621 |
\bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} &\\
|
|
|
622 |
\bl{nullable (CHR c)} & \bl{$=$} & \bl{false} &\\
|
|
|
623 |
\bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} & \\
|
|
|
624 |
\bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} & \\
|
|
|
625 |
\bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \\
|
|
|
626 |
\end{tabular}\medskip
|
|
|
627 |
|
|
|
628 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
|
|
|
629 |
\bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \\
|
|
|
630 |
\bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \\
|
|
|
631 |
\bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \\
|
|
|
632 |
\bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \\
|
|
|
633 |
\bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \\
|
|
|
634 |
& & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
|
|
|
635 |
\bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} &\smallskip\\
|
|
|
636 |
|
|
|
637 |
\bl{derivative r []} & \bl{$=$} & \bl{r} & \\
|
|
|
638 |
\bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \\
|
|
|
639 |
\end{tabular}\medskip
|
|
|
640 |
|
|
|
641 |
\bl{matches r s $=$ nullable (derivative r s)}
|
|
|
642 |
|
|
|
643 |
\only<2>{
|
|
|
644 |
\begin{textblock}{8}(1.5,4)
|
|
|
645 |
\includegraphics[scale=0.3]{approved.png}
|
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|
646 |
\end{textblock}}
|
|
|
647 |
|
|
|
648 |
|
|
|
649 |
\end{frame}}
|
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|
650 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
651 |
*}
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652 |
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653 |
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654 |
text_raw {*
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655 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
656 |
\mode<presentation>{
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|
657 |
\begin{frame}<1->[c]
|
|
|
658 |
\frametitle{Interlude: TCB}
|
|
|
659 |
|
|
|
660 |
\begin{itemize}
|
|
|
661 |
\item The \alert{\bf Trusted Code Base} (TCB) is the code that can make your
|
|
|
662 |
program behave in unintended ways (i.e.~cause bugs).\medskip
|
|
|
663 |
|
|
|
664 |
\item Typically the TCB includes: CPUs, operating systems, C-libraries,
|
|
|
665 |
device drivers, (J)VMs\ldots\bigskip
|
|
|
666 |
\pause
|
|
|
667 |
|
|
|
668 |
\item It also includes the compiler.
|
|
|
669 |
\end{itemize}
|
|
|
670 |
|
|
|
671 |
\end{frame}}
|
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|
672 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
673 |
*}
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|
674 |
|
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|
675 |
text_raw {*
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676 |
|
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|
677 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
678 |
\mode<presentation>{
|
|
|
679 |
\begin{frame}<1-3>
|
|
|
680 |
\frametitle{\LARGE\begin{tabular}{c}Hacking Compilers
|
|
|
681 |
\end{tabular}}
|
|
|
682 |
|
|
|
683 |
%Why is it so paramount to have a small trusted code base (TCB)?
|
|
|
684 |
\bigskip\bigskip
|
|
|
685 |
|
|
|
686 |
\begin{columns}
|
|
|
687 |
\begin{column}{2.7cm}
|
|
|
688 |
\begin{minipage}{2.5cm}%
|
|
|
689 |
\begin{tabular}{c@ {}}
|
|
|
690 |
\includegraphics[scale=0.2]{ken-thompson.jpg}\\[-1.8mm]
|
|
|
691 |
\footnotesize Ken Thompson\\[-1.8mm]
|
|
|
692 |
\footnotesize Turing Award, 1983\\
|
|
|
693 |
\end{tabular}
|
|
|
694 |
\end{minipage}
|
|
|
695 |
\end{column}
|
|
|
696 |
\begin{column}{9cm}
|
|
|
697 |
\begin{tabular}{l@ {\hspace{1mm}}p{8cm}}
|
|
|
698 |
\myitemi
|
|
|
699 |
& Ken Thompson showed how to hide a Trojan Horse in a
|
|
|
700 |
compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm]
|
|
|
701 |
\myitemi
|
|
|
702 |
& No amount of source level verification will protect
|
|
|
703 |
you from such Thompson-hacks.\\[2mm]
|
|
|
704 |
|
|
|
705 |
\myitemi
|
|
|
706 |
& Therefore in safety-critical systems it is important to rely
|
|
|
707 |
on only a very small TCB.
|
|
|
708 |
\end{tabular}
|
|
|
709 |
\end{column}
|
|
|
710 |
\end{columns}
|
|
|
711 |
|
|
|
712 |
\only<2>{
|
|
|
713 |
\begin{textblock}{6}(4,2)
|
|
|
714 |
\begin{tikzpicture}
|
|
|
715 |
\draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
|
716 |
{\normalsize
|
|
|
717 |
\begin{minipage}{8cm}
|
|
|
718 |
\begin{quote}
|
|
|
719 |
\includegraphics[scale=0.05]{evil.png}
|
|
|
720 |
\begin{enumerate}
|
|
|
721 |
\item[1)] Assume you ship the compiler as binary and also with sources.
|
|
|
722 |
\item[2)] Make the compiler aware when it compiles itself.
|
|
|
723 |
\item[3)] Add the Trojan horse.
|
|
|
724 |
\item[4)] Compile.
|
|
|
725 |
\item[5)] Delete Trojan horse from the sources of the compiler.
|
|
|
726 |
\item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{}
|
|
|
727 |
\end{enumerate}
|
|
|
728 |
\end{quote}
|
|
|
729 |
\end{minipage}};
|
|
|
730 |
\end{tikzpicture}
|
|
|
731 |
\end{textblock}}
|
|
|
732 |
|
|
|
733 |
\end{frame}}
|
|
|
734 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
735 |
|
|
|
736 |
*}
|
|
|
737 |
|
|
|
738 |
text_raw {*
|
|
|
739 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
740 |
\mode<presentation>{
|
|
|
741 |
\begin{frame}
|
|
|
742 |
\frametitle{\LARGE\begin{tabular}{c}An Example: Small TCB for\\[-2mm]
|
|
|
743 |
A Critical Infrastructure\end{tabular}}
|
|
|
744 |
\mbox{}\\[-14mm]\mbox{}
|
|
|
745 |
|
|
|
746 |
\begin{columns}
|
|
|
747 |
\begin{column}{0.2\textwidth}
|
|
|
748 |
\begin{tabular}{@ {} c@ {}}
|
|
|
749 |
\includegraphics[scale=0.3]{appel.jpg}\\[-2mm]
|
|
|
750 |
{\footnotesize Andrew Appel}\\[-2.5mm]
|
|
|
751 |
{\footnotesize (Princeton)}
|
|
|
752 |
\end{tabular}
|
|
|
753 |
\end{column}
|
|
|
754 |
|
|
|
755 |
\begin{column}{0.8\textwidth}
|
|
|
756 |
\begin{textblock}{10}(4.5,3.95)
|
|
|
757 |
\begin{block}{Proof-Carrying Code}
|
|
|
758 |
\begin{center}
|
|
|
759 |
\begin{tikzpicture}
|
|
|
760 |
\draw[help lines,cream] (0,0.2) grid (8,4);
|
|
|
761 |
|
|
|
762 |
\draw[line width=1mm, red] (5.5,0.6) rectangle (7.5,4);
|
|
|
763 |
\node[anchor=base] at (6.5,2.8)
|
|
|
764 |
{\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering user needs to run untrusted code\end{tabular}};
|
|
|
765 |
|
|
|
766 |
\draw[line width=1mm, red] (0.5,0.6) rectangle (2.5,4);
|
|
|
767 |
\node[anchor=base] at (1.5,2.3)
|
|
|
768 |
{\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering code developer/ web server/ Apple
|
|
|
769 |
Store\end{tabular}};
|
|
|
770 |
|
|
|
771 |
\onslide<4->{
|
|
|
772 |
\draw[line width=1mm, red, fill=red] (5.5,0.6) rectangle (7.5,1.8);
|
|
|
773 |
\node[anchor=base,white] at (6.5,1.1)
|
|
|
774 |
{\small\begin{tabular}{@ {}p{1.9cm}@ {}}\bf\centering proof- checker\end{tabular}};}
|
|
|
775 |
|
|
|
776 |
\node at (3.8,3.0) [single arrow, fill=red,text=white, minimum height=3cm]{\bf code};
|
|
|
777 |
\onslide<3->{
|
|
|
778 |
\node at (3.8,1.3) [single arrow, fill=red,text=white, minimum height=3cm]{\bf LF proof};
|
|
|
779 |
\node at (3.8,1.9) {\small certificate};
|
|
|
780 |
}
|
|
|
781 |
|
|
|
782 |
\onslide<2>{\node at (4.0,1.3) [text=red]{\begin{tabular}{c}\bf Highly\\\bf Dangerous!\end{tabular}};}
|
|
|
783 |
% Code Developer
|
|
|
784 |
% User (runs untrusted code)
|
|
|
785 |
% transmits a proof that the code is safe
|
|
|
786 |
%
|
|
|
787 |
\end{tikzpicture}
|
|
|
788 |
\end{center}
|
|
|
789 |
\end{block}
|
|
|
790 |
\end{textblock}
|
|
|
791 |
\end{column}
|
|
|
792 |
\end{columns}
|
|
|
793 |
|
|
|
794 |
\small\mbox{}\\[2.5cm]
|
|
|
795 |
\begin{itemize}
|
|
|
796 |
\item<4-> TCB of the checker is $\sim$2700 lines of code (1865 loc of\\ LF definitions;
|
|
|
797 |
803 loc in C including 2 library functions)\\[-3mm]
|
|
|
798 |
\item<5-> 167 loc in C implement a type-checker
|
|
|
799 |
\end{itemize}
|
|
|
800 |
|
|
|
801 |
\end{frame}}
|
|
|
802 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
803 |
|
|
|
804 |
*}
|
|
|
805 |
|
|
|
806 |
|
|
|
807 |
|
|
|
808 |
text {*
|
|
|
809 |
\tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex]
|
|
|
810 |
\tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick,
|
|
|
811 |
draw=black!50, top color=white, bottom color=black!20]
|
|
|
812 |
\tikzstyle{node2}=[rectangle, minimum size=12mm, rounded corners=3mm, very thick,
|
|
|
813 |
draw=red!70, top color=white, bottom color=red!50!black!20]
|
|
|
814 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
815 |
\mode<presentation>{
|
|
|
816 |
\begin{frame}[squeeze]
|
|
|
817 |
\frametitle{Type-Checking in LF}
|
|
|
818 |
|
|
|
819 |
\begin{columns}
|
|
|
820 |
\begin{column}{0.2\textwidth}
|
|
|
821 |
\begin{tabular}{@ {\hspace{-4mm}}c@ {}}
|
|
|
822 |
\\[-4mm]
|
|
|
823 |
\includegraphics[scale=0.1]{harper.jpg}\\[-2mm]
|
|
|
824 |
{\footnotesize Bob Harper}\\[-2.5mm]
|
|
|
825 |
{\footnotesize (CMU)}\\[2mm]
|
|
|
826 |
|
|
|
827 |
\includegraphics[scale=0.3]{pfenning.jpg}\\[-2mm]
|
|
|
828 |
{\footnotesize Frank Pfenning}\\[-2.5mm]
|
|
|
829 |
{\footnotesize (CMU)}\\[2mm]
|
|
|
830 |
|
|
|
831 |
\onslide<-6>{
|
|
|
832 |
{\footnotesize 31 pages in }\\[-2.5mm]
|
|
|
833 |
{\footnotesize ACM Transact.~on}\\[-2.5mm]
|
|
|
834 |
{\footnotesize Comp.~Logic.,~2005}\\}
|
|
|
835 |
\end{tabular}
|
|
|
836 |
\end{column}
|
|
|
837 |
|
|
|
838 |
\begin{column}{0.8\textwidth}
|
|
|
839 |
\begin{textblock}{0}(3.1,2)
|
|
|
840 |
|
|
|
841 |
\begin{tikzpicture}
|
|
|
842 |
\matrix[ampersand replacement=\&,column sep=7mm, row sep=5mm]
|
|
|
843 |
{ \&[-10mm]
|
|
|
844 |
\node (def1) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}}; \&
|
|
|
845 |
\node (proof1) [node1] {\large Proof}; \&
|
|
|
846 |
\node (alg1) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}}; \\
|
|
|
847 |
|
|
|
848 |
\onslide<4->{\node {\begin{tabular}{c}\small 1st\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
|
|
|
849 |
\onslide<4->{\node (def2) [node2] {\large Spec$^\text{+ex}$};} \&
|
|
|
850 |
\onslide<4->{\node (proof2) [node1] {\large Proof};} \&
|
|
|
851 |
\onslide<4->{\node (alg2) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\
|
|
|
852 |
|
|
|
853 |
\onslide<5->{\node {\begin{tabular}{c}\small 2nd\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
|
|
|
854 |
\onslide<5->{\node (def3) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \&
|
|
|
855 |
\onslide<5->{\node (proof3) [node1] {\large Proof};} \&
|
|
|
856 |
\onslide<5->{\node (alg3) [node2] {\large Alg$^\text{-ex}$};} \\
|
|
|
857 |
|
|
|
858 |
\onslide<6->{\node {\begin{tabular}{c}\small 3rd\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
|
|
|
859 |
\onslide<6->{\node (def4) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \&
|
|
|
860 |
\onslide<6->{\node (proof4) [node2] {\large\hspace{1mm}Proof\hspace{1mm}};} \&
|
|
|
861 |
\onslide<6->{\node (alg4) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\
|
|
|
862 |
};
|
|
|
863 |
|
|
|
864 |
\draw[->,black!50,line width=2mm] (proof1) -- (def1);
|
|
|
865 |
\draw[->,black!50,line width=2mm] (proof1) -- (alg1);
|
|
|
866 |
|
|
|
867 |
\onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (def2);}
|
|
|
868 |
\onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (alg2);}
|
|
|
869 |
|
|
|
870 |
\onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (def3);}
|
|
|
871 |
\onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (alg3);}
|
|
|
872 |
|
|
|
873 |
\onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (def4);}
|
|
|
874 |
\onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (alg4);}
|
|
|
875 |
|
|
|
876 |
\onslide<3->{\draw[white,line width=1mm] (1.1,3.2) -- (0.9,2.85) -- (1.1,2.35) -- (0.9,2.0);}
|
|
|
877 |
\end{tikzpicture}
|
|
|
878 |
|
|
|
879 |
\end{textblock}
|
|
|
880 |
\end{column}
|
|
|
881 |
\end{columns}
|
|
|
882 |
|
|
|
883 |
\only<2>{%
|
|
|
884 |
\begin{textblock}{2}(.1,12.85)
|
|
|
885 |
\begin{tikzpicture}
|
|
|
886 |
\draw[line width=1mm, red] (0,0) ellipse (1.5cm and 0.88cm);
|
|
|
887 |
\end{tikzpicture}
|
|
|
888 |
\end{textblock}
|
|
|
889 |
}
|
|
|
890 |
|
|
|
891 |
\begin{textblock}{3}(14,3.6)
|
|
|
892 |
\onslide<4->{
|
|
|
893 |
\begin{tikzpicture}
|
|
|
894 |
\node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{2h};
|
|
|
895 |
\end{tikzpicture}}
|
|
|
896 |
\end{textblock}
|
|
|
897 |
|
|
|
898 |
\only<7->{
|
|
|
899 |
\begin{textblock}{14}(0.6,12.8)
|
|
|
900 |
\begin{block}{}
|
|
|
901 |
\small Each time one needs to check $\sim$31pp~of informal paper proofs.
|
|
|
902 |
You have to be able to keep definitions and proofs consistent.
|
|
|
903 |
\end{block}
|
|
|
904 |
\end{textblock}}
|
|
|
905 |
|
|
|
906 |
\end{frame}}
|
|
|
907 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
908 |
|
|
|
909 |
*}
|
|
|
910 |
|
|
|
911 |
text_raw {*
|
|
|
912 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
913 |
\mode<presentation>{
|
|
|
914 |
\begin{frame}<1>[c]
|
|
|
915 |
\frametitle{Theorem Provers}
|
|
|
916 |
|
|
|
917 |
\begin{itemize}
|
|
|
918 |
\item Theorem provers help with keeping large proofs consistent;
|
|
|
919 |
make them modifiable.\medskip
|
|
|
920 |
|
|
|
921 |
\item They can ensure that all cases are covered.\medskip
|
|
|
922 |
|
|
|
923 |
\item Sometimes, tedious reasoning can be automated.
|
|
|
924 |
\end{itemize}
|
|
|
925 |
|
|
|
926 |
\end{frame}}
|
|
|
927 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
928 |
*}
|
|
|
929 |
|
|
|
930 |
text_raw {*
|
|
|
931 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
932 |
\mode<presentation>{
|
|
|
933 |
\begin{frame}<1>[c]
|
|
|
934 |
\frametitle{Theorem Provers}
|
|
|
935 |
|
|
|
936 |
\begin{itemize}
|
|
|
937 |
\item You also pay a (sometimes heavy) price: reasoning can be much, much harder.\medskip
|
|
|
938 |
|
|
|
939 |
\item Depending on your domain, suitable reasoning infrastructure
|
|
|
940 |
might not yet be available.
|
|
|
941 |
\end{itemize}
|
|
|
942 |
|
|
|
943 |
\end{frame}}
|
|
|
944 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
945 |
*}
|
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|
946 |
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947 |
text_raw {*
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|
948 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
949 |
\mode<presentation>{
|
|
|
950 |
\begin{frame}<1>[c]
|
|
|
951 |
\frametitle{Theorem Provers}
|
|
|
952 |
|
|
|
953 |
Recently impressive work has been accomplished proving the correctness
|
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|
954 |
|
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|
955 |
\begin{itemize}
|
|
|
956 |
\item of a compiler for C-light (compiled code has the same observable
|
|
|
957 |
behaviour as the original source code),\medskip
|
|
|
958 |
|
|
|
959 |
\item a mirco-kernel operating system (absence of certain
|
|
|
960 |
bugs\ldots no nil pointers, no buffer overflows).
|
|
|
961 |
\end{itemize}
|
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|
962 |
|
|
|
963 |
\end{frame}}
|
|
|
964 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
965 |
*}
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|
966 |
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967 |
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|
968 |
text_raw {*
|
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|
969 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
970 |
\mode<presentation>{
|
|
|
971 |
\begin{frame}<1>[c]
|
|
|
972 |
\frametitle{Trust in Theorem Provers}
|
|
|
973 |
|
|
|
974 |
\begin{center}
|
|
|
975 |
Why should we trust theorem provers?
|
|
|
976 |
\end{center}
|
|
|
977 |
|
|
|
978 |
\end{frame}}
|
|
|
979 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
980 |
*}
|
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|
981 |
|
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|
982 |
text_raw {*
|
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|
983 |
|
|
|
984 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
985 |
\mode<presentation>{
|
|
|
986 |
\begin{frame}
|
|
|
987 |
\frametitle{Theorem Provers}
|
|
|
988 |
|
|
|
989 |
\begin{itemize}
|
|
|
990 |
\item Theorem provers are a \textcolor{red}{special kind} of software.
|
|
|
991 |
|
|
|
992 |
\item We do \textcolor{red}{\bf not} need to trust them; we only need to trust:
|
|
|
993 |
\end{itemize}
|
|
|
994 |
|
|
|
995 |
\begin{quote}
|
|
|
996 |
\begin{itemize}
|
|
|
997 |
\item The logic they are based on \textcolor{gray}{(e.g.~HOL)}, and\smallskip
|
|
|
998 |
\item a proof checker that checks the proofs
|
|
|
999 |
\textcolor{gray}{(this can be a very small program)}.\smallskip\pause
|
|
|
1000 |
\item To a little extend, we also need to trust our definitions
|
|
|
1001 |
\textcolor{gray}{(this can be mitigated)}.
|
|
|
1002 |
\end{itemize}
|
|
|
1003 |
\end{quote}
|
|
|
1004 |
|
|
|
1005 |
\end{frame}}
|
|
|
1006 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1007 |
|
|
|
1008 |
*}
|
|
|
1009 |
|
|
|
1010 |
text_raw {*
|
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|
1011 |
|
|
|
1012 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1013 |
\mode<presentation>{
|
|
|
1014 |
\begin{frame}
|
|
|
1015 |
\frametitle{Isabelle}
|
|
|
1016 |
|
|
|
1017 |
\begin{itemize}
|
|
|
1018 |
\item I am using the Isabelle theorem prover (development since 1990).\bigskip\bigskip\bigskip
|
|
|
1019 |
|
|
|
1020 |
\item It follows the LCF-approach:
|
|
|
1021 |
|
|
|
1022 |
\begin{itemize}
|
|
|
1023 |
\item Have a special abstract type \alert{\bf thm}.
|
|
|
1024 |
\item Make the constructors of this abstract type the inference rules
|
|
|
1025 |
of your logic.
|
|
|
1026 |
\item Implement the theorem prover in a strongly-typed language (e.g.~ML).
|
|
|
1027 |
\end{itemize}
|
|
|
1028 |
|
|
|
1029 |
$\Rightarrow$ everything of type {\bf thm} has been proved (even if we do not
|
|
|
1030 |
have to explicitly generate proofs).
|
|
|
1031 |
\end{itemize}
|
|
|
1032 |
|
|
|
1033 |
\only<1>{
|
|
|
1034 |
\begin{textblock}{5}(11,2.3)
|
|
|
1035 |
\begin{center}
|
|
|
1036 |
\includegraphics[scale=0.18]{robin-milner.jpg}\\[-0.8mm]
|
|
|
1037 |
\footnotesize Robin Milner\\[-0.8mm]
|
|
|
1038 |
\footnotesize Turing Award, 1991\\
|
|
|
1039 |
\end{center}
|
|
|
1040 |
\end{textblock}}
|
|
|
1041 |
|
|
|
1042 |
|
|
|
1043 |
\end{frame}}
|
|
|
1044 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1045 |
*}
|
|
|
1046 |
|
|
|
1047 |
text_raw {*
|
|
|
1048 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1049 |
\mode<presentation>{
|
|
|
1050 |
\begin{frame}<1>[c]
|
|
|
1051 |
\frametitle{
|
|
|
1052 |
\begin{tabular}{c}
|
|
|
1053 |
\mbox{}\\[23mm]
|
|
|
1054 |
\LARGE Demo
|
|
|
1055 |
\end{tabular}}
|
|
|
1056 |
|
|
|
1057 |
\end{frame}}
|
|
|
1058 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1059 |
*}
|
|
|
1060 |
|
|
|
1061 |
|
|
|
1062 |
text_raw {*
|
|
|
1063 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1064 |
\mode<presentation>{
|
|
|
1065 |
\begin{frame}<1->[c]
|
|
|
1066 |
\frametitle{Future Research}
|
|
|
1067 |
|
|
|
1068 |
\begin{itemize}
|
|
|
1069 |
\item Make theorem provers more like a programming environment.\medskip\pause
|
|
|
1070 |
|
|
|
1071 |
\item Use all the computational power we get from the hardware to
|
|
|
1072 |
automate reasoning (GPUs).\medskip\pause
|
|
|
1073 |
|
|
|
1074 |
\item Provide a comprehensive reasoning infrastructure for many domains and
|
|
|
1075 |
design automated decision procedures.
|
|
|
1076 |
\end{itemize}\pause
|
|
|
1077 |
|
|
|
1078 |
|
|
|
1079 |
\begin{center}
|
|
|
1080 |
\colorbox{cream}{
|
|
|
1081 |
\begin{minipage}{10cm}
|
|
|
1082 |
\color{gray}
|
|
|
1083 |
\small
|
|
|
1084 |
``Formal methods will never have a significant impact until
|
|
|
1085 |
they can be used by people that don't understand them.''\smallskip\\
|
|
|
1086 |
\mbox{}\footnotesize\hfill attributed to Tom Melham
|
|
|
1087 |
\end{minipage}}
|
|
|
1088 |
\end{center}
|
|
|
1089 |
|
|
|
1090 |
\end{frame}}
|
|
|
1091 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1092 |
*}
|
|
|
1093 |
|
|
|
1094 |
text_raw {*
|
|
|
1095 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1096 |
\mode<presentation>{
|
|
|
1097 |
\begin{frame}<1->[c]
|
|
|
1098 |
\frametitle{Conclusion}
|
|
|
1099 |
|
|
|
1100 |
\begin{itemize}
|
|
|
1101 |
\item The plan is to make this kind of programming the ``future''.\medskip\pause
|
|
|
1102 |
|
|
|
1103 |
\item Though the technology is already there\\ (compiler + micro-kernel os).\medskip\pause
|
|
|
1104 |
|
|
|
1105 |
\item Logic and reasoning (especially induction) are important skills for
|
|
|
1106 |
Computer Scientists.
|
|
|
1107 |
\end{itemize}
|
|
|
1108 |
|
|
|
1109 |
\end{frame}}
|
|
|
1110 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1111 |
*}
|
|
|
1112 |
|
|
|
1113 |
|
|
|
1114 |
text_raw {*
|
|
|
1115 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1116 |
\mode<presentation>{
|
|
|
1117 |
\begin{frame}<1>[c]
|
|
|
1118 |
\frametitle{
|
|
|
1119 |
\begin{tabular}{c}
|
|
|
1120 |
\mbox{}\\[23mm]
|
|
|
1121 |
\alert{\LARGE Thank you very much!}\\
|
|
|
1122 |
\alert{\Large Questions?}
|
|
|
1123 |
\end{tabular}}
|
|
|
1124 |
|
|
|
1125 |
\end{frame}}
|
|
|
1126 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
1127 |
*}
|
|
|
1128 |
|
|
|
1129 |
|
|
|
1130 |
|
|
|
1131 |
(*<*)
|
|
|
1132 |
end
|
|
|
1133 |
(*>*) |