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1 (*<*) |
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2 theory Slides6 |
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3 imports "~~/src/HOL/Library/LaTeXsugar" "Nominal" |
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4 begin |
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5 |
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6 declare [[show_question_marks = false]] |
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7 |
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8 notation (latex output) |
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9 set ("_") and |
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10 Cons ("_::/_" [66,65] 65) |
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11 |
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12 (*>*) |
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13 |
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14 text_raw {* |
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15 \renewcommand{\slidecaption}{Shanghai, 12.~April 2011} |
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16 |
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17 \newcommand{\abst}[2]{#1.#2}% atom-abstraction |
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18 \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing |
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19 \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions |
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20 \newcommand{\unit}{\langle\rangle}% unit |
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21 \newcommand{\app}[2]{#1\,#2}% application |
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22 \newcommand{\eqprob}{\mathrel{{\approx}?}} |
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23 \newcommand{\freshprob}{\mathrel{\#?}} |
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24 \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction |
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25 \newcommand{\id}{\varepsilon}% identity substitution |
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26 |
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27 \newcommand{\bl}[1]{\textcolor{blue}{#1}} |
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28 \newcommand{\gr}[1]{\textcolor{gray}{#1}} |
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29 \newcommand{\rd}[1]{\textcolor{red}{#1}} |
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30 |
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31 \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}} |
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32 \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}} |
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33 \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}} |
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34 |
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35 \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont} |
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36 \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont} |
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37 \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont} |
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38 \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont} |
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39 |
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40 \newcommand{\LL}{$\mathbb{L}\,$} |
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41 |
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42 |
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43 \pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}% |
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44 {rgb(0mm)=(0,0,0.9); |
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45 rgb(0.9mm)=(0,0,0.7); |
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46 rgb(1.3mm)=(0,0,0.5); |
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47 rgb(1.4mm)=(1,1,1)} |
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48 |
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49 \def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex} |
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50 \usebeamercolor[fg]{subitem projected} |
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51 {\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}} |
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52 \pgftext{% |
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53 \usebeamerfont*{subitem projected}} |
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54 \end{pgfpicture}} |
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55 |
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56 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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57 \mode<presentation>{ |
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58 \begin{frame}<1>[t] |
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59 \frametitle{% |
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60 \begin{tabular}{@ {\hspace{-3mm}}c@ {}} |
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61 \\ |
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62 \LARGE Verifying a Regular Expression\\[-1mm] |
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63 \LARGE Matcher and Formal Language\\[-1mm] |
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64 \LARGE Theory\\[5mm] |
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65 \end{tabular}} |
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66 \begin{center} |
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67 Christian Urban\\ |
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68 \small Technical University of Munich, Germany |
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69 \end{center} |
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70 |
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71 |
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72 \begin{center} |
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73 \small joint work with Chunhan Wu and Xingyuan Zhang from the PLA |
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74 University of Science and Technology in Nanjing |
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75 \end{center} |
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76 \end{frame}} |
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77 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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78 |
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79 *} |
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80 text_raw {* |
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81 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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82 \mode<presentation>{ |
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83 \begin{frame}<1->[c] |
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84 \frametitle{My Background} |
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85 |
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86 \begin{itemize} |
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87 \item researcher in Theoretical Computer Science\medskip |
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88 |
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89 \item programmer on a \alert<2->{software system} with 800 kloc (though I am |
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90 responsible only for 35 kloc) |
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91 \end{itemize} |
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92 |
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93 \only<2->{ |
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94 \begin{textblock}{6}(2,11) |
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95 \begin{tikzpicture} |
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96 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
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97 {\color{darkgray} |
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98 \begin{minipage}{4cm}\raggedright |
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99 A theorem prover called {\bf Isabelle}. |
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100 \end{minipage}}; |
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101 \end{tikzpicture} |
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102 \end{textblock}} |
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103 |
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104 |
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105 \only<3>{ |
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106 \begin{textblock}{6}(9,11) |
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107 \begin{tikzpicture} |
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108 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
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109 {\color{darkgray} |
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110 \begin{minipage}{4cm}\raggedright |
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111 Like every other code, this code is very hard to |
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112 get correct. |
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113 \end{minipage}}; |
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114 \end{tikzpicture} |
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115 \end{textblock}} |
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116 |
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117 \end{frame}} |
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118 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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119 *} |
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120 |
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121 text_raw {* |
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122 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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123 \mode<presentation>{ |
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124 \begin{frame}<1->[t] |
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125 \frametitle{Regular Expressions} |
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126 |
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127 An example many (should) know about:\\ |
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128 \rd{\bf Regular Expressions:} |
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129 |
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130 \only<2>{ |
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131 \begin{center} |
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132 \bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$ r$_1$$|$r$_2$ $\;\;\;|\;\;\;$ |
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133 r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$} |
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134 \end{center}} |
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135 \only<3->{ |
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136 \begin{center} |
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137 \begin{tabular}{@ {}rrll@ {}} |
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138 \bl{r} & \bl{$::=$} & \bl{NULL} & \gr{(matches no string)}\\ |
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139 & \bl{$\mid$} & \bl{EMPTY} & \gr{(matches the empty string, [])}\\ |
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140 & \bl{$\mid$} & \bl{CHR c} & \gr{(matches the character c)}\\ |
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141 & \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\ |
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142 & \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\ |
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143 & \bl{$\mid$} & \bl{STAR r} & \gr{(repeat, r$^*$)}\\ |
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144 \end{tabular} |
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145 \end{center}\medskip} |
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146 |
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147 \small |
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148 \begin{textblock}{14.5}(1,12.5) |
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149 \only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\} |
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150 \only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} |
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151 \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}} |
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152 \end{textblock} |
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153 \end{frame}} |
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154 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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155 *} |
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156 |
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157 text_raw {* |
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158 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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159 \mode<presentation>{ |
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160 \begin{frame}<1>[c] |
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161 \frametitle{RegExp Matcher} |
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162 |
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163 Let's implement a regular expression matcher:\bigskip |
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164 |
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165 \begin{center} |
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166 \begin{tikzpicture} |
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167 %%\draw[help lines, black] (-3,0) grid (6,3); |
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168 |
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169 \draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3); |
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170 \node[anchor=base] at (2,1) |
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171 {\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\ |
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172 \Large\bf Expression \\ |
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173 \Large\bf Matcher\end{tabular}}; |
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174 |
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175 \coordinate (m1) at (0,1.5); |
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176 \draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}}; |
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177 \path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1); |
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178 |
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179 \coordinate (s1) at (0,0.5); |
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180 \draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}}; |
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181 \path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1); |
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182 |
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183 \coordinate (r1) at (4,1.2); |
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184 \draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}}; |
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185 \path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2); |
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186 |
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187 \end{tikzpicture} |
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188 \end{center} |
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189 |
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190 |
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191 \end{frame}} |
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192 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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193 *} |
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194 |
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195 text_raw {* |
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196 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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197 \mode<presentation>{ |
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198 \begin{frame}<1->[t] |
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199 \frametitle{RegExp Matcher} |
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200 \small |
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201 |
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202 {\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false |
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203 |
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204 \only<2->{ |
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205 \begin{center} |
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206 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
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207 \bl{match [] []} & \bl{$=$} & \bl{true}\\ |
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208 \bl{match [] \_} & \bl{$=$} & \bl{false}\\ |
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209 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\ |
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210 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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211 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\ |
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212 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\ |
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213 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\ |
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214 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
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215 \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\ |
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216 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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217 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
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218 \end{tabular} |
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219 \end{center}} |
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220 |
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221 \onslide<3->{we start the program with\\ |
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222 \hspace{6mm}\bl{matches r s $=$ match [r] s}} |
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223 |
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224 \end{frame}} |
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225 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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226 *} |
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227 |
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228 |
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229 text_raw {* |
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230 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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231 \mode<presentation>{ |
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232 \begin{frame}<1>[c] |
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233 \frametitle{Program in Scala} |
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234 |
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235 \bl{\footnotesize |
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236 \begin{tabular}{l} |
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237 sealed abstract class Rexp\\ |
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238 sealed case class Null extends Rexp\\ |
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239 sealed case class Empty extends Rexp\\ |
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240 sealed case class Chr(c: Char) extends Rexp\\ |
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241 sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\ |
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242 sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\ |
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243 sealed case class Star(r : Rexp) extends Rexp\medskip\\ |
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244 def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\ |
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245 \hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\ |
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246 \hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\ |
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247 \hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\ |
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248 \hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\ |
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249 \hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\ |
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250 \hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\ |
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251 \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\ |
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252 \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\ |
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253 \hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\ |
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254 \} |
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255 \end{tabular}} |
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256 |
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257 \end{frame}} |
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258 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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259 *} |
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260 |
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261 |
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262 text_raw {* |
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263 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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264 \mode<presentation>{ |
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265 \begin{frame}<1->[c] |
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266 \frametitle{Testing} |
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267 |
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268 \small |
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269 Every good programmer should do thourough tests: |
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270 |
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271 |
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272 \begin{center} |
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273 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
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274 \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\ |
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275 \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\ |
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276 \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\ |
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277 \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ |
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278 \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\ |
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279 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}}\\ |
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280 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}}\\ |
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281 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}} |
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282 \end{tabular} |
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283 \end{center} |
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284 |
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285 \onslide<3-> |
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286 {looks OK \ldots let's ship it to customers\hspace{5mm} |
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287 \raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}} |
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288 |
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289 \end{frame}} |
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290 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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291 *} |
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292 |
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293 text_raw {* |
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294 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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295 \mode<presentation>{ |
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296 \begin{frame}<1->[t] |
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297 \frametitle{Testing} |
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298 |
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299 \begin{itemize} |
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300 \item While testing is an important part in the process of programming development\pause |
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301 |
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302 \item we can only test a {\bf finite} amount of examples\bigskip\pause |
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303 |
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304 \begin{center} |
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305 \colorbox{cream} |
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306 {\gr{\begin{minipage}{10cm} |
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307 ``Testing can only show the presence of errors, never their |
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308 absence'' (Edsger W.~Dijkstra) |
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309 \end{minipage}}} |
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310 \end{center}\bigskip\pause |
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311 |
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312 \item In a theorem prover we can establish properties that apply to |
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313 {\bf all} input and {\bf all} output.\pause |
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314 |
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315 \item For example we can establish that the matcher terminates |
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316 on all input. |
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317 \end{itemize} |
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318 |
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319 \end{frame}} |
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320 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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321 *} |
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322 |
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323 text_raw {* |
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324 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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325 \mode<presentation>{ |
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326 \begin{frame}<1->[t] |
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327 \frametitle{RegExp Matcher} |
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328 |
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329 \small |
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330 We need to find a measure that gets smaller in each recursive call.\bigskip |
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331 |
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332 \onslide<1->{ |
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333 \begin{center} |
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334 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}} |
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335 \bl{match [] []} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
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336 \bl{match [] \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
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337 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
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338 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\ |
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339 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\ |
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340 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
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341 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\ |
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342 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
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343 \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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344 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\ |
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345 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
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346 \end{tabular} |
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347 \end{center}} |
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348 |
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349 |
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350 \begin{textblock}{5}(4,4) |
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351 \begin{tikzpicture} |
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352 %%\draw[help lines, black] (-3,0) grid (6,3); |
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353 |
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354 \coordinate (m1) at (-2,0); |
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355 \coordinate (m2) at ( 2,0); |
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356 \path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2); |
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357 \draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}}; |
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358 \end{tikzpicture} |
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359 \end{textblock} |
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360 |
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361 |
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362 \end{frame}} |
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363 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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364 *} |
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365 |
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366 text_raw {* |
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367 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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368 \mode<presentation>{ |
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369 \begin{frame}<1->[c] |
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370 \frametitle{Bug Hunting} |
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371 |
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372 \only<1>{Several hours later\ldots}\pause |
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373 |
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374 |
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375 \begin{center} |
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376 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
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377 \bl{matches (STAR (EMPTY)) s} & \bl{$\mapsto$} & loops\\ |
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378 \onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s} & \bl{$\mapsto$} & loops\\} |
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379 \end{tabular} |
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380 \end{center} |
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381 |
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382 \small |
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383 \onslide<3->{ |
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384 \begin{center} |
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385 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
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386 \ldots\\ |
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387 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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388 \ldots\\ |
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389 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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390 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
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391 \end{tabular} |
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392 \end{center}} |
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393 |
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394 |
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395 \end{frame}} |
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396 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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397 *} |
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398 |
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399 text_raw {* |
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400 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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401 \mode<presentation>{ |
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402 \begin{frame}<1->[c] |
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403 \frametitle{RegExp Matcher} |
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404 \small |
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405 |
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406 \begin{center} |
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407 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
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408 \bl{match [] []} & \bl{$=$} & \bl{true}\\ |
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409 \bl{match [] \_} & \bl{$=$} & \bl{false}\\ |
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410 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\ |
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411 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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412 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\ |
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413 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\ |
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414 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\ |
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415 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
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416 \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\ |
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417 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
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418 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
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419 \end{tabular} |
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420 \end{center} |
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421 |
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422 \only<1>{ |
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423 \begin{textblock}{5}(4,4) |
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424 \largenotok |
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425 \end{textblock}} |
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426 |
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427 \end{frame}} |
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428 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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429 *} |
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430 |
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431 |
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432 |
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433 text_raw {* |
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434 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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435 \mode<presentation>{ |
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436 \begin{frame}<1->[t] |
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437 \frametitle{Second Attempt} |
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438 |
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439 Can a regular expression match the empty string? |
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440 |
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441 \small |
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442 \begin{center} |
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443 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}} |
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444 \bl{nullable (NULL)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
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445 \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
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446 \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
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447 \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} |
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448 & \onslide<2->{\ok}\\ |
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449 \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} |
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450 & \onslide<2->{\ok}\\ |
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451 \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
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452 \end{tabular} |
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453 \end{center} |
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454 |
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455 \end{frame}} |
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456 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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457 *} |
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458 |
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459 |
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460 text_raw {* |
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461 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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462 \mode<presentation>{ |
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463 \begin{frame}<1->[t] |
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464 \frametitle{RegExp Matcher 2} |
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465 |
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466 If \bl{r} matches \bl{c::s}, which regular expression can match the string \bl{s}? |
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467 |
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468 \small |
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469 \begin{center} |
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470 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}} |
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471 \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\ |
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472 \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\ |
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473 \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \onslide<3->{\ok}\\ |
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474 \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \onslide<3->{\ok}\\ |
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475 \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \onslide<3->{\ok}\\ |
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476 & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\ |
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477 \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} & \onslide<3->{\ok}\medskip\\ |
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478 \pause |
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479 |
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480 \bl{derivative r []} & \bl{$=$} & \bl{r} & \onslide<3->{\ok}\\ |
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481 \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \onslide<3->{\ok}\\ |
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482 \end{tabular} |
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483 \end{center} |
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484 |
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485 we call the program with\\ |
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486 \bl{matches r s $=$ nullable (derivative r s)} |
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487 |
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488 |
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489 \end{frame}} |
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490 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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491 *} |
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492 |
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493 text_raw {* |
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494 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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495 \mode<presentation>{ |
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496 \begin{frame}<1->[c] |
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497 \frametitle{But Now What?} |
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498 |
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499 \begin{center} |
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500 {\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}} |
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501 \end{center} |
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502 |
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503 \end{frame}} |
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504 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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505 *} |
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506 |
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507 text_raw {* |
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508 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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509 \mode<presentation>{ |
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510 \begin{frame}<1->[c] |
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511 \frametitle{Testing} |
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512 |
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513 \small |
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514 |
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515 \begin{center} |
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516 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
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517 \bl{matches []$^*$ []} & \bl{$\mapsto$} & \bl{true}\\ |
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518 \bl{matches ([]$|$a)$^*$ a} & \bl{$\mapsto$} & \bl{true}\medskip\\ |
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519 |
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520 \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\ |
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521 \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\ |
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522 \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\ |
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523 \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ |
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524 \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\ |
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525 |
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526 \bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}\\ |
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527 \bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}\\ |
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528 \bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false} |
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529 \end{tabular} |
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530 \end{center} |
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531 |
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532 |
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533 \end{frame}} |
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534 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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535 *} |
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536 |
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537 text_raw {* |
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538 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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539 \mode<presentation>{ |
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540 \begin{frame}<1->[t] |
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541 \frametitle{Specification} |
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542 |
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543 We have to specify what it means for a regular expression to match |
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544 a string. |
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545 % |
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546 \only<2>{ |
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547 \mbox{}\\[8mm] |
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548 \bl{(a$\cdot$b)$^*$}\\ |
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549 \hspace{7mm}\bl{$\mapsto$\hspace{3mm}\{[], ab, abab, ababab, \ldots\}}\bigskip\\ |
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550 \bl{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9 )$^*$}\\ |
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551 \hspace{7mm}\bl{$\mapsto$\hspace{3mm} |
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552 \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}} |
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553 % |
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554 \only<3->{ |
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555 \begin{center} |
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556 \begin{tabular}{rcl} |
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557 \bl{\LL (NULL)} & \bl{$\dn$} & \bl{\{\}}\\ |
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558 \bl{\LL (EMPTY)} & \bl{$\dn$} & \bl{\{[]\}}\\ |
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559 \bl{\LL (CHR c)} & \bl{$\dn$} & \bl{\{c\}}\\ |
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560 \bl{\LL (ALT r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<4->{\bl{\LL (r$_1$) $\cup$ \LL (r$_2$)}}\\ |
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561 \bl{\LL (SEQ r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<6->{\bl{\LL (r$_1$) ; \LL (r$_2$)}}\\ |
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562 \bl{\LL (STAR r)} & \bl{$\dn$} & \onslide<8->{\bl{(\LL (r))$^\star$}}\\ |
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563 \end{tabular} |
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564 \end{center}} |
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565 |
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566 \only<5-6>{ |
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567 \begin{textblock}{6}(2.9,13.3) |
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568 \colorbox{cream}{\bl{S$_1$ ; S$_2$ $\;\dn\;$ \{ s$_1$@s$_2$ $|$ s$_1$$\in$S$_1$ $\wedge$ |
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569 s$_2$$\in$S$_2$ \}}} |
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570 \end{textblock}} |
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571 |
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572 \only<7->{ |
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573 \begin{textblock}{9}(4,13) |
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574 \colorbox{cream}{\bl{$\infer{\mbox{[]} \in \mbox{S}^\star}{}$}}\hspace{3mm} |
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575 \colorbox{cream}{\bl{$\infer{\mbox{s}_1\mbox{@}\mbox{s}_2 \in \mbox{S}^\star} |
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576 {\mbox{s}_1 \in \mbox{S} & \mbox{s}_2 \in \mbox{S}^\star}$}} |
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577 \end{textblock}} |
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578 |
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579 \end{frame}} |
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580 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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581 *} |
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582 |
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583 text_raw {* |
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584 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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585 \mode<presentation>{ |
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586 \begin{frame}<1->[t] |
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587 \frametitle{Is the Matcher Error-Free?} |
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588 |
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589 We expect that |
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590 |
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591 \begin{center} |
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592 \begin{tabular}{lcl} |
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593 \bl{matches r s = true} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}% |
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594 \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\in$ \LL(r)}\\ |
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595 \bl{matches r s = false} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}% |
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596 \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\notin$ \LL(r)}\\ |
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597 \end{tabular} |
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598 \end{center} |
|
599 \pause\pause\bigskip |
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600 By \alert<4->{induction}, we can {\bf prove} these properties.\bigskip |
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601 |
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602 \begin{tabular}{lrcl} |
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603 Lemmas: & \bl{nullable (r)} & \bl{$\Longleftrightarrow$} & \bl{[] $\in$ \LL (r)}\\ |
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604 & \bl{s $\in$ \LL (der c r)} & \bl{$\Longleftrightarrow$} & \bl{(c::s) $\in$ \LL (r)}\\ |
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605 \end{tabular} |
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606 |
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607 \only<4->{ |
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608 \begin{textblock}{3}(0.9,4.5) |
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609 \rd{\huge$\forall$\large{}r s.} |
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610 \end{textblock}} |
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611 \end{frame}} |
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612 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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613 *} |
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614 |
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615 text_raw {* |
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616 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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617 \mode<presentation>{ |
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618 \begin{frame}<1->[t] |
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619 |
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620 \mbox{}\\[-2mm] |
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621 |
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622 \small |
|
623 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}} |
|
624 \bl{nullable (NULL)} & \bl{$=$} & \bl{false} &\\ |
|
625 \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} &\\ |
|
626 \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} &\\ |
|
627 \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} & \\ |
|
628 \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} & \\ |
|
629 \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \\ |
|
630 \end{tabular}\medskip |
|
631 |
|
632 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}} |
|
633 \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \\ |
|
634 \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \\ |
|
635 \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \\ |
|
636 \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \\ |
|
637 \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \\ |
|
638 & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\ |
|
639 \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} &\smallskip\\ |
|
640 |
|
641 \bl{derivative r []} & \bl{$=$} & \bl{r} & \\ |
|
642 \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \\ |
|
643 \end{tabular}\medskip |
|
644 |
|
645 \bl{matches r s $=$ nullable (derivative r s)} |
|
646 |
|
647 \only<2>{ |
|
648 \begin{textblock}{8}(1.5,4) |
|
649 \includegraphics[scale=0.3]{approved.png} |
|
650 \end{textblock}} |
|
651 |
|
652 |
|
653 \end{frame}} |
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654 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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655 *} |
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656 |
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657 |
|
658 text_raw {* |
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659 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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660 \mode<presentation>{ |
|
661 \begin{frame}<1->[c] |
|
662 \frametitle{Interlude: TCB} |
|
663 |
|
664 \begin{itemize} |
|
665 \item The \alert{\bf Trusted Code Base} (TCB) is the code that can make your |
|
666 program behave in unintended ways (i.e.~cause bugs).\medskip |
|
667 |
|
668 \item Typically the TCB includes: CPUs, operating systems, C-libraries, |
|
669 device drivers, (J)VMs\ldots\bigskip |
|
670 \pause |
|
671 |
|
672 \item It also includes the compiler. |
|
673 \end{itemize} |
|
674 |
|
675 \end{frame}} |
|
676 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
677 *} |
|
678 |
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679 text_raw {* |
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680 |
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681 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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682 \mode<presentation>{ |
|
683 \begin{frame}<1-3> |
|
684 \frametitle{\LARGE\begin{tabular}{c}Hacking Compilers |
|
685 \end{tabular}} |
|
686 |
|
687 %Why is it so paramount to have a small trusted code base (TCB)? |
|
688 \bigskip\bigskip |
|
689 |
|
690 \begin{columns} |
|
691 \begin{column}{2.7cm} |
|
692 \begin{minipage}{2.5cm}% |
|
693 \begin{tabular}{c@ {}} |
|
694 \includegraphics[scale=0.2]{ken-thompson.jpg}\\[-1.8mm] |
|
695 \footnotesize Ken Thompson\\[-1.8mm] |
|
696 \footnotesize Turing Award, 1983\\ |
|
697 \end{tabular} |
|
698 \end{minipage} |
|
699 \end{column} |
|
700 \begin{column}{9cm} |
|
701 \begin{tabular}{l@ {\hspace{1mm}}p{8cm}} |
|
702 \myitemi |
|
703 & Ken Thompson showed how to hide a Trojan Horse in a |
|
704 compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm] |
|
705 \myitemi |
|
706 & No amount of source level verification will protect |
|
707 you from such Thompson-hacks.\\[2mm] |
|
708 |
|
709 \myitemi |
|
710 & Therefore in safety-critical systems it is important to rely |
|
711 on only a very small TCB. |
|
712 \end{tabular} |
|
713 \end{column} |
|
714 \end{columns} |
|
715 |
|
716 \only<2>{ |
|
717 \begin{textblock}{6}(4,2) |
|
718 \begin{tikzpicture} |
|
719 \draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
|
720 {\normalsize |
|
721 \begin{minipage}{8cm} |
|
722 \begin{quote} |
|
723 \includegraphics[scale=0.05]{evil.png} |
|
724 \begin{enumerate} |
|
725 \item[1)] Assume you ship the compiler as binary and also with sources. |
|
726 \item[2)] Make the compiler aware when it compiles itself. |
|
727 \item[3)] Add the Trojan horse. |
|
728 \item[4)] Compile. |
|
729 \item[5)] Delete Trojan horse from the sources of the compiler. |
|
730 \item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{} |
|
731 \end{enumerate} |
|
732 \end{quote} |
|
733 \end{minipage}}; |
|
734 \end{tikzpicture} |
|
735 \end{textblock}} |
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736 |
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737 \end{frame}} |
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738 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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739 |
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740 *} |
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741 |
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742 text_raw {* |
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743 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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744 \mode<presentation>{ |
|
745 \begin{frame} |
|
746 \frametitle{\LARGE\begin{tabular}{c}An Example: Small TCB for\\[-2mm] |
|
747 A Critical Infrastructure\end{tabular}} |
|
748 \mbox{}\\[-14mm]\mbox{} |
|
749 |
|
750 \begin{columns} |
|
751 \begin{column}{0.2\textwidth} |
|
752 \begin{tabular}{@ {} c@ {}} |
|
753 \includegraphics[scale=0.3]{appel.jpg}\\[-2mm] |
|
754 {\footnotesize Andrew Appel}\\[-2.5mm] |
|
755 {\footnotesize (Princeton)} |
|
756 \end{tabular} |
|
757 \end{column} |
|
758 |
|
759 \begin{column}{0.8\textwidth} |
|
760 \begin{textblock}{10}(4.5,3.95) |
|
761 \begin{block}{Proof-Carrying Code} |
|
762 \begin{center} |
|
763 \begin{tikzpicture} |
|
764 \draw[help lines,cream] (0,0.2) grid (8,4); |
|
765 |
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766 \draw[line width=1mm, red] (5.5,0.6) rectangle (7.5,4); |
|
767 \node[anchor=base] at (6.5,2.8) |
|
768 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering user needs to run untrusted code\end{tabular}}; |
|
769 |
|
770 \draw[line width=1mm, red] (0.5,0.6) rectangle (2.5,4); |
|
771 \node[anchor=base] at (1.5,2.3) |
|
772 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering code developer/ web server/ Apple |
|
773 Store\end{tabular}}; |
|
774 |
|
775 \onslide<4->{ |
|
776 \draw[line width=1mm, red, fill=red] (5.5,0.6) rectangle (7.5,1.8); |
|
777 \node[anchor=base,white] at (6.5,1.1) |
|
778 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\bf\centering proof- checker\end{tabular}};} |
|
779 |
|
780 \node at (3.8,3.0) [single arrow, fill=red,text=white, minimum height=3cm]{\bf code}; |
|
781 \onslide<3->{ |
|
782 \node at (3.8,1.3) [single arrow, fill=red,text=white, minimum height=3cm]{\bf LF proof}; |
|
783 \node at (3.8,1.9) {\small certificate}; |
|
784 } |
|
785 |
|
786 \onslide<2>{\node at (4.0,1.3) [text=red]{\begin{tabular}{c}\bf Highly\\\bf Dangerous!\end{tabular}};} |
|
787 % Code Developer |
|
788 % User (runs untrusted code) |
|
789 % transmits a proof that the code is safe |
|
790 % |
|
791 \end{tikzpicture} |
|
792 \end{center} |
|
793 \end{block} |
|
794 \end{textblock} |
|
795 \end{column} |
|
796 \end{columns} |
|
797 |
|
798 \small\mbox{}\\[2.5cm] |
|
799 \begin{itemize} |
|
800 \item<4-> TCB of the checker is $\sim$2700 lines of code (1865 loc of\\ LF definitions; |
|
801 803 loc in C including 2 library functions)\\[-3mm] |
|
802 \item<5-> 167 loc in C implement a type-checker |
|
803 \end{itemize} |
|
804 |
|
805 \end{frame}} |
|
806 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
807 |
|
808 *} |
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809 |
|
810 |
|
811 |
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812 text {* |
|
813 \tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex] |
|
814 \tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick, |
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815 draw=black!50, top color=white, bottom color=black!20] |
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816 \tikzstyle{node2}=[rectangle, minimum size=12mm, rounded corners=3mm, very thick, |
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817 draw=red!70, top color=white, bottom color=red!50!black!20] |
|
818 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
819 \mode<presentation>{ |
|
820 \begin{frame}[squeeze] |
|
821 \frametitle{Type-Checking in LF} |
|
822 |
|
823 \begin{columns} |
|
824 \begin{column}{0.2\textwidth} |
|
825 \begin{tabular}{@ {\hspace{-4mm}}c@ {}} |
|
826 \\[-4mm] |
|
827 \includegraphics[scale=0.1]{harper.jpg}\\[-2mm] |
|
828 {\footnotesize Bob Harper}\\[-2.5mm] |
|
829 {\footnotesize (CMU)}\\[2mm] |
|
830 |
|
831 \includegraphics[scale=0.3]{pfenning.jpg}\\[-2mm] |
|
832 {\footnotesize Frank Pfenning}\\[-2.5mm] |
|
833 {\footnotesize (CMU)}\\[2mm] |
|
834 |
|
835 \onslide<-6>{ |
|
836 {\footnotesize 31 pages in }\\[-2.5mm] |
|
837 {\footnotesize ACM Transact.~on}\\[-2.5mm] |
|
838 {\footnotesize Comp.~Logic.,~2005}\\} |
|
839 \end{tabular} |
|
840 \end{column} |
|
841 |
|
842 \begin{column}{0.8\textwidth} |
|
843 \begin{textblock}{0}(3.1,2) |
|
844 |
|
845 \begin{tikzpicture} |
|
846 \matrix[ampersand replacement=\&,column sep=7mm, row sep=5mm] |
|
847 { \&[-10mm] |
|
848 \node (def1) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}}; \& |
|
849 \node (proof1) [node1] {\large Proof}; \& |
|
850 \node (alg1) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}}; \\ |
|
851 |
|
852 \onslide<4->{\node {\begin{tabular}{c}\small 1st\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
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853 \onslide<4->{\node (def2) [node2] {\large Spec$^\text{+ex}$};} \& |
|
854 \onslide<4->{\node (proof2) [node1] {\large Proof};} \& |
|
855 \onslide<4->{\node (alg2) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\ |
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856 |
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857 \onslide<5->{\node {\begin{tabular}{c}\small 2nd\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
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858 \onslide<5->{\node (def3) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \& |
|
859 \onslide<5->{\node (proof3) [node1] {\large Proof};} \& |
|
860 \onslide<5->{\node (alg3) [node2] {\large Alg$^\text{-ex}$};} \\ |
|
861 |
|
862 \onslide<6->{\node {\begin{tabular}{c}\small 3rd\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
|
863 \onslide<6->{\node (def4) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \& |
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864 \onslide<6->{\node (proof4) [node2] {\large\hspace{1mm}Proof\hspace{1mm}};} \& |
|
865 \onslide<6->{\node (alg4) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\ |
|
866 }; |
|
867 |
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879 |
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880 \onslide<3->{\draw[white,line width=1mm] (1.1,3.2) -- (0.9,2.85) -- (1.1,2.35) -- (0.9,2.0);} |
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881 \end{tikzpicture} |
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882 |
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883 \end{textblock} |
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884 \end{column} |
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885 \end{columns} |
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886 |
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887 \only<2>{% |
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888 \begin{textblock}{2}(.1,12.85) |
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889 \begin{tikzpicture} |
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890 \draw[line width=1mm, red] (0,0) ellipse (1.5cm and 0.88cm); |
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891 \end{tikzpicture} |
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892 \end{textblock} |
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893 } |
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894 |
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895 \begin{textblock}{3}(14,3.6) |
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896 \onslide<4->{ |
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897 \begin{tikzpicture} |
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898 \node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{2h}; |
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899 \end{tikzpicture}} |
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900 \end{textblock} |
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901 |
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902 \only<7->{ |
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903 \begin{textblock}{14}(0.6,12.8) |
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904 \begin{block}{} |
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905 \small Each time one needs to check $\sim$31pp~of informal paper proofs. |
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906 You have to be able to keep definitions and proofs consistent. |
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907 \end{block} |
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908 \end{textblock}} |
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909 |
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910 \end{frame}} |
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911 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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912 |
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913 *} |
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914 |
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915 text_raw {* |
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916 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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917 \mode<presentation>{ |
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918 \begin{frame}<1>[c] |
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919 \frametitle{Theorem Provers} |
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920 |
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921 \begin{itemize} |
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922 \item Theorem provers help with keeping large proofs consistent; |
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923 make them modifiable.\medskip |
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924 |
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925 \item They can ensure that all cases are covered.\medskip |
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926 |
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927 \item Sometimes, tedious reasoning can be automated. |
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928 \end{itemize} |
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929 |
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930 \end{frame}} |
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931 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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932 *} |
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933 |
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934 text_raw {* |
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935 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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936 \mode<presentation>{ |
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937 \begin{frame}<1>[c] |
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938 \frametitle{Theorem Provers} |
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939 |
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940 \begin{itemize} |
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941 \item You also pay a (sometimes heavy) price: reasoning can be much, much harder.\medskip |
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942 |
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943 \item Depending on your domain, suitable reasoning infrastructure |
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944 might not yet be available. |
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945 \end{itemize} |
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946 |
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947 \end{frame}} |
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948 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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949 *} |
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950 |
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951 text_raw {* |
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952 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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953 \mode<presentation>{ |
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954 \begin{frame}<1>[c] |
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955 \frametitle{Theorem Provers} |
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956 |
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957 Recently impressive work has been accomplished proving the correctness |
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958 |
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959 \begin{itemize} |
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960 \item of a compiler for C-light (compiled code has the same observable |
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961 behaviour as the original source code),\medskip |
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962 |
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963 \item a mirco-kernel operating system (absence of certain |
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964 bugs\ldots no nil pointers, no buffer overflows). |
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965 \end{itemize} |
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966 |
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967 \end{frame}} |
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968 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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969 *} |
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970 |
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971 |
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972 text_raw {* |
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973 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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974 \mode<presentation>{ |
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975 \begin{frame}<1>[c] |
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976 \frametitle{Trust in Theorem Provers} |
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977 |
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978 \begin{center} |
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979 Why should we trust theorem provers? |
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980 \end{center} |
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981 |
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982 \end{frame}} |
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983 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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984 *} |
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985 |
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986 text_raw {* |
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987 |
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988 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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989 \mode<presentation>{ |
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990 \begin{frame} |
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991 \frametitle{Theorem Provers} |
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992 |
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993 \begin{itemize} |
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994 \item Theorem provers are a \textcolor{red}{special kind} of software. |
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995 |
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996 \item We do \textcolor{red}{\bf not} need to trust them; we only need to trust: |
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997 \end{itemize} |
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998 |
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999 \begin{quote} |
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1000 \begin{itemize} |
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1001 \item The logic they are based on \textcolor{gray}{(e.g.~HOL)}, and\smallskip |
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1002 \item a proof checker that checks the proofs |
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1003 \textcolor{gray}{(this can be a very small program)}.\smallskip\pause |
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1004 \item To a little extend, we also need to trust our definitions |
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1005 \textcolor{gray}{(this can be mitigated)}. |
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1006 \end{itemize} |
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1007 \end{quote} |
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1008 |
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1009 \end{frame}} |
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1010 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1011 |
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1012 *} |
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1013 |
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1014 text_raw {* |
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1015 |
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1016 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1017 \mode<presentation>{ |
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1018 \begin{frame} |
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1019 \frametitle{Isabelle} |
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1020 |
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1021 \begin{itemize} |
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1022 \item I am using the Isabelle theorem prover (development since 1990).\bigskip\bigskip\bigskip |
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1023 |
|
1024 \item It follows the LCF-approach: |
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1025 |
|
1026 \begin{itemize} |
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1027 \item Have a special abstract type \alert{\bf thm}. |
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1028 \item Make the constructors of this abstract type the inference rules |
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1029 of your logic. |
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1030 \item Implement the theorem prover in a strongly-typed language (e.g.~ML). |
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1031 \end{itemize} |
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1032 |
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1033 $\Rightarrow$ everything of type {\bf thm} has been proved (even if we do not |
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1034 have to explicitly generate proofs). |
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1035 \end{itemize} |
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1036 |
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1037 \only<1>{ |
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1038 \begin{textblock}{5}(11,2.3) |
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1039 \begin{center} |
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1040 \includegraphics[scale=0.18]{robin-milner.jpg}\\[-0.8mm] |
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1041 \footnotesize Robin Milner\\[-0.8mm] |
|
1042 \footnotesize Turing Award, 1991\\ |
|
1043 \end{center} |
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1044 \end{textblock}} |
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1045 |
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1046 |
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1047 \end{frame}} |
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1048 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1049 *} |
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1050 |
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1051 text_raw {* |
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1052 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1053 \mode<presentation>{ |
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1054 \begin{frame}<1>[c] |
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1055 \frametitle{ |
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1056 \begin{tabular}{c} |
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1057 \mbox{}\\[23mm] |
|
1058 \LARGE Demo |
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1059 \end{tabular}} |
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1060 |
|
1061 \end{frame}} |
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1062 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1063 *} |
|
1064 |
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1065 |
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1066 text_raw {* |
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1067 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1068 \mode<presentation>{ |
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1069 \begin{frame}<1->[c] |
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1070 \frametitle{Future Research} |
|
1071 |
|
1072 \begin{itemize} |
|
1073 \item Make theorem provers more like a programming environment.\medskip\pause |
|
1074 |
|
1075 \item Use all the computational power we get from the hardware to |
|
1076 automate reasoning (GPUs).\medskip\pause |
|
1077 |
|
1078 \item Provide a comprehensive reasoning infrastructure for many domains and |
|
1079 design automated decision procedures. |
|
1080 \end{itemize}\pause |
|
1081 |
|
1082 |
|
1083 \begin{center} |
|
1084 \colorbox{cream}{ |
|
1085 \begin{minipage}{10cm} |
|
1086 \color{gray} |
|
1087 \small |
|
1088 ``Formal methods will never have a significant impact until |
|
1089 they can be used by people that don't understand them.''\smallskip\\ |
|
1090 \mbox{}\footnotesize\hfill attributed to Tom Melham |
|
1091 \end{minipage}} |
|
1092 \end{center} |
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1093 |
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1094 \end{frame}} |
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1095 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1096 *} |
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1097 |
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1098 text_raw {* |
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1099 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1100 \mode<presentation>{ |
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1101 \begin{frame}<1->[c] |
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1102 \frametitle{Conclusion} |
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1103 |
|
1104 \begin{itemize} |
|
1105 \item The plan is to make this kind of programming the ``future''.\medskip\pause |
|
1106 |
|
1107 \item Though the technology is already there\\ (compiler + micro-kernel os).\medskip\pause |
|
1108 |
|
1109 \item Logic and reasoning (especially induction) are important skills for |
|
1110 Computer Scientists. |
|
1111 \end{itemize} |
|
1112 |
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1113 \end{frame}} |
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1114 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1115 *} |
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1116 |
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1117 |
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1118 text_raw {* |
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1119 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1120 \mode<presentation>{ |
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1121 \begin{frame}<1>[c] |
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1122 \frametitle{ |
|
1123 \begin{tabular}{c} |
|
1124 \mbox{}\\[23mm] |
|
1125 \alert{\LARGE Thank you very much!}\\ |
|
1126 \alert{\Large Questions?} |
|
1127 \end{tabular}} |
|
1128 |
|
1129 \end{frame}} |
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1130 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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1131 *} |
|
1132 |
|
1133 |
|
1134 |
|
1135 (*<*) |
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1136 end |
|
1137 (*>*) |