Slides/Slides4.thy
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     1 (*<*)
       
     2 theory Slides4
       
     3 imports "LaTeXsugar" "Nominal"
       
     4 begin
       
     5 
       
     6 notation (latex output)
       
     7   set ("_") and
       
     8   Cons  ("_::/_" [66,65] 65) 
       
     9 
       
    10 (*>*)
       
    11 
       
    12 text_raw {*
       
    13   \renewcommand{\slidecaption}{Nanjing, 31.~August 2010}
       
    14 
       
    15   \newcommand{\abst}[2]{#1.#2}% atom-abstraction
       
    16   \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing
       
    17   \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions
       
    18   \newcommand{\unit}{\langle\rangle}% unit
       
    19   \newcommand{\app}[2]{#1\,#2}% application
       
    20   \newcommand{\eqprob}{\mathrel{{\approx}?}}
       
    21   \newcommand{\freshprob}{\mathrel{\#?}}
       
    22   \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction
       
    23   \newcommand{\id}{\varepsilon}% identity substitution
       
    24   
       
    25   \newcommand{\bl}[1]{\textcolor{blue}{#1}}
       
    26   \newcommand{\gr}[1]{\textcolor{gray}{#1}}
       
    27   \newcommand{\rd}[1]{\textcolor{red}{#1}}
       
    28 
       
    29   \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}}
       
    30   \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}}
       
    31   \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}}
       
    32 
       
    33   \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont}
       
    34   \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont}
       
    35   \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont}
       
    36   \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont}
       
    37 
       
    38   \newcommand{\LL}{$\mathbb{L}\,$}
       
    39 
       
    40 
       
    41   \pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}%
       
    42   {rgb(0mm)=(0,0,0.9);
       
    43   rgb(0.9mm)=(0,0,0.7);
       
    44   rgb(1.3mm)=(0,0,0.5);
       
    45   rgb(1.4mm)=(1,1,1)}
       
    46 
       
    47   \def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex}
       
    48     \usebeamercolor[fg]{subitem projected}
       
    49     {\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}}
       
    50     \pgftext{%
       
    51       \usebeamerfont*{subitem projected}}
       
    52   \end{pgfpicture}}
       
    53 
       
    54   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
    55   \mode<presentation>{
       
    56   \begin{frame}<1>[t]
       
    57   \frametitle{%
       
    58   \begin{tabular}{@ {\hspace{-3mm}}c@ {}}
       
    59   \\
       
    60   \huge Error-Free Programming\\[-1mm] 
       
    61   \huge with Theorem Provers\\[5mm]
       
    62   \end{tabular}}
       
    63   \begin{center}
       
    64   Christian Urban
       
    65   \end{center}
       
    66   \begin{center}
       
    67   \small Technical University of Munich, Germany\\[7mm]
       
    68 
       
    69   \small in Nanjing on the kind invitation of\\ Professor Xingyuan Zhang
       
    70   and his group
       
    71   \end{center}
       
    72   \end{frame}}
       
    73   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
    74 
       
    75 *}
       
    76 text_raw {*
       
    77   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
    78   \mode<presentation>{
       
    79   \begin{frame}<1->[c]
       
    80   \frametitle{My Background}
       
    81 
       
    82   \begin{itemize}
       
    83   \item researcher in Theoretical Computer Science\medskip
       
    84 
       
    85   \item programmer on a \alert<2->{software system} with 800 kloc (though I am 
       
    86   responsible only for 35 kloc)
       
    87   \end{itemize}
       
    88 
       
    89   \only<2->{
       
    90   \begin{textblock}{6}(2,11)
       
    91   \begin{tikzpicture}
       
    92   \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
       
    93   {\color{darkgray}
       
    94   \begin{minipage}{4cm}\raggedright
       
    95   A theorem prover called {\bf Isabelle}.
       
    96   \end{minipage}};
       
    97   \end{tikzpicture}
       
    98   \end{textblock}}
       
    99 
       
   100   
       
   101   \only<3>{
       
   102   \begin{textblock}{6}(9,11)
       
   103   \begin{tikzpicture}
       
   104   \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
       
   105   {\color{darkgray}
       
   106   \begin{minipage}{4cm}\raggedright
       
   107   Like every other code, this code is very hard to 
       
   108   get correct.
       
   109   \end{minipage}};
       
   110   \end{tikzpicture}
       
   111   \end{textblock}}
       
   112 
       
   113   \end{frame}}
       
   114   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   115 *}
       
   116 
       
   117 text_raw {*
       
   118   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   119   \mode<presentation>{
       
   120   \begin{frame}<1->[t]
       
   121   \frametitle{Regular Expressions}
       
   122 
       
   123   An example many (should) know about:\\ 
       
   124   \rd{\bf Regular Expressions:} 
       
   125 
       
   126   \only<2>{
       
   127   \begin{center}
       
   128   \bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$  r$_1$$|$r$_2$  $\;\;\;|\;\;\;$  
       
   129    r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$}
       
   130   \end{center}}
       
   131   \only<3->{
       
   132   \begin{center}
       
   133   \begin{tabular}{@ {}rrll@ {}}
       
   134   \bl{r} & \bl{$::=$}  & \bl{NULL}            & \gr{(matches no string)}\\ 
       
   135          & \bl{$\mid$} & \bl{EMPTY}           & \gr{(matches the empty string, [])}\\ 
       
   136          & \bl{$\mid$} & \bl{CHR c}           & \gr{(matches the character c)}\\ 
       
   137          & \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\ 
       
   138          & \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\ 
       
   139          & \bl{$\mid$} & \bl{STAR r}          & \gr{(repeat, r$^*$)}\\
       
   140   \end{tabular}
       
   141   \end{center}\medskip}
       
   142 
       
   143   \small
       
   144   \begin{textblock}{14.5}(1,12.5)
       
   145   \only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\}
       
   146   \only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2  \ldots  8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} 
       
   147   \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
       
   148   \end{textblock}
       
   149   \end{frame}}
       
   150   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   151 *}
       
   152 
       
   153 text_raw {*
       
   154   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   155   \mode<presentation>{
       
   156   \begin{frame}<1>[c]
       
   157   \frametitle{RegExp Matcher}
       
   158 
       
   159   Let's implement a regular expression matcher:\bigskip
       
   160 
       
   161   \begin{center}
       
   162   \begin{tikzpicture}
       
   163   %%\draw[help lines, black] (-3,0) grid (6,3);
       
   164   
       
   165   \draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3);
       
   166   \node[anchor=base] at (2,1) 
       
   167      {\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\ 
       
   168                                       \Large\bf Expression \\ 
       
   169                                       \Large\bf Matcher\end{tabular}};
       
   170   
       
   171   \coordinate (m1) at (0,1.5);
       
   172   \draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}};
       
   173   \path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1);
       
   174   
       
   175   \coordinate (s1) at (0,0.5);
       
   176   \draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}};
       
   177   \path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1);
       
   178 
       
   179   \coordinate (r1) at (4,1.2);
       
   180   \draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}};
       
   181   \path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2);
       
   182 
       
   183   \end{tikzpicture}
       
   184   \end{center}
       
   185 
       
   186 
       
   187   \end{frame}}
       
   188   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   189 *}
       
   190 
       
   191 text_raw {*
       
   192   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   193   \mode<presentation>{
       
   194   \begin{frame}<1->[t]
       
   195   \frametitle{RegExp Matcher}
       
   196   \small
       
   197 
       
   198   {\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false
       
   199 
       
   200   \only<2->{
       
   201   \begin{center}
       
   202   \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
       
   203   \bl{match [] []}                   & \bl{$=$} & \bl{true}\\
       
   204   \bl{match [] \_}                   & \bl{$=$} & \bl{false}\\
       
   205   \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false}\\
       
   206   \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
       
   207   \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s}\\         
       
   208   \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false}\\    
       
   209   \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
       
   210                                      &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
       
   211   \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
       
   212   \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s}\\
       
   213                                      &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
       
   214   \end{tabular}
       
   215   \end{center}}
       
   216 
       
   217   \onslide<3->{we start the program with\\
       
   218   \hspace{6mm}\bl{matches r s $=$ match [r] s}}
       
   219 
       
   220   \end{frame}}
       
   221   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   222 *}
       
   223 
       
   224 
       
   225 text_raw {*
       
   226   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   227   \mode<presentation>{
       
   228   \begin{frame}<1>[c]
       
   229   \frametitle{Program in Scala}
       
   230 
       
   231   \bl{\footnotesize
       
   232   \begin{tabular}{l}
       
   233   sealed abstract class Rexp\\ 
       
   234   sealed case class Null extends Rexp\\
       
   235   sealed case class Empty extends Rexp\\
       
   236   sealed case class Chr(c: Char) extends Rexp\\
       
   237   sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\
       
   238   sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\
       
   239   sealed case class Star(r : Rexp) extends Rexp\medskip\\
       
   240   def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\
       
   241   \hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\
       
   242   \hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\
       
   243   \hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\
       
   244   \hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\
       
   245   \hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\
       
   246   \hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\
       
   247   \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\
       
   248   \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\
       
   249   \hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\
       
   250   \}
       
   251   \end{tabular}}
       
   252 
       
   253   \end{frame}}
       
   254   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   255 *}
       
   256 
       
   257 
       
   258 text_raw {*
       
   259   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   260   \mode<presentation>{
       
   261   \begin{frame}<1->[c]
       
   262   \frametitle{Testing}
       
   263   
       
   264   \small
       
   265   Every good programmer should do thourough tests: 
       
   266 
       
   267 
       
   268   \begin{center}
       
   269   \begin{tabular}{@ {\hspace{-20mm}}lcl}
       
   270   \bl{matches (a$\cdot$b)$^*\;$ []}     & \bl{$\mapsto$} & \bl{true}\\
       
   271   \bl{matches (a$\cdot$b)$^*\;$ ab}   & \bl{$\mapsto$} & \bl{true}\\ 
       
   272   \bl{matches (a$\cdot$b)$^*\;$ aba}  & \bl{$\mapsto$} & \bl{false}\\
       
   273   \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ 
       
   274   \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
       
   275   \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x}   & \bl{$\mapsto$} & \bl{true}}\\
       
   276   \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0}  & \bl{$\mapsto$} & \bl{true}}\\
       
   277   \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3}  & \bl{$\mapsto$} & \bl{false}}
       
   278   \end{tabular}
       
   279   \end{center}
       
   280  
       
   281   \onslide<3->
       
   282   {looks OK \ldots let's ship it to customers\hspace{5mm} 
       
   283    \raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}}
       
   284   
       
   285   \end{frame}}
       
   286   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   287 *}
       
   288 
       
   289 text_raw {*
       
   290   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   291   \mode<presentation>{
       
   292   \begin{frame}<1->[t]
       
   293   \frametitle{Testing}
       
   294 
       
   295   \begin{itemize}
       
   296   \item While testing is an important part in the process of programming development\pause
       
   297 
       
   298   \item we can only test a {\bf finite} amount of examples\bigskip\pause
       
   299 
       
   300   \begin{center}
       
   301   \colorbox{cream}
       
   302   {\gr{\begin{minipage}{10cm}
       
   303   ``Testing can only show the presence of errors, never their
       
   304   absence'' (Edsger W.~Dijkstra)
       
   305   \end{minipage}}}
       
   306   \end{center}\bigskip\pause
       
   307 
       
   308   \item In a theorem prover we can establish properties that apply to 
       
   309   {\bf all} input and {\bf all} output.\pause 
       
   310 
       
   311   \item For example we can establish that the matcher terminates 
       
   312   on all input.
       
   313   \end{itemize}
       
   314 
       
   315   \end{frame}}
       
   316   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   317 *}
       
   318 
       
   319 text_raw {*
       
   320   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   321   \mode<presentation>{
       
   322   \begin{frame}<1->[t]
       
   323   \frametitle{RegExp Matcher}
       
   324 
       
   325   \small
       
   326   We need to find a measure that gets smaller in each recursive call.\bigskip
       
   327 
       
   328   \onslide<1->{
       
   329   \begin{center}
       
   330   \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}}
       
   331   \bl{match [] []}                   & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
       
   332   \bl{match [] \_}                   & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
       
   333   \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
       
   334   \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\
       
   335   \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\         
       
   336   \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\    
       
   337   \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\
       
   338                                      &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
       
   339   \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s} & \onslide<6->{\ok}\\
       
   340   \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\
       
   341                                      &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
       
   342   \end{tabular}
       
   343   \end{center}}
       
   344 
       
   345 
       
   346   \begin{textblock}{5}(4,4)
       
   347   \begin{tikzpicture}
       
   348   %%\draw[help lines, black] (-3,0) grid (6,3);
       
   349   
       
   350   \coordinate (m1) at (-2,0);
       
   351   \coordinate (m2) at ( 2,0);
       
   352   \path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2);
       
   353   \draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}};
       
   354   \end{tikzpicture}
       
   355   \end{textblock}
       
   356 
       
   357 
       
   358   \end{frame}}
       
   359   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   360 *}
       
   361 
       
   362 text_raw {*
       
   363   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   364   \mode<presentation>{
       
   365   \begin{frame}<1->[c]
       
   366   \frametitle{Bug Hunting}
       
   367 
       
   368   \only<1>{Several hours later\ldots}\pause
       
   369 
       
   370 
       
   371   \begin{center}
       
   372   \begin{tabular}{@ {\hspace{-20mm}}lcl}
       
   373   \bl{matches (STAR (EMPTY)) s}     & \bl{$\mapsto$} & loops\\
       
   374   \onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s}   & \bl{$\mapsto$} & loops\\} 
       
   375   \end{tabular}
       
   376   \end{center}
       
   377 
       
   378   \small
       
   379   \onslide<3->{
       
   380   \begin{center}
       
   381   \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
       
   382   \ldots\\
       
   383   \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
       
   384   \ldots\\
       
   385   \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s}\\
       
   386                                      &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
       
   387   \end{tabular}
       
   388   \end{center}}
       
   389   
       
   390 
       
   391   \end{frame}}
       
   392   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   393 *}
       
   394 
       
   395 text_raw {*
       
   396   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   397   \mode<presentation>{
       
   398   \begin{frame}<1->[c]
       
   399   \frametitle{RegExp Matcher}
       
   400   \small
       
   401 
       
   402   \begin{center}
       
   403   \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
       
   404   \bl{match [] []}                   & \bl{$=$} & \bl{true}\\
       
   405   \bl{match [] \_}                   & \bl{$=$} & \bl{false}\\
       
   406   \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false}\\
       
   407   \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
       
   408   \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s}\\         
       
   409   \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false}\\    
       
   410   \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
       
   411                                      &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
       
   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}\\
       
   415   \end{tabular}
       
   416   \end{center}
       
   417 
       
   418   \only<1>{
       
   419   \begin{textblock}{5}(4,4)
       
   420   \largenotok
       
   421   \end{textblock}}
       
   422 
       
   423   \end{frame}}
       
   424   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   425 *}
       
   426 
       
   427 
       
   428 
       
   429 text_raw {*
       
   430   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   431   \mode<presentation>{
       
   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}}
       
   452   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   453 *}
       
   454 
       
   455 
       
   456 text_raw {*
       
   457   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   458   \mode<presentation>{
       
   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 {*
       
   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 *}
       
   502 
       
   503 text_raw {*
       
   504   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   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   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   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}}
       
   576   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   577 *}
       
   578 
       
   579 text_raw {*
       
   580   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   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 {*
       
   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}
       
   646   \end{textblock}}
       
   647   
       
   648 
       
   649   \end{frame}}
       
   650   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   651 *}
       
   652 
       
   653 
       
   654 text_raw {*
       
   655   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   656   \mode<presentation>{
       
   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}}
       
   672   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   673 *}
       
   674 
       
   675 text_raw {*
       
   676 
       
   677   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   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->{
       
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   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 *}
       
   946 
       
   947 text_raw {*
       
   948   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
       
   949   \mode<presentation>{
       
   950   \begin{frame}<1>[c]
       
   951   \frametitle{Theorem Provers}
       
   952 
       
   953   Recently impressive work has been accomplished proving the correctness
       
   954 
       
   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}
       
   962 
       
   963   \end{frame}}
       
   964   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   965 *}
       
   966 
       
   967 
       
   968 text_raw {*
       
   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   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
       
   980 *}
       
   981 
       
   982 text_raw {*
       
   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 {*
       
  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 (*>*)