
diff -r 78d828f43cdf -r 4b4742aa43f2 Slides/Slides4.thy
--- a/Slides/Slides4.thy	Sat Dec 17 16:58:11 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,1135 +0,0 @@
-(*<*)
-theory Slides4
-imports "~~/src/HOL/Library/LaTeXsugar" "Nominal"
-begin
-
-declare [[show_question_marks = false]]
-
-notation (latex output)
-  set ("_") and
-  Cons  ("_::/_" [66,65] 65) 
-
-(*>*)
-
-text_raw {*
-  \renewcommand{\slidecaption}{Nanjing, 31.~August 2010}
-
-  \newcommand{\abst}[2]{#1.#2}% atom-abstraction
-  \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing
-  \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions
-  \newcommand{\unit}{\langle\rangle}% unit
-  \newcommand{\app}[2]{#1\,#2}% application
-  \newcommand{\eqprob}{\mathrel{{\approx}?}}
-  \newcommand{\freshprob}{\mathrel{\#?}}
-  \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction
-  \newcommand{\id}{\varepsilon}% identity substitution
-  
-  \newcommand{\bl}[1]{\textcolor{blue}{#1}}
-  \newcommand{\gr}[1]{\textcolor{gray}{#1}}
-  \newcommand{\rd}[1]{\textcolor{red}{#1}}
-
-  \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}}
-  \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}}
-  \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}}
-
-  \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont}
-  \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont}
-  \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont}
-  \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont}
-
-  \newcommand{\LL}{$\mathbb{L}\,$}
-
-
-  \pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}%
-  {rgb(0mm)=(0,0,0.9);
-  rgb(0.9mm)=(0,0,0.7);
-  rgb(1.3mm)=(0,0,0.5);
-  rgb(1.4mm)=(1,1,1)}
-
-  \def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex}
-    \usebeamercolor[fg]{subitem projected}
-    {\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}}
-    \pgftext{%
-      \usebeamerfont*{subitem projected}}
-  \end{pgfpicture}}
-
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[t]
-  \frametitle{%
-  \begin{tabular}{@ {\hspace{-3mm}}c@ {}}
-  \\
-  \huge Error-Free Programming\\[-1mm] 
-  \huge with Theorem Provers\\[5mm]
-  \end{tabular}}
-  \begin{center}
-  Christian Urban
-  \end{center}
-  \begin{center}
-  \small Technical University of Munich, Germany\\[7mm]
-
-  \small in Nanjing on the kind invitation of\\ Professor Xingyuan Zhang
-  and his group
-  \end{center}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{My Background}
-
-  \begin{itemize}
-  \item researcher in Theoretical Computer Science\medskip
-
-  \item programmer on a \alert<2->{software system} with 800 kloc (though I am 
-  responsible only for 35 kloc)
-  \end{itemize}
-
-  \only<2->{
-  \begin{textblock}{6}(2,11)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\color{darkgray}
-  \begin{minipage}{4cm}\raggedright
-  A theorem prover called {\bf Isabelle}.
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  
-  \only<3>{
-  \begin{textblock}{6}(9,11)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\color{darkgray}
-  \begin{minipage}{4cm}\raggedright
-  Like every other code, this code is very hard to 
-  get correct.
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{Regular Expressions}
-
-  An example many (should) know about:\\ 
-  \rd{\bf Regular Expressions:} 
-
-  \only<2>{
-  \begin{center}
-  \bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$  r$_1$$|$r$_2$  $\;\;\;|\;\;\;$  
-   r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$}
-  \end{center}}
-  \only<3->{
-  \begin{center}
-  \begin{tabular}{@ {}rrll@ {}}
-  \bl{r} & \bl{$::=$}  & \bl{NULL}            & \gr{(matches no string)}\\ 
-         & \bl{$\mid$} & \bl{EMPTY}           & \gr{(matches the empty string, [])}\\ 
-         & \bl{$\mid$} & \bl{CHR c}           & \gr{(matches the character c)}\\ 
-         & \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\ 
-         & \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\ 
-         & \bl{$\mid$} & \bl{STAR r}          & \gr{(repeat, r$^*$)}\\
-  \end{tabular}
-  \end{center}\medskip}
-
-  \small
-  \begin{textblock}{14.5}(1,12.5)
-  \only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\}
-  \only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2  \ldots  8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} 
-  \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
-  \end{textblock}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{RegExp Matcher}
-
-  Let's implement a regular expression matcher:\bigskip
-
-  \begin{center}
-  \begin{tikzpicture}
-  %%\draw[help lines, black] (-3,0) grid (6,3);
-  
-  \draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3);
-  \node[anchor=base] at (2,1) 
-     {\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\ 
-                                      \Large\bf Expression \\ 
-                                      \Large\bf Matcher\end{tabular}};
-  
-  \coordinate (m1) at (0,1.5);
-  \draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}};
-  \path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1);
-  
-  \coordinate (s1) at (0,0.5);
-  \draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}};
-  \path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1);
-
-  \coordinate (r1) at (4,1.2);
-  \draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}};
-  \path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2);
-
-  \end{tikzpicture}
-  \end{center}
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{RegExp Matcher}
-  \small
-
-  {\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false
-
-  \only<2->{
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
-  \bl{match [] []}                   & \bl{$=$} & \bl{true}\\
-  \bl{match [] \_}                   & \bl{$=$} & \bl{false}\\
-  \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false}\\
-  \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
-  \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s}\\         
-  \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false}\\    
-  \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
-                                     &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
-  \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
-  \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s}\\
-                                     &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
-  \end{tabular}
-  \end{center}}
-
-  \onslide<3->{we start the program with\\
-  \hspace{6mm}\bl{matches r s $=$ match [r] s}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{Program in Scala}
-
-  \bl{\footnotesize
-  \begin{tabular}{l}
-  sealed abstract class Rexp\\ 
-  sealed case class Null extends Rexp\\
-  sealed case class Empty extends Rexp\\
-  sealed case class Chr(c: Char) extends Rexp\\
-  sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\
-  sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\
-  sealed case class Star(r : Rexp) extends Rexp\medskip\\
-  def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\
-  \hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\
-  \hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\
-  \hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\
-  \hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\
-  \hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\
-  \hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\
-  \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\
-  \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\
-  \hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\
-  \}
-  \end{tabular}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Testing}
-  
-  \small
-  Every good programmer should do thourough tests: 
-
-
-  \begin{center}
-  \begin{tabular}{@ {\hspace{-20mm}}lcl}
-  \bl{matches (a$\cdot$b)$^*\;$ []}     & \bl{$\mapsto$} & \bl{true}\\
-  \bl{matches (a$\cdot$b)$^*\;$ ab}   & \bl{$\mapsto$} & \bl{true}\\ 
-  \bl{matches (a$\cdot$b)$^*\;$ aba}  & \bl{$\mapsto$} & \bl{false}\\
-  \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ 
-  \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
-  \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x}   & \bl{$\mapsto$} & \bl{true}}\\
-  \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0}  & \bl{$\mapsto$} & \bl{true}}\\
-  \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3}  & \bl{$\mapsto$} & \bl{false}}
-  \end{tabular}
-  \end{center}
- 
-  \onslide<3->
-  {looks OK \ldots let's ship it to customers\hspace{5mm} 
-   \raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{Testing}
-
-  \begin{itemize}
-  \item While testing is an important part in the process of programming development\pause
-
-  \item we can only test a {\bf finite} amount of examples\bigskip\pause
-
-  \begin{center}
-  \colorbox{cream}
-  {\gr{\begin{minipage}{10cm}
-  ``Testing can only show the presence of errors, never their
-  absence'' (Edsger W.~Dijkstra)
-  \end{minipage}}}
-  \end{center}\bigskip\pause
-
-  \item In a theorem prover we can establish properties that apply to 
-  {\bf all} input and {\bf all} output.\pause 
-
-  \item For example we can establish that the matcher terminates 
-  on all input.
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{RegExp Matcher}
-
-  \small
-  We need to find a measure that gets smaller in each recursive call.\bigskip
-
-  \onslide<1->{
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}}
-  \bl{match [] []}                   & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
-  \bl{match [] \_}                   & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
-  \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
-  \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\
-  \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\         
-  \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\    
-  \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\
-                                     &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
-  \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s} & \onslide<6->{\ok}\\
-  \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\
-                                     &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
-  \end{tabular}
-  \end{center}}
-
-
-  \begin{textblock}{5}(4,4)
-  \begin{tikzpicture}
-  %%\draw[help lines, black] (-3,0) grid (6,3);
-  
-  \coordinate (m1) at (-2,0);
-  \coordinate (m2) at ( 2,0);
-  \path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2);
-  \draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}};
-  \end{tikzpicture}
-  \end{textblock}
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Bug Hunting}
-
-  \only<1>{Several hours later\ldots}\pause
-
-
-  \begin{center}
-  \begin{tabular}{@ {\hspace{-20mm}}lcl}
-  \bl{matches (STAR (EMPTY)) s}     & \bl{$\mapsto$} & loops\\
-  \onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s}   & \bl{$\mapsto$} & loops\\} 
-  \end{tabular}
-  \end{center}
-
-  \small
-  \onslide<3->{
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
-  \ldots\\
-  \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
-  \ldots\\
-  \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s}\\
-                                     &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
-  \end{tabular}
-  \end{center}}
-  
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{RegExp Matcher}
-  \small
-
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
-  \bl{match [] []}                   & \bl{$=$} & \bl{true}\\
-  \bl{match [] \_}                   & \bl{$=$} & \bl{false}\\
-  \bl{match (NULL::rs) s}            & \bl{$=$} & \bl{false}\\
-  \bl{match (EMPTY::rs) s}           & \bl{$=$} & \bl{match rs s}\\
-  \bl{match (CHR c::rs) (c::s)}      & \bl{$=$} & \bl{match rs s}\\         
-  \bl{match (CHR c::rs) \_}          & \bl{$=$} & \bl{false}\\    
-  \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
-                                     &          & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ 
-  \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
-  \bl{match (STAR r::rs) s}          & \bl{$=$} & \bl{match rs s}\\
-                                     &          & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
-  \end{tabular}
-  \end{center}
-
-  \only<1>{
-  \begin{textblock}{5}(4,4)
-  \largenotok
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{Second Attempt}
-
-  Can a regular expression match the empty string?
-
-  \small
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
-  \bl{nullable (NULL)}            & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
-  \bl{nullable (EMPTY)}           & \bl{$=$} & \bl{true}  & \onslide<2->{\ok}\\
-  \bl{nullable (CHR c)}           & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\         
-  \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)}
-    & \onslide<2->{\ok}\\ 
-  \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)}
-    & \onslide<2->{\ok}\\ 
-  \bl{nullable (STAR r)}          & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
-  \end{tabular}
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{RegExp Matcher 2}
-
-  If \bl{r} matches \bl{c::s}, which regular expression can match the string \bl{s}?
-
-  \small
-  \begin{center}
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
-  \bl{der c (NULL)}            & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
-  \bl{der c (EMPTY)}           & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
-  \bl{der c (CHR d)}           & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \onslide<3->{\ok}\\
-  \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \onslide<3->{\ok}\\ 
-  \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \onslide<3->{\ok}\\
-       &          & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
-  \bl{der c (STAR r)}          & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} & \onslide<3->{\ok}\medskip\\
-  \pause
-
-  \bl{derivative r []}     & \bl{$=$} & \bl{r} & \onslide<3->{\ok}\\
-  \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \onslide<3->{\ok}\\
-  \end{tabular}
-  \end{center}
-
-  we call the program with\\
-  \bl{matches r s $=$ nullable (derivative r s)}
-  
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{But Now What?}
-
-  \begin{center}
-  {\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}}
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Testing}
-  
-  \small
-
-  \begin{center}
-  \begin{tabular}{@ {\hspace{-20mm}}lcl}
-  \bl{matches []$^*$ []} & \bl{$\mapsto$} & \bl{true}\\
-  \bl{matches ([]$|$a)$^*$ a}  & \bl{$\mapsto$} & \bl{true}\medskip\\
-
-  \bl{matches (a$\cdot$b)$^*\;$ []}     & \bl{$\mapsto$} & \bl{true}\\
-  \bl{matches (a$\cdot$b)$^*\;$ ab}   & \bl{$\mapsto$} & \bl{true}\\ 
-  \bl{matches (a$\cdot$b)$^*\;$ aba}  & \bl{$\mapsto$} & \bl{false}\\
-  \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ 
-  \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
-  
-  \bl{matches x$\cdot$(0$|$1)$^*\;$ x}   & \bl{$\mapsto$} & \bl{true}\\
-  \bl{matches x$\cdot$(0$|$1)$^*\;$ x0}  & \bl{$\mapsto$} & \bl{true}\\
-  \bl{matches x$\cdot$(0$|$1)$^*\;$ x3}  & \bl{$\mapsto$} & \bl{false}
-  \end{tabular}
-  \end{center}
- 
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{Specification}
-
-  We have to specify what it means for a regular expression to match
-  a string. 
-  %
-  \only<2>{
-  \mbox{}\\[8mm]
-  \bl{(a$\cdot$b)$^*$}\\ 
-  \hspace{7mm}\bl{$\mapsto$\hspace{3mm}\{[], ab, abab, ababab, \ldots\}}\bigskip\\
-  \bl{x$\cdot$(0 $|$ 1 $|$ 2  \ldots  8 $|$ 9 )$^*$}\\ 
-  \hspace{7mm}\bl{$\mapsto$\hspace{3mm} 
-  \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
-  %
-  \only<3->{
-  \begin{center}
-  \begin{tabular}{rcl}
-  \bl{\LL (NULL)}            & \bl{$\dn$} & \bl{\{\}}\\
-  \bl{\LL (EMPTY)}           & \bl{$\dn$} & \bl{\{[]\}}\\
-  \bl{\LL (CHR c)}           & \bl{$\dn$} & \bl{\{c\}}\\
-  \bl{\LL (ALT r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<4->{\bl{\LL (r$_1$) $\cup$ \LL (r$_2$)}}\\
-  \bl{\LL (SEQ r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<6->{\bl{\LL (r$_1$) ; \LL (r$_2$)}}\\
-  \bl{\LL (STAR r)}          & \bl{$\dn$} & \onslide<8->{\bl{(\LL (r))$^\star$}}\\
-  \end{tabular}
-  \end{center}}
-
-  \only<5-6>{
-  \begin{textblock}{6}(2.9,13.3)
-  \colorbox{cream}{\bl{S$_1$ ; S$_2$ $\;\dn\;$ \{ s$_1$@s$_2$ $|$ s$_1$$\in$S$_1$ $\wedge$
-                                                          s$_2$$\in$S$_2$ \}}}
-  \end{textblock}}
-
-  \only<7->{
-  \begin{textblock}{9}(4,13)
-  \colorbox{cream}{\bl{$\infer{\mbox{[]} \in \mbox{S}^\star}{}$}}\hspace{3mm}
-  \colorbox{cream}{\bl{$\infer{\mbox{s}_1\mbox{@}\mbox{s}_2 \in \mbox{S}^\star}
-                      {\mbox{s}_1 \in \mbox{S} & \mbox{s}_2 \in \mbox{S}^\star}$}}
-  \end{textblock}}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{Is the Matcher Error-Free?}
-
-  We expect that
-
-  \begin{center}
-  \begin{tabular}{lcl}
-  \bl{matches r s = true}  & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}% 
-  \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\in$ \LL(r)}\\
-  \bl{matches r s = false} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}%
-  \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\notin$ \LL(r)}\\
-  \end{tabular}
-  \end{center}
-  \pause\pause\bigskip
-  By \alert<4->{induction}, we can {\bf prove} these properties.\bigskip
-
-  \begin{tabular}{lrcl}
-  Lemmas:  & \bl{nullable (r)}          & \bl{$\Longleftrightarrow$} & \bl{[] $\in$ \LL (r)}\\
-           & \bl{s $\in$ \LL (der c r)} & \bl{$\Longleftrightarrow$} & \bl{(c::s) $\in$ \LL (r)}\\
-  \end{tabular}
-  
-  \only<4->{
-  \begin{textblock}{3}(0.9,4.5)
-  \rd{\huge$\forall$\large{}r s.}
-  \end{textblock}}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-
-  \mbox{}\\[-2mm]
-
-  \small
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
-  \bl{nullable (NULL)}            & \bl{$=$} & \bl{false} &\\
-  \bl{nullable (EMPTY)}           & \bl{$=$} & \bl{true}  &\\
-  \bl{nullable (CHR c)}           & \bl{$=$} & \bl{false} &\\
-  \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} & \\ 
-  \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} & \\
-  \bl{nullable (STAR r)}          & \bl{$=$} & \bl{true} & \\
-  \end{tabular}\medskip
-
-  \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
-  \bl{der c (NULL)}            & \bl{$=$} & \bl{NULL} & \\
-  \bl{der c (EMPTY)}           & \bl{$=$} & \bl{NULL} & \\
-  \bl{der c (CHR d)}           & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \\
-  \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \\
-  \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \\
-       &          & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
-  \bl{der c (STAR r)}          & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} &\smallskip\\
-
-  \bl{derivative r []}     & \bl{$=$} & \bl{r} & \\
-  \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \\
-  \end{tabular}\medskip
-
-  \bl{matches r s $=$ nullable (derivative r s)}
-  
-  \only<2>{
-  \begin{textblock}{8}(1.5,4)
-  \includegraphics[scale=0.3]{approved.png}
-  \end{textblock}}
-  
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Interlude: TCB}
-
-  \begin{itemize}
-  \item The \alert{\bf Trusted Code Base} (TCB) is the code that can make your 
-  program behave in unintended ways (i.e.~cause bugs).\medskip
-
-  \item Typically the TCB includes: CPUs, operating systems, C-libraries,
-  device drivers, (J)VMs\ldots\bigskip
-  \pause
-
-  \item It also includes the compiler.
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-3>
-  \frametitle{\LARGE\begin{tabular}{c}Hacking Compilers 
-  \end{tabular}}
-  
-  %Why is it so paramount to have a small trusted code base (TCB)?
-  \bigskip\bigskip
-
-  \begin{columns}
-  \begin{column}{2.7cm}
-  \begin{minipage}{2.5cm}%
-  \begin{tabular}{c@ {}}
-  \includegraphics[scale=0.2]{ken-thompson.jpg}\\[-1.8mm]
-  \footnotesize Ken Thompson\\[-1.8mm]
-  \footnotesize Turing Award, 1983\\
-  \end{tabular}
-  \end{minipage}
-  \end{column}
-  \begin{column}{9cm}
-  \begin{tabular}{l@ {\hspace{1mm}}p{8cm}}
-  \myitemi
-  & Ken Thompson showed how to hide a Trojan Horse in a 
-  compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm]
-  \myitemi
-  & No amount of source level verification will protect 
-  you from such Thompson-hacks.\\[2mm]
-
-  \myitemi
-  & Therefore in safety-critical systems it is important to rely 
-  on only a very small TCB.
-  \end{tabular}
-  \end{column}
-  \end{columns}
-
-  \only<2>{
-  \begin{textblock}{6}(4,2)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\normalsize
-  \begin{minipage}{8cm}
-  \begin{quote}
-  \includegraphics[scale=0.05]{evil.png}
-  \begin{enumerate}
-  \item[1)] Assume you ship the compiler as binary and also with sources.
-  \item[2)] Make the compiler aware when it compiles itself.
-  \item[3)] Add the Trojan horse.
-  \item[4)] Compile.
-  \item[5)] Delete Trojan horse from the sources of the compiler.
-  \item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{}
-  \end{enumerate}
-  \end{quote}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}
-  \frametitle{\LARGE\begin{tabular}{c}An Example: Small TCB for\\[-2mm] 
-  A Critical Infrastructure\end{tabular}}
-  \mbox{}\\[-14mm]\mbox{}
-
-  \begin{columns}
-  \begin{column}{0.2\textwidth}
-  \begin{tabular}{@ {} c@ {}}
-  \includegraphics[scale=0.3]{appel.jpg}\\[-2mm] 
-  {\footnotesize Andrew Appel}\\[-2.5mm]
-  {\footnotesize (Princeton)}
-  \end{tabular}
-  \end{column}
-  
-  \begin{column}{0.8\textwidth}
-  \begin{textblock}{10}(4.5,3.95)
-  \begin{block}{Proof-Carrying Code}
-  \begin{center}
-  \begin{tikzpicture}
-  \draw[help lines,cream] (0,0.2) grid (8,4);
-  
-  \draw[line width=1mm, red] (5.5,0.6) rectangle (7.5,4);
-  \node[anchor=base] at (6.5,2.8) 
-     {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering  user needs to run untrusted code\end{tabular}};
-
-  \draw[line width=1mm, red] (0.5,0.6) rectangle (2.5,4);
-  \node[anchor=base] at (1.5,2.3) 
-     {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering  code developer/ web server/ Apple 
-  Store\end{tabular}};
-  
-  \onslide<4->{
-  \draw[line width=1mm, red, fill=red] (5.5,0.6) rectangle (7.5,1.8);
-  \node[anchor=base,white] at (6.5,1.1) 
-     {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\bf\centering proof- checker\end{tabular}};}
-
-  \node at (3.8,3.0) [single arrow, fill=red,text=white, minimum height=3cm]{\bf code};
-  \onslide<3->{
-  \node at (3.8,1.3) [single arrow, fill=red,text=white, minimum height=3cm]{\bf LF proof};
-  \node at (3.8,1.9) {\small certificate};
-  }
-
-  \onslide<2>{\node at (4.0,1.3) [text=red]{\begin{tabular}{c}\bf Highly\\\bf Dangerous!\end{tabular}};}
-  % Code Developer
-  % User (runs untrusted code)
-  % transmits a proof that the code is safe
-  % 
-  \end{tikzpicture}
-  \end{center}
-  \end{block}
-  \end{textblock}
-  \end{column}
-  \end{columns}
-  
-  \small\mbox{}\\[2.5cm]
-  \begin{itemize}
-  \item<4-> TCB of the checker is $\sim$2700 lines of code (1865 loc of\\ LF definitions; 
-  803 loc in C including 2 library functions)\\[-3mm]
-  \item<5-> 167 loc in C implement a type-checker
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-
-
-
-text {*
-  \tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex]
-  \tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick, 
-                     draw=black!50, top color=white, bottom color=black!20]
-  \tikzstyle{node2}=[rectangle, minimum size=12mm, rounded corners=3mm, very thick, 
-                     draw=red!70, top color=white, bottom color=red!50!black!20]
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}[squeeze]
-  \frametitle{Type-Checking in LF} 
-  
-  \begin{columns}
-  \begin{column}{0.2\textwidth}
-  \begin{tabular}{@ {\hspace{-4mm}}c@ {}}
-  \\[-4mm]
-  \includegraphics[scale=0.1]{harper.jpg}\\[-2mm] 
-  {\footnotesize Bob Harper}\\[-2.5mm]
-  {\footnotesize (CMU)}\\[2mm]
-
-  \includegraphics[scale=0.3]{pfenning.jpg}\\[-2mm] 
-  {\footnotesize Frank Pfenning}\\[-2.5mm]
-  {\footnotesize (CMU)}\\[2mm]
-
-  \onslide<-6>{
-  {\footnotesize 31 pages in }\\[-2.5mm]
-  {\footnotesize ACM Transact.~on}\\[-2.5mm]
-  {\footnotesize Comp.~Logic.,~2005}\\}
-  \end{tabular}
-  \end{column}
-
-  \begin{column}{0.8\textwidth}
-  \begin{textblock}{0}(3.1,2)
-
-  \begin{tikzpicture}
-  \matrix[ampersand replacement=\&,column sep=7mm, row sep=5mm]
-  { \&[-10mm] 
-    \node (def1)   [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}}; \&
-    \node (proof1) [node1] {\large Proof}; \&
-    \node (alg1)   [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}}; \\
-    
-    \onslide<4->{\node {\begin{tabular}{c}\small 1st\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
-    \onslide<4->{\node (def2)   [node2] {\large Spec$^\text{+ex}$};} \&
-    \onslide<4->{\node (proof2) [node1] {\large Proof};} \&
-    \onslide<4->{\node (alg2)   [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\
-     
-    \onslide<5->{\node {\begin{tabular}{c}\small 2nd\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
-    \onslide<5->{\node (def3)   [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \&
-    \onslide<5->{\node (proof3) [node1] {\large Proof};} \&
-    \onslide<5->{\node (alg3)   [node2] {\large Alg$^\text{-ex}$};} \\
-
-    \onslide<6->{\node {\begin{tabular}{c}\small 3rd\\[-2.5mm] \footnotesize solution\end{tabular}};} \&
-    \onslide<6->{\node (def4)   [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \&
-    \onslide<6->{\node (proof4) [node2] {\large\hspace{1mm}Proof\hspace{1mm}};} \&
-    \onslide<6->{\node (alg4)   [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\
-  };
-
-  \draw[->,black!50,line width=2mm] (proof1) -- (def1);
-  \draw[->,black!50,line width=2mm] (proof1) -- (alg1);
-  
-  \onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (def2);}
-  \onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (alg2);}
-
-  \onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (def3);}
-  \onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (alg3);}
-  
-  \onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (def4);}
-  \onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (alg4);}
-
-  \onslide<3->{\draw[white,line width=1mm] (1.1,3.2) -- (0.9,2.85) -- (1.1,2.35) -- (0.9,2.0);} 
-  \end{tikzpicture}
-
-  \end{textblock}
-  \end{column}
-  \end{columns}
-
-  \only<2>{%
-  \begin{textblock}{2}(.1,12.85)
-  \begin{tikzpicture}
-  \draw[line width=1mm, red] (0,0) ellipse (1.5cm and 0.88cm);
-  \end{tikzpicture}
-  \end{textblock}
-  }
-
-  \begin{textblock}{3}(14,3.6)
-  \onslide<4->{
-  \begin{tikzpicture}
-  \node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{2h};
-  \end{tikzpicture}}
-  \end{textblock}
-
-  \only<7->{
-  \begin{textblock}{14}(0.6,12.8)
-  \begin{block}{}
-  \small Each time one needs to check $\sim$31pp~of informal paper proofs.
-  You have to be able to keep definitions and proofs consistent.
-  \end{block}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{Theorem Provers}
-
-  \begin{itemize}
-  \item Theorem provers help with keeping large proofs consistent;
-  make them modifiable.\medskip
-  
-  \item They can ensure that all cases are covered.\medskip
-
-  \item Sometimes, tedious reasoning can be automated.
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{Theorem Provers}
-
-  \begin{itemize}
-  \item You also pay a (sometimes heavy) price: reasoning can be much, much harder.\medskip
-
-  \item Depending on your domain, suitable reasoning infrastructure
-  might not yet be available.
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{Theorem Provers}
-
-  Recently impressive work has been accomplished proving the correctness
-
-  \begin{itemize}
-  \item of a compiler for C-light (compiled code has the same observable
-  behaviour as the original source code),\medskip
-
-  \item a mirco-kernel operating system (absence of certain 
-  bugs\ldots no nil pointers, no buffer overflows).
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{Trust in Theorem Provers}
-
-  \begin{center}
-  Why should we trust theorem provers? 
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}
-  \frametitle{Theorem Provers}
-  
-   \begin{itemize}
-  \item Theorem provers are a \textcolor{red}{special kind} of software.
-  
-  \item We do \textcolor{red}{\bf not} need to trust them; we only need to trust:
-  \end{itemize}
-
-  \begin{quote}
-  \begin{itemize}
-  \item The logic they are based on \textcolor{gray}{(e.g.~HOL)}, and\smallskip
-  \item a proof checker that checks the proofs
-  \textcolor{gray}{(this can be a very small program)}.\smallskip\pause
-  \item To a little extend, we also need to trust our definitions
-  \textcolor{gray}{(this can be mitigated)}.
-  \end{itemize}
-  \end{quote}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-
-text_raw {*
-
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}
-  \frametitle{Isabelle}
-  
-  \begin{itemize}
-  \item I am using the Isabelle theorem prover (development since 1990).\bigskip\bigskip\bigskip
-  
-  \item It follows the LCF-approach:
-  
-  \begin{itemize}
-  \item Have a special abstract type \alert{\bf thm}.
-  \item Make the constructors of this abstract type the inference rules 
-  of your logic.
-  \item Implement the theorem prover in a strongly-typed language (e.g.~ML).
-  \end{itemize}
-
-  $\Rightarrow$ everything of type {\bf thm} has been proved (even if we do not
-  have to explicitly generate proofs).
-  \end{itemize}
-  
-  \only<1>{
-  \begin{textblock}{5}(11,2.3)
-  \begin{center}
-  \includegraphics[scale=0.18]{robin-milner.jpg}\\[-0.8mm]
-  \footnotesize Robin Milner\\[-0.8mm]
-  \footnotesize Turing Award, 1991\\
-  \end{center}
-  \end{textblock}}
-
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{
-  \begin{tabular}{c}
-  \mbox{}\\[23mm]
-  \LARGE Demo
-  \end{tabular}}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Future Research}
-  
-  \begin{itemize}
-  \item Make theorem provers more like a programming environment.\medskip\pause 
-
-  \item Use all the computational power we get from the hardware to
-  automate reasoning (GPUs).\medskip\pause
-
-  \item Provide a comprehensive reasoning infrastructure for many domains and 
-  design automated decision procedures. 
-  \end{itemize}\pause
-
-  
-  \begin{center}
-  \colorbox{cream}{
-  \begin{minipage}{10cm} 
-  \color{gray}
-  \small
-  ``Formal methods will never have a significant impact until
-   they can be used by people that don't understand them.''\smallskip\\
-  \mbox{}\footnotesize\hfill attributed to Tom Melham
-  \end{minipage}}
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{Conclusion}
-  
-  \begin{itemize}
-  \item The plan is to make this kind of programming the ``future''.\medskip\pause
-
-  \item Though the technology is already there\\ (compiler + micro-kernel os).\medskip\pause
-
-  \item Logic and reasoning (especially induction) are important skills for 
-  Computer Scientists.
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{
-  \begin{tabular}{c}
-  \mbox{}\\[23mm]
-  \alert{\LARGE Thank you very much!}\\
-  \alert{\Large Questions?}
-  \end{tabular}}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-(*<*)
-end
-(*>*)
\ No newline at end of file




