--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/Slides4.thy Tue Aug 31 21:03:08 2010 +0800
@@ -0,0 +1,1133 @@
+(*<*)
+theory Slides4
+imports "LaTeXsugar" "Nominal"
+begin
+
+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