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{ - \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{ - \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{ - \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{ - \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{ - \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{ - \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 "\"} if (s == Nil) true else false\\ - \hspace{3mm}case (Null()::rs) @{text "\"} false\\ - \hspace{3mm}case (Empty()::rs) @{text "\"} match1 (rs, s)\\ - \hspace{3mm}case (Chr(c)::rs) @{text "\"} s match \\ - \hspace{6mm}\{ case Nil @{text "\"} false\\ - \hspace{8mm}case (d::s) @{text "\"} if (c==d) match1 (rs,s) else false \}\\ - \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\"} match1 (r1::rs, s) || match1 (r2::rs, s)\\ - \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\"} match1 (r1::r2::rs, s) \\ - \hspace{3mm}case (Star (r)::rs) @{text "\"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\ - \} - \end{tabular}} - - \end{frame}} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*} - - -text_raw {* - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \mode{ - \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{ - \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{ - \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{ - \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{ - \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{ - \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{ - \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{ - \begin{frame}<1->[c] - \frametitle{But Now What?} - - \begin{center} - {\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}} - \end{center} - - \end{frame}} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*} - -text_raw {* - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \mode{ - \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{ - \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{ - \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{ - \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{ - \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{ - \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{ - \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$2700 lines of code (1865 loc of\\ LF definitions; - 803 loc in C including 2 library functions)\\[-3mm] - \item<5-> 167 loc in C implement a type-checker - \end{itemize} - - \end{frame}} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -*} - - - -text {* - \tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex] - \tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick, - draw=black!50, top color=white, bottom color=black!20] - \tikzstyle{node2}=[rectangle, minimum size=12mm, rounded corners=3mm, very thick, - draw=red!70, top color=white, bottom color=red!50!black!20] - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \mode{ - \begin{frame}[squeeze] - \frametitle{Type-Checking in LF} - - \begin{columns} - \begin{column}{0.2\textwidth} - \begin{tabular}{@ {\hspace{-4mm}}c@ {}} - \\[-4mm] - \includegraphics[scale=0.1]{harper.jpg}\\[-2mm] - {\footnotesize Bob Harper}\\[-2.5mm] - {\footnotesize (CMU)}\\[2mm] - - \includegraphics[scale=0.3]{pfenning.jpg}\\[-2mm] - {\footnotesize Frank Pfenning}\\[-2.5mm] - {\footnotesize (CMU)}\\[2mm] - - \onslide<-6>{ - {\footnotesize 31 pages in }\\[-2.5mm] - {\footnotesize ACM Transact.~on}\\[-2.5mm] - {\footnotesize Comp.~Logic.,~2005}\\} - \end{tabular} - \end{column} - - \begin{column}{0.8\textwidth} - \begin{textblock}{0}(3.1,2) - - \begin{tikzpicture} - \matrix[ampersand replacement=\&,column sep=7mm, row sep=5mm] - { \&[-10mm] - \node (def1) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}}; \& - \node (proof1) [node1] {\large Proof}; \& - \node (alg1) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}}; \\ - - \onslide<4->{\node {\begin{tabular}{c}\small 1st\\[-2.5mm] \footnotesize solution\end{tabular}};} \& - \onslide<4->{\node (def2) [node2] {\large Spec$^\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{ - \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{ - \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{ - \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{ - \begin{frame}<1>[c] - \frametitle{Trust in Theorem Provers} - - \begin{center} - Why should we trust theorem provers? - \end{center} - - \end{frame}} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*} - -text_raw {* - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \mode{ - \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{ - \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{ - \begin{frame}<1>[c] - \frametitle{ - \begin{tabular}{c} - \mbox{}\\[23mm] - \LARGE Demo - \end{tabular}} - - \end{frame}} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*} - - -text_raw {* - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \mode{ - \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{ - \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{ - \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