# HG changeset patch # User Christian Urban # Date 1283259788 -28800 # Node ID ac3470e1e5af4109abfb7e62804bd6309d215b52 # Parent 0bc1db726f81c7438193a15ccfcba610b94326a8 slides of my talk diff -r 0bc1db726f81 -r ac3470e1e5af IsaMakefile --- a/IsaMakefile Mon Aug 30 11:02:13 2010 +0900 +++ b/IsaMakefile Tue Aug 31 21:03:08 2010 +0800 @@ -95,7 +95,18 @@ cd Slides/generated3 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex cp Slides/generated3/root.beamer.pdf Slides/slides3.pdf -slides: slides1 +session4: Slides/ROOT4.ML \ + Slides/document/root* \ + Slides/Slides4.thy + @$(USEDIR) -D generated4 -f ROOT4.ML HOL-Nominal Slides + +slides4: session4 + rm -f Slides/generated4/*.aux # otherwise latex will fall over + cd Slides/generated4 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex + cd Slides/generated4 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex + cp Slides/generated4/root.beamer.pdf Slides/slides4.pdf + +slides: slides4 diff -r 0bc1db726f81 -r ac3470e1e5af Slides/ROOT4.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Slides/ROOT4.ML Tue Aug 31 21:03:08 2010 +0800 @@ -0,0 +1,6 @@ +show_question_marks := false; +quick_and_dirty := true; + +no_document use_thy "LaTeXsugar"; + +use_thy "Slides4" \ No newline at end of file diff -r 0bc1db726f81 -r ac3470e1e5af Slides/Slides4.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Slides/Slides4.thy Tue Aug 31 21:03:08 2010 +0800 @@ -0,0 +1,1133 @@ +(*<*) +theory Slides4 +imports "LaTeXsugar" "Nominal" +begin + +notation (latex output) + set ("_") and + Cons ("_::/_" [66,65] 65) + +(*>*) + +text_raw {* + \renewcommand{\slidecaption}{Nanjing, 31.~August 2010} + + \newcommand{\abst}[2]{#1.#2}% atom-abstraction + \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing + \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions + \newcommand{\unit}{\langle\rangle}% unit + \newcommand{\app}[2]{#1\,#2}% application + \newcommand{\eqprob}{\mathrel{{\approx}?}} + \newcommand{\freshprob}{\mathrel{\#?}} + \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction + \newcommand{\id}{\varepsilon}% identity substitution + + \newcommand{\bl}[1]{\textcolor{blue}{#1}} + \newcommand{\gr}[1]{\textcolor{gray}{#1}} + \newcommand{\rd}[1]{\textcolor{red}{#1}} + + \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}} + \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}} + \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}} + + \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont} + \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont} + \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont} + \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont} + + \newcommand{\LL}{$\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{ + \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