--- a/Slides/Slides4.thy Sat Dec 17 16:58:11 2011 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1135 +0,0 @@
-(*<*)
-theory Slides4
-imports "~~/src/HOL/Library/LaTeXsugar" "Nominal"
-begin
-
-declare [[show_question_marks = false]]
-
-notation (latex output)
- set ("_") and
- Cons ("_::/_" [66,65] 65)
-
-(*>*)
-
-text_raw {*
- \renewcommand{\slidecaption}{Nanjing, 31.~August 2010}
-
- \newcommand{\abst}[2]{#1.#2}% atom-abstraction
- \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing
- \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions
- \newcommand{\unit}{\langle\rangle}% unit
- \newcommand{\app}[2]{#1\,#2}% application
- \newcommand{\eqprob}{\mathrel{{\approx}?}}
- \newcommand{\freshprob}{\mathrel{\#?}}
- \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction
- \newcommand{\id}{\varepsilon}% identity substitution
-
- \newcommand{\bl}[1]{\textcolor{blue}{#1}}
- \newcommand{\gr}[1]{\textcolor{gray}{#1}}
- \newcommand{\rd}[1]{\textcolor{red}{#1}}
-
- \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}}
- \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}}
- \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}}
-
- \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont}
- \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont}
- \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont}
- \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont}
-
- \newcommand{\LL}{$\mathbb{L}\,$}
-
-
- \pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}%
- {rgb(0mm)=(0,0,0.9);
- rgb(0.9mm)=(0,0,0.7);
- rgb(1.3mm)=(0,0,0.5);
- rgb(1.4mm)=(1,1,1)}
-
- \def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex}
- \usebeamercolor[fg]{subitem projected}
- {\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}}
- \pgftext{%
- \usebeamerfont*{subitem projected}}
- \end{pgfpicture}}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1>[t]
- \frametitle{%
- \begin{tabular}{@ {\hspace{-3mm}}c@ {}}
- \\
- \huge Error-Free Programming\\[-1mm]
- \huge with Theorem Provers\\[5mm]
- \end{tabular}}
- \begin{center}
- Christian Urban
- \end{center}
- \begin{center}
- \small Technical University of Munich, Germany\\[7mm]
-
- \small in Nanjing on the kind invitation of\\ Professor Xingyuan Zhang
- and his group
- \end{center}
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-*}
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{My Background}
-
- \begin{itemize}
- \item researcher in Theoretical Computer Science\medskip
-
- \item programmer on a \alert<2->{software system} with 800 kloc (though I am
- responsible only for 35 kloc)
- \end{itemize}
-
- \only<2->{
- \begin{textblock}{6}(2,11)
- \begin{tikzpicture}
- \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
- {\color{darkgray}
- \begin{minipage}{4cm}\raggedright
- A theorem prover called {\bf Isabelle}.
- \end{minipage}};
- \end{tikzpicture}
- \end{textblock}}
-
-
- \only<3>{
- \begin{textblock}{6}(9,11)
- \begin{tikzpicture}
- \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
- {\color{darkgray}
- \begin{minipage}{4cm}\raggedright
- Like every other code, this code is very hard to
- get correct.
- \end{minipage}};
- \end{tikzpicture}
- \end{textblock}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{Regular Expressions}
-
- An example many (should) know about:\\
- \rd{\bf Regular Expressions:}
-
- \only<2>{
- \begin{center}
- \bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$ r$_1$$|$r$_2$ $\;\;\;|\;\;\;$
- r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$}
- \end{center}}
- \only<3->{
- \begin{center}
- \begin{tabular}{@ {}rrll@ {}}
- \bl{r} & \bl{$::=$} & \bl{NULL} & \gr{(matches no string)}\\
- & \bl{$\mid$} & \bl{EMPTY} & \gr{(matches the empty string, [])}\\
- & \bl{$\mid$} & \bl{CHR c} & \gr{(matches the character c)}\\
- & \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\
- & \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\
- & \bl{$\mid$} & \bl{STAR r} & \gr{(repeat, r$^*$)}\\
- \end{tabular}
- \end{center}\medskip}
-
- \small
- \begin{textblock}{14.5}(1,12.5)
- \only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\}
- \only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm}
- \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
- \end{textblock}
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1>[c]
- \frametitle{RegExp Matcher}
-
- Let's implement a regular expression matcher:\bigskip
-
- \begin{center}
- \begin{tikzpicture}
- %%\draw[help lines, black] (-3,0) grid (6,3);
-
- \draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3);
- \node[anchor=base] at (2,1)
- {\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\
- \Large\bf Expression \\
- \Large\bf Matcher\end{tabular}};
-
- \coordinate (m1) at (0,1.5);
- \draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}};
- \path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1);
-
- \coordinate (s1) at (0,0.5);
- \draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}};
- \path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1);
-
- \coordinate (r1) at (4,1.2);
- \draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}};
- \path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2);
-
- \end{tikzpicture}
- \end{center}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{RegExp Matcher}
- \small
-
- {\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false
-
- \only<2->{
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
- \bl{match [] []} & \bl{$=$} & \bl{true}\\
- \bl{match [] \_} & \bl{$=$} & \bl{false}\\
- \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\
- \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
- \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\
- \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\
- \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
- & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
- \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
- \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
- & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
- \end{tabular}
- \end{center}}
-
- \onslide<3->{we start the program with\\
- \hspace{6mm}\bl{matches r s $=$ match [r] s}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1>[c]
- \frametitle{Program in Scala}
-
- \bl{\footnotesize
- \begin{tabular}{l}
- sealed abstract class Rexp\\
- sealed case class Null extends Rexp\\
- sealed case class Empty extends Rexp\\
- sealed case class Chr(c: Char) extends Rexp\\
- sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\
- sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\
- sealed case class Star(r : Rexp) extends Rexp\medskip\\
- def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\
- \hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\
- \hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\
- \hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\
- \hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\
- \hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\
- \hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\
- \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\
- \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\
- \hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\
- \}
- \end{tabular}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{Testing}
-
- \small
- Every good programmer should do thourough tests:
-
-
- \begin{center}
- \begin{tabular}{@ {\hspace{-20mm}}lcl}
- \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\
- \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
- \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}}\\
- \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}}\\
- \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}}
- \end{tabular}
- \end{center}
-
- \onslide<3->
- {looks OK \ldots let's ship it to customers\hspace{5mm}
- \raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{Testing}
-
- \begin{itemize}
- \item While testing is an important part in the process of programming development\pause
-
- \item we can only test a {\bf finite} amount of examples\bigskip\pause
-
- \begin{center}
- \colorbox{cream}
- {\gr{\begin{minipage}{10cm}
- ``Testing can only show the presence of errors, never their
- absence'' (Edsger W.~Dijkstra)
- \end{minipage}}}
- \end{center}\bigskip\pause
-
- \item In a theorem prover we can establish properties that apply to
- {\bf all} input and {\bf all} output.\pause
-
- \item For example we can establish that the matcher terminates
- on all input.
- \end{itemize}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{RegExp Matcher}
-
- \small
- We need to find a measure that gets smaller in each recursive call.\bigskip
-
- \onslide<1->{
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}}
- \bl{match [] []} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
- \bl{match [] \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
- \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
- \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\
- \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\
- \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
- \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\
- & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
- \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s} & \onslide<6->{\ok}\\
- \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\
- & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
- \end{tabular}
- \end{center}}
-
-
- \begin{textblock}{5}(4,4)
- \begin{tikzpicture}
- %%\draw[help lines, black] (-3,0) grid (6,3);
-
- \coordinate (m1) at (-2,0);
- \coordinate (m2) at ( 2,0);
- \path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2);
- \draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}};
- \end{tikzpicture}
- \end{textblock}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{Bug Hunting}
-
- \only<1>{Several hours later\ldots}\pause
-
-
- \begin{center}
- \begin{tabular}{@ {\hspace{-20mm}}lcl}
- \bl{matches (STAR (EMPTY)) s} & \bl{$\mapsto$} & loops\\
- \onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s} & \bl{$\mapsto$} & loops\\}
- \end{tabular}
- \end{center}
-
- \small
- \onslide<3->{
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
- \ldots\\
- \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
- \ldots\\
- \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
- & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
- \end{tabular}
- \end{center}}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{RegExp Matcher}
- \small
-
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
- \bl{match [] []} & \bl{$=$} & \bl{true}\\
- \bl{match [] \_} & \bl{$=$} & \bl{false}\\
- \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\
- \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\
- \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\
- \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\
- \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\
- & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\
- \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\
- \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\
- & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\
- \end{tabular}
- \end{center}
-
- \only<1>{
- \begin{textblock}{5}(4,4)
- \largenotok
- \end{textblock}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{Second Attempt}
-
- Can a regular expression match the empty string?
-
- \small
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
- \bl{nullable (NULL)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
- \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
- \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\
- \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)}
- & \onslide<2->{\ok}\\
- \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)}
- & \onslide<2->{\ok}\\
- \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\
- \end{tabular}
- \end{center}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{RegExp Matcher 2}
-
- If \bl{r} matches \bl{c::s}, which regular expression can match the string \bl{s}?
-
- \small
- \begin{center}
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
- \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
- \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\
- \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \onslide<3->{\ok}\\
- \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \onslide<3->{\ok}\\
- \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \onslide<3->{\ok}\\
- & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
- \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} & \onslide<3->{\ok}\medskip\\
- \pause
-
- \bl{derivative r []} & \bl{$=$} & \bl{r} & \onslide<3->{\ok}\\
- \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \onslide<3->{\ok}\\
- \end{tabular}
- \end{center}
-
- we call the program with\\
- \bl{matches r s $=$ nullable (derivative r s)}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{But Now What?}
-
- \begin{center}
- {\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}}
- \end{center}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{Testing}
-
- \small
-
- \begin{center}
- \begin{tabular}{@ {\hspace{-20mm}}lcl}
- \bl{matches []$^*$ []} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches ([]$|$a)$^*$ a} & \bl{$\mapsto$} & \bl{true}\medskip\\
-
- \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\
- \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\
-
- \bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}\\
- \bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}
- \end{tabular}
- \end{center}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{Specification}
-
- We have to specify what it means for a regular expression to match
- a string.
- %
- \only<2>{
- \mbox{}\\[8mm]
- \bl{(a$\cdot$b)$^*$}\\
- \hspace{7mm}\bl{$\mapsto$\hspace{3mm}\{[], ab, abab, ababab, \ldots\}}\bigskip\\
- \bl{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9 )$^*$}\\
- \hspace{7mm}\bl{$\mapsto$\hspace{3mm}
- \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}}
- %
- \only<3->{
- \begin{center}
- \begin{tabular}{rcl}
- \bl{\LL (NULL)} & \bl{$\dn$} & \bl{\{\}}\\
- \bl{\LL (EMPTY)} & \bl{$\dn$} & \bl{\{[]\}}\\
- \bl{\LL (CHR c)} & \bl{$\dn$} & \bl{\{c\}}\\
- \bl{\LL (ALT r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<4->{\bl{\LL (r$_1$) $\cup$ \LL (r$_2$)}}\\
- \bl{\LL (SEQ r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<6->{\bl{\LL (r$_1$) ; \LL (r$_2$)}}\\
- \bl{\LL (STAR r)} & \bl{$\dn$} & \onslide<8->{\bl{(\LL (r))$^\star$}}\\
- \end{tabular}
- \end{center}}
-
- \only<5-6>{
- \begin{textblock}{6}(2.9,13.3)
- \colorbox{cream}{\bl{S$_1$ ; S$_2$ $\;\dn\;$ \{ s$_1$@s$_2$ $|$ s$_1$$\in$S$_1$ $\wedge$
- s$_2$$\in$S$_2$ \}}}
- \end{textblock}}
-
- \only<7->{
- \begin{textblock}{9}(4,13)
- \colorbox{cream}{\bl{$\infer{\mbox{[]} \in \mbox{S}^\star}{}$}}\hspace{3mm}
- \colorbox{cream}{\bl{$\infer{\mbox{s}_1\mbox{@}\mbox{s}_2 \in \mbox{S}^\star}
- {\mbox{s}_1 \in \mbox{S} & \mbox{s}_2 \in \mbox{S}^\star}$}}
- \end{textblock}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
- \frametitle{Is the Matcher Error-Free?}
-
- We expect that
-
- \begin{center}
- \begin{tabular}{lcl}
- \bl{matches r s = true} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}%
- \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\in$ \LL(r)}\\
- \bl{matches r s = false} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}%
- \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\notin$ \LL(r)}\\
- \end{tabular}
- \end{center}
- \pause\pause\bigskip
- By \alert<4->{induction}, we can {\bf prove} these properties.\bigskip
-
- \begin{tabular}{lrcl}
- Lemmas: & \bl{nullable (r)} & \bl{$\Longleftrightarrow$} & \bl{[] $\in$ \LL (r)}\\
- & \bl{s $\in$ \LL (der c r)} & \bl{$\Longleftrightarrow$} & \bl{(c::s) $\in$ \LL (r)}\\
- \end{tabular}
-
- \only<4->{
- \begin{textblock}{3}(0.9,4.5)
- \rd{\huge$\forall$\large{}r s.}
- \end{textblock}}
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[t]
-
- \mbox{}\\[-2mm]
-
- \small
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}}
- \bl{nullable (NULL)} & \bl{$=$} & \bl{false} &\\
- \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} &\\
- \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} &\\
- \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} & \\
- \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} & \\
- \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \\
- \end{tabular}\medskip
-
- \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
- \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \\
- \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \\
- \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \\
- \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \\
- \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \\
- & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\
- \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} &\smallskip\\
-
- \bl{derivative r []} & \bl{$=$} & \bl{r} & \\
- \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \\
- \end{tabular}\medskip
-
- \bl{matches r s $=$ nullable (derivative r s)}
-
- \only<2>{
- \begin{textblock}{8}(1.5,4)
- \includegraphics[scale=0.3]{approved.png}
- \end{textblock}}
-
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1->[c]
- \frametitle{Interlude: TCB}
-
- \begin{itemize}
- \item The \alert{\bf Trusted Code Base} (TCB) is the code that can make your
- program behave in unintended ways (i.e.~cause bugs).\medskip
-
- \item Typically the TCB includes: CPUs, operating systems, C-libraries,
- device drivers, (J)VMs\ldots\bigskip
- \pause
-
- \item It also includes the compiler.
- \end{itemize}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-*}
-
-text_raw {*
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}<1-3>
- \frametitle{\LARGE\begin{tabular}{c}Hacking Compilers
- \end{tabular}}
-
- %Why is it so paramount to have a small trusted code base (TCB)?
- \bigskip\bigskip
-
- \begin{columns}
- \begin{column}{2.7cm}
- \begin{minipage}{2.5cm}%
- \begin{tabular}{c@ {}}
- \includegraphics[scale=0.2]{ken-thompson.jpg}\\[-1.8mm]
- \footnotesize Ken Thompson\\[-1.8mm]
- \footnotesize Turing Award, 1983\\
- \end{tabular}
- \end{minipage}
- \end{column}
- \begin{column}{9cm}
- \begin{tabular}{l@ {\hspace{1mm}}p{8cm}}
- \myitemi
- & Ken Thompson showed how to hide a Trojan Horse in a
- compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm]
- \myitemi
- & No amount of source level verification will protect
- you from such Thompson-hacks.\\[2mm]
-
- \myitemi
- & Therefore in safety-critical systems it is important to rely
- on only a very small TCB.
- \end{tabular}
- \end{column}
- \end{columns}
-
- \only<2>{
- \begin{textblock}{6}(4,2)
- \begin{tikzpicture}
- \draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
- {\normalsize
- \begin{minipage}{8cm}
- \begin{quote}
- \includegraphics[scale=0.05]{evil.png}
- \begin{enumerate}
- \item[1)] Assume you ship the compiler as binary and also with sources.
- \item[2)] Make the compiler aware when it compiles itself.
- \item[3)] Add the Trojan horse.
- \item[4)] Compile.
- \item[5)] Delete Trojan horse from the sources of the compiler.
- \item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{}
- \end{enumerate}
- \end{quote}
- \end{minipage}};
- \end{tikzpicture}
- \end{textblock}}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-*}
-
-text_raw {*
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \mode<presentation>{
- \begin{frame}
- \frametitle{\LARGE\begin{tabular}{c}An Example: Small TCB for\\[-2mm]
- A Critical Infrastructure\end{tabular}}
- \mbox{}\\[-14mm]\mbox{}
-
- \begin{columns}
- \begin{column}{0.2\textwidth}
- \begin{tabular}{@ {} c@ {}}
- \includegraphics[scale=0.3]{appel.jpg}\\[-2mm]
- {\footnotesize Andrew Appel}\\[-2.5mm]
- {\footnotesize (Princeton)}
- \end{tabular}
- \end{column}
-
- \begin{column}{0.8\textwidth}
- \begin{textblock}{10}(4.5,3.95)
- \begin{block}{Proof-Carrying Code}
- \begin{center}
- \begin{tikzpicture}
- \draw[help lines,cream] (0,0.2) grid (8,4);
-
- \draw[line width=1mm, red] (5.5,0.6) rectangle (7.5,4);
- \node[anchor=base] at (6.5,2.8)
- {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering user needs to run untrusted code\end{tabular}};
-
- \draw[line width=1mm, red] (0.5,0.6) rectangle (2.5,4);
- \node[anchor=base] at (1.5,2.3)
- {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering code developer/ web server/ Apple
- Store\end{tabular}};
-
- \onslide<4->{
- \draw[line width=1mm, red, fill=red] (5.5,0.6) rectangle (7.5,1.8);
- \node[anchor=base,white] at (6.5,1.1)
- {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\bf\centering proof- checker\end{tabular}};}
-
- \node at (3.8,3.0) [single arrow, fill=red,text=white, minimum height=3cm]{\bf code};
- \onslide<3->{
- \node at (3.8,1.3) [single arrow, fill=red,text=white, minimum height=3cm]{\bf LF proof};
- \node at (3.8,1.9) {\small certificate};
- }
-
- \onslide<2>{\node at (4.0,1.3) [text=red]{\begin{tabular}{c}\bf Highly\\\bf Dangerous!\end{tabular}};}
- % Code Developer
- % User (runs untrusted code)
- % transmits a proof that the code is safe
- %
- \end{tikzpicture}
- \end{center}
- \end{block}
- \end{textblock}
- \end{column}
- \end{columns}
-
- \small\mbox{}\\[2.5cm]
- \begin{itemize}
- \item<4-> TCB of the checker is $\sim$2700 lines of code (1865 loc of\\ LF definitions;
- 803 loc in C including 2 library functions)\\[-3mm]
- \item<5-> 167 loc in C implement a type-checker
- \end{itemize}
-
- \end{frame}}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-*}
-
-
-
-text {*
- \tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex]
- \tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick,
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- \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}
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-
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-
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- \onslide<4->{
- \begin{tikzpicture}
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- \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