--- a/slides/slides05.tex Tue Oct 29 10:33:21 2013 +0000
+++ b/slides/slides05.tex Tue Oct 29 12:09:44 2013 +0000
@@ -1,8 +1,8 @@
\documentclass[dvipsnames,14pt,t]{beamer}
\usepackage{proof}
\usepackage{beamerthemeplaincu}
-%\usepackage[T1]{fontenc}
-%\usepackage[latin1]{inputenc}
+\usepackage{fontenc}
+\usepackage[latin1]{inputenc}
\usepackage{mathpartir}
\usepackage{isabelle}
\usepackage{isabellesym}
@@ -15,6 +15,7 @@
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
\usepackage{graphicx}
+\setmonofont{Consolas}
\isabellestyle{rm}
\renewcommand{\isastyle}{\rm}%
@@ -35,27 +36,19 @@
\renewcommand{\isasymsharp}{\isamath{\#}}
\renewcommand{\isasymdots}{\isamath{...}}
\renewcommand{\isasymbullet}{\act}
-
-
+\newcommand{\isaliteral}[1]{}
+\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
\definecolor{javared}{rgb}{0.6,0,0} % for strings
\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
-\lstset{language=Java,
- basicstyle=\ttfamily,
- keywordstyle=\color{javapurple}\bfseries,
- stringstyle=\color{javagreen},
- commentstyle=\color{javagreen},
- morecomment=[s][\color{javadocblue}]{/**}{*/},
- numbers=left,
- numberstyle=\tiny\color{black},
- stepnumber=1,
- numbersep=10pt,
- tabsize=2,
- showspaces=false,
- showstringspaces=false}
+\makeatletter
+\lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}}
+\@empty\z@\@empty
+\makeatother
+
\lstdefinelanguage{scala}{
morekeywords={abstract,case,catch,class,def,%
@@ -74,6 +67,18 @@
morestring=[b]"""
}
+\lstdefinelanguage{while}{
+ morekeywords={while, if, then. else, read, write},
+ otherkeywords={=>,<-,<\%,<:,>:,\#,@},
+ sensitive=true,
+ morecomment=[l]{//},
+ morecomment=[n]{/*}{*/},
+ morestring=[b]",
+ morestring=[b]',
+ morestring=[b]"""
+}
+
+
\lstset{language=Scala,
basicstyle=\ttfamily,
keywordstyle=\color{javapurple}\bfseries,
@@ -87,6 +92,7 @@
tabsize=2,
showspaces=false,
showstringspaces=false}
+
% beamer stuff
\renewcommand{\slidecaption}{APP 05, King's College London, 29 October 2013}
@@ -546,6 +552,781 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{\Large\begin{tabular}{@ {}c@ {}}Logic(s)\end{tabular}}
+
+ \begin{itemize}
+ \item Formulas
+
+ \begin{center}\color{blue}
+ \begin{tabular}{rcl@ {\hspace{10mm}}l}
+ \isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F} & \textcolor{black}{implies}\\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ F} & \textcolor{black}{negation}\\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} & \textcolor{black}{predicates}\\
+ & \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}} &
+ \onslide<2->{\textcolor{black}{forall quantification}}\\
+ & \onslide<2->{\isa{{\isaliteral{7C}{\isacharbar}}}} & \onslide<2->{\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ F}} &
+ \onslide<2->{\textcolor{black}{exists quantification}}\\[-7mm]
+ \end{tabular}
+ \end{center}
+
+ \end{itemize}
+
+ \begin{textblock}{12}(1,14)
+ Terms \textcolor{blue}{\isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ c\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}}
+ \end{textblock}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{../programs/formulas.scala}}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Judgements}
+
+ \begin{center}
+ \LARGE
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}
+ \end{center}
+
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}} is a collection of formulas, called the \alert{assumptions}\bigskip\pause
+
+ \begin{itemize}
+ \item Example\mbox{}\\[-3mm]
+
+ \only<2>{\begin{center}\tiny
+ \textcolor{blue}{
+ \begin{tabular}{l}
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
+ \end{tabular}\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
+ \end{center}}
+ \only<3>{\small
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
+ {\mbox{\begin{tabular}{@ {}l@ {}}
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
+ \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
+ \end{tabular}}
+ }
+ }
+ \end{center}
+ }}
+ \only<4>{\small
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
+ {\mbox{\begin{tabular}{@ {}l@ {}}
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
+ \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
+ \end{tabular}}
+ }
+ }
+ \end{center}
+ }}
+
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{../programs/judgement.scala}}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Inference Rules}
+
+ \textcolor{blue}{
+ \begin{center}
+ \Large
+ \mbox{
+ \infer{\mbox{\isa{conclusion}}}
+ {\mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}} & \mbox{\isa{premise\isaliteral{5C3C5E697375623E}{}\isactrlisub n}}}}
+ \end{center}}
+
+ The conlusion and premises are judgements\bigskip\pause
+
+ \begin{itemize}
+ \item Examples
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
+ \end{center}}\pause
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
+ \hspace{10mm}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
+ \end{center}}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Implication}
+ \Large
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}}
+ \end{center}}
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Universal Quantification}
+ \Large
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F{\isaliteral{5B}{$\isacharbrackleft$}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{5D}{$\isacharbrackright$}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ F}}}}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Start Rules / Axioms}
+
+ \normalsize
+ \alert{if \textcolor{blue}{\isa{F\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}}
+
+ \textcolor{blue}{\Large
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
+ \end{center}}\bigskip\pause
+
+ \normalsize
+ Also written as:
+ \textcolor{blue}{\Large
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{2C}{\isacharcomma}}\ F\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}{}}
+ \end{center}}\pause
+
+ \textcolor{blue}{\Large
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ true}}}{}}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{}
+
+ \begin{minipage}{1.1\textwidth}
+ Let \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\footnotesize\begin{tabular}{l}
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
+ \end{tabular}}
+ \end{minipage}
+
+ \only<2>{
+ \begin{textblock}{12}(4,3)\footnotesize
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}\hspace{10mm}
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
+ \end{textblock}}
+
+ \only<3->{
+ \begin{textblock}{12}(4,3)\footnotesize
+ \mbox{\textcolor{blue}{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}} &\hspace{10mm}
+ \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
+ }}
+ \end{textblock}}
+
+ \only<4>{
+ \begin{textblock}{14}(0.5,6)\footnotesize
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}
+ \end{textblock}}
+
+ \only<5->{
+ \begin{textblock}{14}(0.5,6)\footnotesize
+ \textcolor{blue}{
+ \infer{\mbox{\begin{tabular}{l}\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\\
+ \hspace{40mm}\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}\end{tabular}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}}}}
+ \end{textblock}}
+
+ \only<6->{
+ \begin{textblock}{14}(5,10)\footnotesize
+ \textcolor{blue}{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}}
+ {\vdots & \hspace{30mm} \vdots}}
+ \end{textblock}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Access Control}
+ \Large
+
+ \textcolor{blue}{
+ \begin{center}
+ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}
+ \end{center}}\bigskip
+
+ \normalsize
+ \begin{itemize}
+ \item If there is a proof \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} yes (granted)
+ \item If there isn't \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} no (denied)
+ \end{itemize}\bigskip\pause
+
+\begin{minipage}{1.1\textwidth}
+ \small
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}at{\isaliteral{5F}{\isacharunderscore}}library\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}\\
+ \end{tabular}}\medskip
+
+ \textcolor{blue}{
+ \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} $\not\vdash$ \isa{may{\isaliteral{5F}{\isacharunderscore}}obtain{\isaliteral{5F}{\isacharunderscore}}email\ {\isaliteral{28}{\isacharparenleft}}Alice{\isaliteral{29}{\isacharparenright}}}}}
+\end{minipage}
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{The Access Control Problem}
+
+
+\begin{center}
+ \begin{tikzpicture}[scale=1]
+
+ \draw[line width=1mm] (-.3, 0) rectangle (1.5,2);
+ \draw (-2.7,1) node {\begin{tabular}{l}access\\request\\ (\bl{$F$})\end{tabular}};
+ \draw (4.2,1) node {\begin{tabular}{l}granted/\\not granted\end{tabular}};
+ \draw (0.6,1.2) node {\footnotesize \begin{tabular}{l}Access\\Control\\Checker\end{tabular}};
+
+ \draw[red, ->, line width = 2mm] (1.7,1) -- (2.7,1);
+ \draw[red,<-, line width = 2mm] (-0.6,1) -- (-1.6,1);
+ \draw[red, <-, line width = 3mm] (0.6,2.2) -- (0.6,3.2);
+
+ \draw (0.6,4) node {\begin{tabular}{l}\large Access Policy (\bl{$\Gamma$})\end{tabular}};
+
+ \end{tikzpicture}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Bad News}
+
+ \begin{itemize}
+ \item We introduced (roughly) first-order logic. \bigskip\pause
+
+ \item Judgements
+ \begin{center}
+ \textcolor{blue}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
+ \end{center}
+
+ are in general \alert{undecidable}.\pause\medskip\\
+
+ The problem is \alert{semi-decidable}.
+
+ \end{itemize}
+
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{\Large\begin{tabular}{@ {}c@ {}}Access Control Logic\end{tabular}}
+
+ \begin{itemize}
+ \item[]
+
+ \begin{center}\color{blue}
+ \begin{tabular}[t]{rcl@ {\hspace{10mm}}l}
+ \isa{F} & \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}} & \isa{true} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{false} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ F} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C6F723E}{\isasymor}}\ F} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{F\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}\\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \isa{p\ {\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}t\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} \\
+ & \isa{{\isaliteral{7C}{\isacharbar}}} & \alert{\isa{P\ says\ F}} & \textcolor{black}{``saying predicate''}\\
+ \end{tabular}
+ \end{center}\medskip
+
+ where \textcolor{blue}{\isa{P\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ Alice{\isaliteral{2C}{\isacharcomma}}\ Bob{\isaliteral{2C}{\isacharcomma}}\ Christian{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}} (principals)\bigskip\pause
+
+ \item \textcolor{blue}{\isa{HoD\ says\ is{\isaliteral{5F}{\isacharunderscore}}staff\ {\isaliteral{28}{\isacharparenleft}}Christian{\isaliteral{29}{\isacharparenright}}}}
+ \end{itemize}
+
+
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{../programs/formulas1.scala}}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{Rules about Says}
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}
+ \end{center}}
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{10mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
+ \end{center}}
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}}}}}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{}
+
+ Consider the following scenario:
+
+ \begin{itemize}
+ \item If \textcolor{blue}{Admin} says that \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
+ should be deleted, then this file must be deleted.
+ \item \textcolor{blue}{Admin} trusts \textcolor{blue}{Bob} to decide whether
+ \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}} should be deleted.
+ \item \textcolor{blue}{Bob} wants to delete \textcolor{blue}{\isa{file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}.
+ \end{itemize}\bigskip\pause
+
+ \small
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
+ \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
+ \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
+ \end{tabular}}\medskip\pause
+
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{}
+
+ \textcolor{blue}{
+ \begin{center}
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}}\\\bigskip
+ \mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ {\isaliteral{28}{\isacharparenleft}}F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}} & \hspace{5mm}\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}}}
+ \end{center}}\bigskip
+
+ \small
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}}\small\begin{tabular}{l}
+ \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}},\\
+ \isa{{\isaliteral{28}{\isacharparenleft}}Admin\ says\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}},\\
+ \isa{Bob\ says\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}\\
+ \end{tabular}}\medskip
+
+ \textcolor{blue}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ del{\isaliteral{5F}{\isacharunderscore}}file\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}}
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[t]
+ \frametitle{}
+ \small
+
+ \textcolor{blue}{
+ \begin{center}
+ \only<1>{$ \underbrace{
+ \mbox{\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file)}}
+ {\infer{\Gamma \vdash \mbox{Bob says del\_file}}{}}}}_{X}$}
+ \end{center}}
+
+ \textcolor{blue}{
+ \begin{center}
+ \only<1>{
+ $ \underbrace{
+ \mbox{\infer{\Gamma \vdash \mbox{Admin says del\_file}}
+ {\infer{\Gamma \vdash \mbox{Admin says (Bob says del\_file \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file)}}{}
+ &
+ \deduce[$\vdots$]{X}{}
+ }}}_{Y}$}
+ \end{center}}
+
+ \textcolor{blue}{
+ \begin{center}
+ \only<1>{\mbox{\infer{\Gamma \vdash \mbox{del\_file}}
+ {\infer{\Gamma \vdash \mbox{(Admin says del\_file) \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} del\_file}}{}
+ &
+ \deduce[$\vdots$]{Y}{}
+ }}}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Controls}
+ \small
+
+ \begin{itemize}
+ \item \bl{\isa{P\ controls\ F\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}}
+
+ \item its meaning ``\bl{P} is entitled to do \bl{F}''
+ \item if \bl{P controls F} and \bl{P says F} then \bl{F}\pause
+
+ \begin{center}
+ \bl{\mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ }}
+ \end{center}\pause
+
+ \begin{center}
+ \bl{\mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ F}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ }}
+ \end{center}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Speaks For}
+ \small
+
+ \begin{itemize}
+ \item \bl{\isa{P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}F{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}P\ says\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Q\ says\ F{\isaliteral{29}{\isacharparenright}}}}
+
+ \item its meaning ``\bl{P} speaks for \bl{Q}''
+
+
+ \begin{center}
+ \bl{\mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ says\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ says\ F}}}
+ }}
+ \end{center}\pause
+
+ \begin{center}
+ \bl{\mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ controls\ F}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ controls\ F}}}
+ }}
+ \end{center}
+
+ \begin{center}
+ \bl{\mbox{
+ \infer{\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
+ {\mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ Q}} & \mbox{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ Q\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ R}}}
+ }}
+ \end{center}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Security Levels}
+ \small
+
+ \begin{itemize}
+ \item Top secret (\bl{$T\!S$})
+ \item Secret (\bl{$S$})
+ \item Public (\bl{$P$})
+ \end{itemize}
+
+ \begin{center}
+ \bl{$slev(P) < slev(S) < slev(T\!S)$}\pause
+ \end{center}
+
+ \begin{itemize}
+ \item Bob has a clearance for ``secret''
+ \item Bob can read documents that are public or sectret, but not top secret
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Reading a File}
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ \begin{tabular}{@ {}l@ {}}
+ \only<2->{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$}}\\
+ \only<2->{\hspace{3cm}}Bob controls Permitted $($File, read$)$\\
+ Bob says Permitted $($File, read$)$\only<2->{\\}
+ \only<2>{\textcolor{red}{$slev($File$)$ $<$ $slev($Bob$)$}}%
+ \only<3>{\textcolor{red}{$slev($File$)$ $=$ $P$}\\}%
+ \only<3>{\textcolor{red}{$slev($Bob$)$ $=$ $S$}\\}%
+ \only<3>{\textcolor{red}{$slev(P)$ $<$ $slev(S)$}\\}%
+ \end{tabular}\\
+ \hline
+ Permitted $($File, read$)$
+ \end{tabular}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Substitution Rule}
+ \small
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ $\Gamma \vdash slev(P) = l_1$ \hspace{4mm} $\Gamma \vdash slev(Q) = l_2$
+ \hspace{4mm} $\Gamma \vdash l_1 < l_2$\\\hline
+ $\Gamma \vdash slev(P) < slev(Q)$
+ \end{tabular}
+ \end{center}}\bigskip\pause
+
+ \begin{itemize}
+ \item \bl{$slev($Bob$)$ $=$ $S$}
+ \item \bl{$slev($File$)$ $=$ $P$}
+ \item \bl{$slev(P) < slev(S)$}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Reading a File}
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ \begin{tabular}{@ {}l@ {}}
+ $slev($File$)$ $<$ $slev($Bob$)$ $\Rightarrow$\\
+ \hspace{3cm}Bob controls Permitted $($File, read$)$\\
+ Bob says Permitted $($File, read$)$\\
+ $slev($File$)$ $=$ $P$\\
+ $slev($Bob$)$ $=$ $T\!S$\\
+ \only<1>{\textcolor{red}{$?$}}%
+ \only<2>{\textcolor{red}{$slev(P) < slev(S)$}\\}%
+ \only<2>{\textcolor{red}{$slev(S) < slev(T\!S)$}}%
+ \end{tabular}\\
+ \hline
+ Permitted $($File, read$)$
+ \end{tabular}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Transitivity Rule}
+ \small
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ $\Gamma \vdash l_1 < l_2$
+ \hspace{4mm} $\Gamma \vdash l_2 < l_3$\\\hline
+ $\Gamma \vdash l_1 < l_3$
+ \end{tabular}
+ \end{center}}\bigskip
+
+ \begin{itemize}
+ \item \bl{$slev(P) < slev (S)$}
+ \item \bl{$slev(S) < slev (T\!S)$}
+ \item[] \bl{$slev(P) < slev (T\!S)$}
+ \end{itemize}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Reading Files}
+
+ \begin{itemize}
+ \item Access policy for reading
+ \end{itemize}
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ \begin{tabular}{@ {}l@ {}}
+ $\forall f.\;slev(f)$ \only<1>{$<$}\only<2>{\textcolor{red}{$\le$}} $slev($Bob$)$ $\Rightarrow$\\
+ \hspace{3cm}Bob controls Permitted $(f$, read$)$\\
+ Bob says Permitted $($File, read$)$\\
+ $slev($File$)$ $=$ \only<1>{$P$}\only<2>{\textcolor{red}{$T\!S$}}\\
+ $slev($Bob$)$ $=$ $T\!S$\\
+ $slev(P) < slev(S)$\\
+ $slev(S) < slev(T\!S)$
+ \end{tabular}\\
+ \hline
+ Permitted $($File, read$)$
+ \end{tabular}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \mode<presentation>{
+ \begin{frame}[c]
+ \frametitle{Writing Files}
+
+ \begin{itemize}
+ \item Access policy for \underline{writing}
+ \end{itemize}
+
+ \bl{\begin{center}
+ \begin{tabular}{c}
+ \begin{tabular}{@ {}l@ {}}
+ $\forall f.\;slev($Bob$)$ $\le$ $slev(f)$ $\Rightarrow$\\
+ \hspace{3cm}Bob controls Permitted $(f$, write$)$\\
+ Bob says Permitted $($File, write$)$\\
+ $slev($File$)$ $=$ $T\!S$\\
+ $slev($Bob$)$ $=$ $S$\\
+ $slev(P) < slev(S)$\\
+ $slev(S) < slev(T\!S)$
+ \end{tabular}\\
+ \hline
+ Permitted $($File, write$)$
+ \end{tabular}
+ \end{center}}
+
+ \end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
\end{document}