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+% latex main
+% dvips -Pprosper -o main.ps main.dvi
+% ps2pdf main.ps main.pdf
+\documentclass[pdf,nototal,myframes,slideColor,colorBG]{prosper}
+
+\usepackage{pstricks,pst-node,pst-text,pst-3d}
+\usepackage[latin1]{inputenc}
+\usepackage{amsmath}
+
+
+\usepackage{graphicx,color,latexsym}
+
+\newenvironment{cslide}[1]{\begin{slide}{\blue #1}}{\end{slide}}
+\newcommand{\emcolorbox}[1]{\colorbox{yellow}{#1}}
+
+\slideCaption{}
+
+\begin{document}
+
+\title{Isabelle/HOL --- A Practical Introduction}
+\author{Tobias Nipkow
+\\{\small joint work with Larry Paulson and Markus Wenzel}
+}
+\institution{Technische Universität München
+\\ \vspace{0.5cm}\includegraphics[scale=.4]{isabelle_hol}
+}
+\maketitle
+
+%-----------------------------------------------------------------------------
+\begin{cslide}{What is {\blue Isabelle}?}
+\begin{itemize}
+\item A \emph{logical framwork}
+\item A generic theorem prover
+\item A system for implementing proof assistants
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\overlays{5}{
+\begin{cslide}{What is {\blue Isabelle/HOL}?}
+\FromSlide{2}
+\begin{itemize}
+\item An interactive proof assistant
+\FromSlide{3}
+\item {\small for higher-order logic}
+\FromSlide{4}
+\item Similar to HOL, PVS, Coq, \dots
+\FromSlide{5}
+\item But different enough (e.g. \emph{structured proofs})
+\end{itemize}
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\overlays{2}{
+\begin{cslide}{Why Theorem Proving/Verification/\dots?}
+\FromSlide{2}
+\vfill
+\begin{center}
+\Large \emph{\red Because!}
+\end{center}
+\vfill
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\overlays{2}{
+\begin{cslide}{Overview of course}
+\begin{enumerate}
+\item Introduction to Isabelle/HOL (LNCS 2283)
+\begin{itemize}
+\item Definitions (datatypes, functions, relations, \dots)
+\item Proofs (tactic style)
+\end{itemize}
+\FromSlide{2}
+\item Structured proofs (\emph{Isar})
+\end{enumerate}
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\overlays{2}{
+\begin{cslide}{Proof styles}
+\begin{tabular}{cc}
+\begin{tabular}{l}
+\texttt{apply(induct\_tac $x$)}\\
+\texttt{apply simp}\\
+\texttt{apply(rule allI)+}\\
+\texttt{apply assumption}\\
+\vdots
+\end{tabular}
+&
+\FromSlide{2}
+\begin{tabular}{l}
+\texttt{proof (induct $x$)}\\
+\quad \texttt{show $P(0)$ by simp}\\
+\texttt{next}\\
+\quad \texttt{assume $P(n)$}\\
+\quad \texttt{hence $Q$  by simp}\\
+\quad \texttt{thus $P(n+1)$  by blast}\\
+\texttt{qed}
+\end{tabular}\\\\
+Tactic style & \FromSlide{2} Structured (Mizar, Isar)
+\end{tabular}
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\begin{cslide}{}
+\vfill
+\begin{center}
+\Large Part 1\\[2em]
+Introduction to Isabelle/HOL
+\end{center}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Overview of Part 1}
+\begin{itemize}
+\item Functional Programming
+\item Logic
+\item Sets and Relations
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Functional Programming}
+\begin{itemize}
+\item An introductory example
+\item Proof by simplification
+\item Case study: Expression compiler
+\item Advanced datatypes
+\item Advanced recursive functions
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Logic (Natural Deduction)}
+\begin{itemize}
+\item Propositional logic
+\item Quantifiers
+\item Automation
+\item Forward proof
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Sets and Relations}
+\begin{itemize}
+\item Introduction to the library
+\item Case study: verified model checking
+\item Inductively defined sets
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{}
+\vfill
+\begin{center}
+\Large Part 2\\[2em]
+Structured Proofs in Isabelle/Isar/HOL
+\end{center}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Motto}
+\vfill
+\begin{center}
+\Large\emcolorbox{Proofs should be readable}
+\end{center}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Why Readable Proofs?}
+\begin{itemize}
+\item Communication
+\item Maintenance
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+\overlays{2}{
+\begin{cslide}{A Proof Skeleton}
+\begin{tabular}{l}
+\textbf{proof}\\
+\quad\textbf{assume} {\blue\sl assumption}\\
+\quad\textbf{have} {\blue\sl intermediate result} \textbf{by} ...\\
+\quad\vdots\\
+\quad\textbf{have} {\blue\sl intermediate result} \textbf{by} ...\\
+\quad\textbf{show} {\blue\sl conclusion}\\
+\textbf{qed}
+\end{tabular}
+\bigskip
+
+\FromSlide{2}
+Proves {\blue\sl assumption $\Longrightarrow$ conclusion}
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\overlays{2}{
+\begin{cslide}{Proofs and Statements}
+\begin{center}
+\begin{tabular}{@{}lrl@{}}
+\emph{proof} & ::= & \textbf{proof} \emph{statement}* \textbf{qed} \\
+                 &$\mid$& \textbf{by} \emph{method}\\[2ex]
+\FromSlide{2}
+\emph{statement} &\FromSlide{2}::= & \FromSlide{2}\textbf{assume} \emph{propositions} \\
+             &\FromSlide{2}$\mid$& \FromSlide{2}(\textbf{show} $\mid$ \textbf{have})
+                      \emph{proposition} \emph{proof}
+\end{tabular}
+\end{center}
+\end{cslide}}
+%-----------------------------------------------------------------------------
+\begin{cslide}{Overview of Part 2}
+\begin{itemize}
+\item Logic
+\item Induction
+\end{itemize}
+\end{cslide}
+%-----------------------------------------------------------------------------
+
+\end{document}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 




