doc-src/AxClass/axclass.tex

A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
the tactic has also changed and allows the abstaction over fuction occurences whose type is nat or int.

\documentclass[12pt,a4paper,fleqn]{report}
\usepackage{graphicx,../iman,../extra,../isar}
\usepackage{generated/isabelle,generated/isabellesym}
\usepackage{../pdfsetup}  % last one!

\isabellestyle{it}
\newcommand{\isasyminv}{\isamath{{}^{-1}}}
\renewcommand{\isasymzero}{\isamath{0}}
\renewcommand{\isasymone}{\isamath{1}}

\newcommand{\secref}[1]{\S\ref{#1}}
\newcommand{\figref}[1]{figure~\ref{#1}}

\hyphenation{Isabelle}
\hyphenation{Isar}
\hyphenation{Haskell}

\title{\includegraphics[scale=0.5]{isabelle_isar}
  \\[4ex] Using Axiomatic Type Classes in Isabelle}
\author{\emph{Markus Wenzel} \\ TU M\"unchen}


\setcounter{secnumdepth}{2} \setcounter{tocdepth}{2}

\pagestyle{headings}
\sloppy
\binperiod     %%%treat . like a binary operator


\begin{document}

\underscoreoff

\maketitle 

\begin{abstract}
  Isabelle offers order-sorted type classes on top of the simple types of
  plain Higher-Order Logic.  The resulting type system is similar to that of
  the programming language Haskell.  Its interpretation within the logic
  enables further application, though, apart from restricting polymorphism
  syntactically.  In particular, the concept of \emph{Axiomatic Type Classes}
  provides a useful light-weight mechanism for hierarchically-structured
  abstract theories. Subsequently, we demonstrate typical uses of Isabelle's
  axiomatic type classes to model basic algebraic structures.
  
  This document describes axiomatic type classes using Isabelle/Isar theories,
  with proofs expressed via Isar proof language elements.  The new theory
  format greatly simplifies the arrangement of the overall development, since
  definitions and proofs may be freely intermixed.  Users who prefer tactic
  scripts over structured proofs do not need to fall back on separate ML
  scripts, though, but may refer to Isar's tactic emulation commands.
\end{abstract}


\pagenumbering{roman} \tableofcontents \clearfirst

\include{body}

%FIXME
\nocite{nipkow-types93}
\nocite{nipkow-sorts93}
\nocite{Wenzel:1997:TPHOL}
\nocite{paulson-isa-book}
\nocite{isabelle-isar-ref}
\nocite{Wenzel:1999:TPHOL}

\begingroup
  \bibliographystyle{plain} \small\raggedright\frenchspacing
  \bibliography{../manual}
\endgroup

\end{document}


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