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\documentclass[11pt,a4paper]{article}
\usepackage{isabelle,isabellesym}
% further packages required for unusual symbols (see also
% isabellesym.sty), use only when needed
%\usepackage{amssymb}
%for \<leadsto>, \<box>, \<diamond>, \<sqsupset>, \<mho>, \<Join>,
%\<lhd>, \<lesssim>, \<greatersim>, \<lessapprox>, \<greaterapprox>,
%\<triangleq>, \<yen>, \<lozenge>
%\usepackage[greek,english]{babel}
%option greek for \<euro>
%option english (default language) for \<guillemotleft>, \<guillemotright>
%\usepackage[latin1]{inputenc}
%for \<onesuperior>, \<onequarter>, \<twosuperior>, \<onehalf>,
%\<threesuperior>, \<threequarters>, \<degree>
%\usepackage[only,bigsqcap]{stmaryrd}
%for \<Sqinter>
%\usepackage{eufrak}
%for \<AA> ... \<ZZ>, \<aa> ... \<zz> (also included in amssymb)
%\usepackage{textcomp}
%for \<cent>, \<currency>
% this should be the last package used
\usepackage{pdfsetup}
% urls in roman style, theory text in math-similar italics
\urlstyle{rm}
\isabellestyle{it}
\begin{document}
\title{Locally Nameless Sigma Calculus}
\author{Ludovic Henrio and Florian Kamm\"uller and Bianca Lutz and Henry Sudhof}
\maketitle
\begin{abstract}
We present a Theory of Objects based on the original functional
$\varsigma$-calculus by Abadi and Cardelli \cite{AC96a} but with an
additional parameter to methods. We prove confluence of the operational
semantics following the outline of Nipkow's proof of confluence for the
$\lambda$-calculus reusing his general \texttt{Commutation.thy}
\cite{nip:01} a generic diamond lemma reduction.
We furthermore formalize a simple type system for our $\varsigma$-calculus
including a proof of type safety.
The entire development uses the concept of Locally Nameless representation
for binders \cite{ACPPW:POPL08}. We reuse an earlier proof of confluence
\cite{HK:FMOODS07} for a simpler $\varsigma$-calculus based on de Bruijn indices
and lists to represent objects.
\end{abstract}
\tableofcontents
% sane default for proof documents
\parindent 0pt\parskip 0.5ex
% generated text of all theories
\input{session}
% optional bibliography
%\bibliographystyle{abbrv}
%\bibliography{root}
\bibliographystyle{entcs}
\begin{thebibliography}{10}
\bibitem{AC96a}
M. Abadi and L. Cardelli.
\newblock {``A Theory of Objects''}.
\newblock Springer, New York, 1996.
\bibitem{ACPPW:POPL08}
B. Aydemir, A, Chargu��raud, B.~C. Pierce, R. Pollack, and
S. Weirich.
\newblock Engineering formal metatheory.
\newblock {\em Princ. of Programming Languages, POPL'08}, ACM, 2008.
\bibitem{HK:FMOODS07}
L. Henrio and F. Kamm��ller.
\newblock A mechanized model of the theory of objects.
\newblock {\em Formal Methods for Open Object-Based Distributed Systems,}.
LNCS \textbf{4468} Springer, 2007.
\bibitem{nip:01}
Tobias Nipkow.
\newblock{More Church Rosser Proofs.}
\newblock{\em Journal of Automated Reasoning}.
\newblock{\textbf{26}:51--66, 2001.}
\end{thebibliography}
\end{document}
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