\documentclass[10pt, conference, compsocconf]{IEEEtran}
\usepackage{isabelle}
\usepackage{isabellesym}
\usepackage{times}
\usepackage{amssymb}
\usepackage{mathpartir}
\usepackage{pdfsetup}

% urls in roman style, theory text in math-similar italics
\urlstyle{rm}
\isabellestyle{it}

% for uniform font size
%\renewcommand{\isastyle}{\isastyleminor}


\begin{document}

\title{Formalising Computability Theory in Isabelle/HOL}


\author{
\IEEEauthorblockN{Jian Xu, Xingyuan Zhang}
\IEEEauthorblockA{PLA University of Science and Technology Nanjing, China}
\and
\IEEEauthorblockN{Christian Urban}
\IEEEauthorblockA{King's College London, UK}
}

\maketitle


\begin{abstract}
We present a formalised theory of computability in the 
theorem prover Isabelle/HOL. This theorem prover is based on classical 
logic which precludes \emph{direct} reasoning about computability: every 
boolean predicate is either true or false because of the law of excluded 
middle. The only way to reason about computability in a classical theorem 
prover is to formalise a concrete model for computation. 
We formalise Turing machines and relate them to abacus machines and recursive
functions. Our theory can be used to formalise other computability results:
we give one example about the undecidability of Wang tilings, whose proof uses
the notion of a universal Turing machine.
\end{abstract}

\begin{IEEEkeywords}
Turing Machines, Computability, Isabelle/HOL, Wang tilings
\end{IEEEkeywords}


\IEEEpeerreviewmaketitle

% generated text of all theories
\input{session}

% optional bibliography
\bibliographystyle{abbrv}
\bibliography{root}

\end{document}

%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: