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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\documentclass[10pt, conference, compsocconf]{IEEEtran}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{isabelle}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{isabellesym}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{times}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{amssymb}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{mathpartir}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{pdfsetup}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{tikz}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\usepackage{pgf}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% urls in roman style, theory text in math-similar italics
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\urlstyle{rm}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\isabellestyle{it}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% for uniform font size
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%\renewcommand{\isastyle}{\isastyleminor}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\isasymequiv}{$\dn$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\isasymemptyset}{$\varnothing$}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\isacharunderscore}{\mbox{$\_$}}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\renewcommand{\isasymiota}{}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{document}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\title{Formalising Computability Theory in Isabelle/HOL}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\author{
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\IEEEauthorblockN{Jian Xu, Xingyuan Zhang}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\IEEEauthorblockA{PLA University of Science and Technology Nanjing, China}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\and
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\IEEEauthorblockN{Christian Urban}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\IEEEauthorblockA{King's College London, UK}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\maketitle
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{abstract}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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We present a formalised theory of computability in the
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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theorem prover Isabelle/HOL. This theorem prover is based on classical
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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logic which precludes \emph{direct} reasoning about computability: every
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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boolean predicate is either true or false because of the law of excluded
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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middle. The only way to reason about computability in a classical theorem
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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prover is to formalise a concrete model for computation.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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We formalise Turing machines and relate them to abacus machines and recursive
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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functions. Our theory can be used to formalise other computability results:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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we give one example about the undecidability of Wang's tiling problem, whose proof uses
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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the notion of a universal Turing machine.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{abstract}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\begin{IEEEkeywords}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Turing Machines, Computability, Isabelle/HOL, Wang tilings
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{IEEEkeywords}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\IEEEpeerreviewmaketitle
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% generated text of all theories
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\input{session}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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% optional bibliography
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bibliographystyle{abbrv}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\bibliography{root}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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\end{document}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%% Local Variables:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%% mode: latex
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%% TeX-master: t
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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%%% End:
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