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\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's tiling problem, whose proof uses
the notion of a universal Turing machine.
\end{abstract}

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


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