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\begin{document}

\author{Jian Xu\inst{1} \and Xingyuan Zhang\inst{1} \and Christian Urban\inst{2}}

\institute{PLA University of Science and Technology, China \and 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:

{\it we give one example about the undecidability of Wang's tiling problem, whose proof uses

the notion of a universal Turing machine.}

\end{abstract}

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