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\begin{document}


\title{Mechanising Computability Theory in Isabelle/HOL}
\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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