Zammit, Vincent
(1996)
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A Mechanisation of Computability Theory in HOL.
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In: von Wright, Joakim and Grundy, Jim and Harrison, John, eds.
Theorem Proving in Higher Order Logics 9th International Conference.
Lecture Notes in Computer Science
.
Springer, Berlin, Germany, pp. 431-446.
ISBN 978-3-540-61587-3.
E-ISBN 978-3-540-70641-0.
(doi:10.1007/BFb0105420)

## Abstract

This paper describes a mechanisation of computability theory in HOL using the Unlimited Register Machine (URM) model of computation. The URM model is first specified as a rudimentary machine language and then the notion of a computable function is derived. This is followed by an illustration of the proof of a number of basic results of computability which include various closure properties of computable functions. These are used in the implementation of a mechanism which partly automates the proof of the computability of functions and a number of functions are then proved to be computable. This work forms part of a comparative study of different theorem proving approaches and a brief discussion regarding theorem proving in HOL follows the description of the mechanisation.

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