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A Mechanisation of Computability Theory in HOL

Zammit, Vincent (1996) A Mechanisation of Computability Theory in HOL. 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) (KAR id:21347)


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.

Item Type: Book section
DOI/Identification number: 10.1007/BFb0105420
Uncontrolled keywords: Computability Theory, URM, Theorem Proving, Formalization of Mathematics
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Mark Wheadon
Date Deposited: 27 Aug 2009 18:44 UTC
Last Modified: 16 Nov 2021 09:59 UTC
Resource URI: (The current URI for this page, for reference purposes)

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