A Mechanisation of Computability Theory in HOL

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.