Mechanised Computability Theory

This paper presents a mechanisation of some basic computability theory. The mechanisation uses two models: the recursive functions and the ?- calculus, and shows that they have equivalent computational power. Results proved include the Recursion Theorem, an instance of the s-m-n theorem, the existence of a universal machine, Rice's Theorem, and closure facts about the recursive and recursively enumerable sets. The mechanisation was performed in the HOL4 system and is available online.