Non-primitive Recursive Function Definitions

This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termination, the original specification can be derived easily. A collection of algorithms are presented which hide the domain theory from a user. Hence, the derivation of a domain theory specification has been automated completely, and for well-founded recursive function specifications the process of deriving the original specification from the domain theory one has been automated as well, though a user must supply a well-founded relation and prove certain termination properties of the specification. There are constructions for building well-founded relations easily.