Non-primitive Recursive Function Definitions

Abstract

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.