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.KeywordsRecursive FunctionRecursive CallFunction ExtensionDomain TheoryProof ObligationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.