Inference of Equational Programs by Inverse Reduction

Abstract

In this paper we discuss an approach to the inference of recursive equational programs from non-recursive equations for the target functions. We call the research area Inductive Equational Programming (IEP). We firstly give a definition of IEP problems. Then we give three inference methods for inferring target programs from given concrete examples under some background knowledge. The inference methods are inverse reduction, generalization, and finding subsidiary functions which are not given in examples. We show the soundness of these inference methods. We also compare them with other methods which have already been developed for inference of recursive functions.