Inverse Narrowing for the Induction of Functional Logic Programs

We present a framework for the Induction of Functional Logic Programs (IFLP) from facts. This can be seen as an extension to the now consolidated field of Inductive Logic Programming (ILP). Inspired in the inverse resolution operator of ILP, we study the reversal of narrowing, the more usual operational mechanism for Functional Logic Programming. We also generalize the selection criteria for guiding the search, including coherence criteria in addition to the MDL principle. A non-incremental learning algorithm and a more sophisticated incremental extension of it are presented. We discuss the advantages of IFLP over ILP, most of which are inherited from the power of narrowing w.r.t. resolution. At the end of this paper, we comment on the plausibility of extending the presented techniques to higher-order induction and its appropriateness for function invention, a topic which is difficult to incorporate homogeneously with the basic first-order inductive rules of inference in ILP.