Inverse Narrowing for the Inductive Inference 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). For that purpose we study the reversal of narrowing, the more usual operational mechanism for Functional Logic Programming. Also we fix the goal and heuristics in consilient programs rather than look for the shortest one as it is common in ILP. Initially, a simple nonincremental algorithm for the induction of functional programs is suggested for toy problems. Next, a more sophisticated incremental algorithm is presented to face more real problems. We discuss the advantages of IFLP in front of ILP, most of them inherited from the power of narrowing w.r.t. resolution. In the end, we comment the plausibility of extending the presented techniques to higher-order induction and its appropiateness for function invention, a topic which is difficult to incorporate homogeneously with the basic first-order inductive rules of inference in ILP.