A Strong Complete Schema For Inductive Functional Logic Programming

A new IFLP scheme is presented as a general framework for the induction of functional logic programs (FLP). Since narrowing (which is the most usual operational semantics of FLP) performs a unification (mgu) followed by a replacement, we introduce two main operators in our IFLP schema: a generalisation and an inverse replacement or intra-replacement, which results in a. generic inversion of the transitive property of equality. We prove that this schema is strong complete in the way that, given some evidence, it is possible to induce any program which could have generated that evidence. We outline some possible restrictions in order to improve the tractability of the scheme. We also show that inverse narrowing is just a special case of our IFLP scheme. Finally, a straightforward extension of the IFLP scheme to function invention is illustrated.