Logic Program Synthesis via Proof Planning

Abstract

We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form\( \forall \xrightarrow[{\arg s.}]{}prog(\xrightarrow[{\arg s}]{}) \leftrightarrow spec(\xrightarrow[{\arg s}]{}). \) . At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning.This technique is an application of the Clam proof planning system [Bundy et al 90c]. Clam is currently powerful enough to plan verification proofs for given programs. We show that, if Clam’s use of middle-out reasoning is extended, it will also be able to synthesize programs.KeywordsLogic ProgramLogic DescriptionSymbolic EvaluationStep CaseRecursion AnalysisThese 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.