Positive Boolean Functions as Multiheaded Clauses

Boolean functions are ubiquitous in the analysis of (constraint) logic programs. The domain of positive Boolean functions, Pos, has been used for expressing, for example, groundness, finiteness and sharing dependencies. The performance of an analyser based on Boolean functions is critically dependent on the way in which the functions are represented. This paper discusses multiheaded clauses as a representation of positive Boolean functions. The domain operations for multiheaded clauses are conceptually simple and can be implemented straightforwardly in Prolog. Moreover these operations generalise those for the less algorithmically complex operations of propositional Horn clauses, leading to naturally stratified algorithms. The multiheaded clause representation is used to build a Pos-based groundness analyser. The analyser performs surprisingly well and scales smoothly, not requiring widening to analyse any program in the benchmark suite.