A Complete Gentzen-Style Axiomatization for Set Constraints

Set constraints are inclusion relations between expressions denoting sets of ground terms over a ranked alphabet They are the main ingredient in set based program analysis In this paper we pro vide a Gentzen style axiomatization for sequents where and are nite sets of set constraints based on the axioms of termset al gebra Sequents of the restricted form correspond to positive set constraints and those of the more general form correspond to sys tems of mixed positive and negative set constraints We show that the deductive system is i complete for the restricted sequents over standard models ii incomplete for general sequents over stan dard models but iii complete for general sequents over set theoretic termset algebras