Abstract Interpretation over Non-lattice Abstract Domains

Interpretation over Non-Lattice Abstract Domains Graeme Gange, Jorge A. Navas, Peter Schachte, Harald Søndergaard, and Peter J. Stuckey Department of Computing and Information Systems, The University of Melbourne, Victoria 3010, Australia {gkgange,jorge.navas,schachte,harald,pstuckey}@unimelb.edu.au Abstract. The classical theoretical framework for static analysis of programs is abstract interpretation. Much of the power and elegance of that framework rests on the assumption that an abstract domain is a lattice. Nonetheless, and for good reason, the literature on program analysis provides many examples of non-lattice domains, including non-convex numeric domains. The lack of domain structure, however, has negative consequences, both for the precision of program analysis and for the termination of standard Kleene iteration. In this paper we explore these consequences and present general remedies. The classical theoretical framework for static analysis of programs is abstract interpretation. Much of the power and elegance of that framework rests on the assumption that an abstract domain is a lattice. Nonetheless, and for good reason, the literature on program analysis provides many examples of non-lattice domains, including non-convex numeric domains. The lack of domain structure, however, has negative consequences, both for the precision of program analysis and for the termination of standard Kleene iteration. In this paper we explore these consequences and present general remedies.