Integrating Cardinality Constraints into Constraint Logic Programming with Sets

Formal reasoning about finite sets and cardinality is important for many applications. including software verification, where very often one needs to reason about the size of a given data structure. The Constraint Logic Programming tool {log} provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, although it does not provide cardinality constraints. In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into {log}. The proposed solver is proved to be a decision procedure for its formulas. Besides, the new CLP instance is implemented as part of the {log} tool. In turn, the implementation uses Howe and King's Prolog SAT solver and Prolog's CLP(Q) library. as an integer linear programming solver. The empirical evaluation of this implementation based on +250 real verification conditions shows that it can be useful in practice.