Static Analysis of CLP Programs over Numeric Domains

Constraint logic programming (CLP) is a generalization of the pure logic programming paradigm, having similar model-theoretic, fixpoint and operational semantics [9]. Since the basic operational step in program execution is a test for solvability of constraints in a given algebraic structure, CLP has in addition an algebraic semantics. CLP is then a general paradigm which may be instantiated on various semantic domains, thus achieving a good expressive power. One relevant feature is the distinction between testing for solvability and computing a solution of a given constraint formula. In the logic programming case, this corresponds to the unification process, which tests for solvability by computing a solution (a set of equations in solved form or most general unifier). In CLP, the computation of a solution of a constraint is left to a constraint solver, which does not affect the semantic definition of the language. This allows different computational domains, e.g. real arithmetic, to be considered without requiring complicated encodings of data objects as first order terms. Since the fundamental linguistic aspects of CLP can be separated from the details specific to particular constraint systems, it seems natural to parameterize the semantics of CLP languages with respect to the underlying constraint system [16]. For example, considering a domain of “abstract constraints” instead of the “concrete constraints” that are actually manipulated during program execution, we obtain for free a formal treatment of abstract interpretation of CLP programs: this provides a foundation for dataflow analysis and program manipulation of CLP programs.