Static Analysis of CLP Programs overNumeric

Extended Abstract Constraint logic programming (CLP) is a generalization of the pure logic programming paradigm, having similar model-theoretic, xpoint 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 uniication process, which tests for solvability by computing a solution (a set of equations in solved form or most general uniier). In CLP, the computation of a solution of a constraint is left to a constraint solver, which does not aaect the semantic deenition of the language. This allows diierent computational domains, e.g. real arithmetic, to be considered without requiring complicated encodings of data objects as rst order terms. Since the fundamental linguistic aspects of CLP can be separated from the details speciic 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 dataaow analysis and program manipulation of CLP programs. The original contribution of the present work is the integration of approximate inference techniques, well known in the eld of artiicial