Typing Linear Constraints for Moding CLP() Programs

We present a type system for linear constraints over reals and its use in mode analysis of CLP programs. The type system is designed to reason about the properties of definiteness, lower and upper bounds of variables of a linear constraint. Two proof procedures are presented for checking validity of type assertions. The first one considers lower and upper bound types, and it relies on solving homogeneous linear programming problems. The second procedure, which deals with definiteness as well, relies on computing the Minkowski’s form of a parameterized polyhedron. The two procedures are sound and complete. We extend the approach to deal with strict inequalities and disequalities. Type assertions are at the basis of moding constraint logic programs. We extend the notion of well-moding from pure logic programming to CLP(R).