Typing Linear Constraints for Moding CLP() Programs

International audienceWe 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 deØniteness, lower and upper bounds of variables of a linear constraint. Two proof procedures are resented for checking validity of type assertions. The Ørst one considers lower and upper bound types, and it relies on solving homogeneous linear programming problems. The second procedure, which deals with deØniteness as well, relies on computing the Minkowski's form of a parameterized poly-hedron. 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)