Combining Constraint Languages via Abstract Interpretation

Abstract

Constraint programming initially aims to be a declarative paradigm, but its quest for efficiency is mainly achieved through the development of ad-hoc algorithms, which are encapsulated in global constraints. In this paper, we explore the idea of extending constraint programming with abstract domains, a structure from program analysis by abstract interpretation. Abstract domains allow us to efficiently process constraints of the same form, such as linear constraints or difference constraints. This classification by constraint sub-languages instead of sub-problems, makes abstract domains more general and more reusable in many problems. We contribute to the definition of an abstract domain encapsulating a constraint solver in a conservative way w.r.t. constraint programming. We also define a product of abstract domains based on reified constraints and under-approximations. We study a well-known scheduling problem to motivate our approach and experiment its feasibility.