Generalised Constraint Propagation

Constraint logic programming is often described as logic programming with uni cation replaced by constraint solving over a computation domain. There is another, very di erent, CLP paradigm based on constraint satisfaction, where program-de ned goals can be treated as constraints and handled using propagation. This paper proposes a generalisation of propagation, which enables it to be applied on arbitrary computation domains, revealing that the two paradigms of CLP are orthogonal, and can be freely combined. The main idea behind generalised propagation is to use whatever constraints are available over the computation domain to express restrictions on problem variables. Generalised propagation on a goal G requires that the system extracts a constraint approximating all the answers to G. The paper introduces a generic algorithm for generalised propagation called topological branch and bound which avoids enumerating all the answers to G. Generalised propagation over the Herbrand universe has been implemented in a system called Propia, and we describe its behaviour on some applications.