Consider a propagator for the constraint

2over a constraint store^{ . }X=Y

Under domain propagation, the propagator can narrow the domains to

Under interval propagation, the propagator can narrow only the domain bounds, which yields

In practice, interval propagation is usually preferable over domain propagation because of its lower computational costs. But domain propagation often leads to considerably smaller search trees (figure 2). In Alice, some propagators have an additional argument conlevel. There you can specify the propagators consistency level.

Andreas Rossberg 2006-08-28