Propagators for binary constraints

There are different levels of consistency for constraints. A unary constraint p(X) is said to be domain-consistent if, for any element x in the domain of X, the constraint p(x) is satisfied. The propagation rule that maintains domain-consistency is called forward-checking. A constraint is said to be interval-consistent if, for any bound of the domain of any variable, there are supporting elements in the domains of the all of the other variables, such that the constraint is satisfied. Propagators for maintaining interval consistency are activated whenever a bound of a variable is updated, or whenever a variable is instantiated. A constraint is said to be arc-consistent if, for any element in the domain of any variable, there are supporting elements in the domains of all of the other variables, such that the constraint is satisfied. Propagators for maintaining domain consistency are triggered whenever changes occur to the domain of a variable. This section considers how to implement various propagators for the binary constraint A*X #= B*Y+C, where X and Y are domain variables, A and B are positive integers, and C is an integer of any kind.