Constraintthat

Constraintthat is a concept proposed for constraint programming to represent conditional constraints. It denotes a constraint C that is enforced only when a specified condition φ holds. The construct is intended to make conditional dependencies explicit in models and to align with how many solvers implement reified constraints or implication constraints.

Formal definition: In a finite-domain constraint satisfaction problem, let C be a constraint over a set of variables and φ be a boolean condition over the same or related variables. The constraint constraintthat(C, φ) is satisfied by a variable assignment if either φ evaluates to false under the assignment or C is satisfied. Equivalently, it expresses φ → C.

Relation to existing concepts: constraintthat corresponds to the common practice of reified or conditional constraints in constraint programming. In many solvers, φ is represented by a boolean variable and the enforcement of C is gated by the value of that variable, implemented as an implication or as a reified constraint.

Examples: In a scheduling problem, a constraint that a projector is required only if the meeting type is 'presentation' can be written as constraintthat(hasProjector, type == 'presentation'). Another example: a discount applies only to premium customers, expressed as constraintthat(discountApplies, isPremium).

Implementation considerations: Efficiency depends on solver support for reification and implication constraints. Overhead may arise from maintaining additional booleans and from propagation interactions with other constraints. Careful modeling can prevent unnecessary relaxation when φ is undecided.

See also: Constraint programming, reified constraints, conditional constraints, implication constraints, modeling patterns.