Constraintssuch

Constraintssuch is a term used in constraint programming and formal methods to describe a class of constraint expressions that pair a base relation with a contextual qualifier introduced by the phrase such that. The concept is discussed in relation to modular constraint design and reusable modeling patterns, but it is not a widely standardized operator across constraint programming systems.

Semantically, a constraintssuch consists of two parts: a core constraint C over a set of variables, and a predicate S that describes a condition on the variable assignments or on the solution space. The combined constraint is satisfied only when both C and S hold. In practice, solvers implement such constraints by restricting the domain of variables, by constraint rewriting, or by introducing auxiliary variables to encode the such that condition.

Example: constraintssuch(x, y) such that x + y = 10 and x > 0 specifies that valid solutions must have two variables summing to 10 with a positive x.

Applications include modular modeling, template-based constraint definitions, and conditional constraints in scheduling, resource allocation, and configuration problems. Limitations include inconsistent syntax across tools, potential ambiguity about scope, and additional computational overhead from domain filtering or rewriting.

See also: constraint satisfaction problem, constraint programming, guarded constraints, conditional constraints, parameterized constraints.