Constraint Satisfaction Techniques for the Generation Phase in Declarative Modeling

Class Domain Main fields V: Variable variable associated with this domain Main methods abstract boolean isEmpty() returns true iff the domain is empty abstract List discretize() returns a discrete representation of the domain (a list of values) Domain clone() returns a copy of the Domain object abstract void setSingleValue(in val:Value) reduce domain to a single value Table 3. Domain class description. In the solver, constraints are generic. They can be defined according to the application. Abstract Class Constraint Main fields V: list variables of this constraint RM : listClass Constraint Main fields V: list variables of this constraint RM : list Main methods abstract boolean testConsistency(in t: Assignment) returns true if the constraint is satisfied, false otherwise Assignment t is a list of pairs (variable, value) boolean revise() constraint filtering method: applies reduction methods on free parameters (i.e. not yet instanciated); returns false iff inconsistency has been detected, (at least one domain is empty) Table 4. Constraint class description. A reduction method is an over-estimated projection function of a constraint on one of its variables (see definition 6). In the search process reduction methods are used to tighten domains. Abstract Class ReductionMethod Main fields C : Constraint outVar : Variable variable on which the constraint is projectedClass ReductionMethod Main fields C : Constraint outVar : Variable variable on which the constraint is projected Main methods abstract Domain proj() the projection method of C on outVar Table 5. ReductionMethod class description. Requirements: let CE be a constraint on E = D1x...xDn. Let F a set such that F ⊆ E. We denote CF the restriction of the constraint CE to F. The method proj – here written proj(C, outVar) must satisfy the two following conditions: (1): ∀i∈{1..n} CE↓Vi ⊆ proj(CE,Vi) (2): ∀i∈{1..n} proj(CF,Vi) ⊆ proj(CE,Vi)