Semantics of OCL Operation Specifications

The semantics of OCL operation specifications is discussed from a model theoretic perspective. It is argued that the semantics of operation specifications as defined in the OCL 2.0 proposal is not compatible with the view of operation specifications as contracts between a client and a supplier. As a solution, a semantics of OCL operation specifications based on standard model theory is presented. This semantics introduces the concept of a model over a UML class signature — which is a labelled transition system with output — together with a notion of the satisfiability of an OCL operation specification w.r.t. a model. The models respect the OCL features for methods with and without results, constructors, and queries. Regarding inheritance, the combination of several OCL operation specifications is introduced based on a lattice structure on models with respect to generalisation and refinement. Satisfiability is parametric in the underlying signature, and thus the notion can be transferred from UML class signatures to signatures including invariants.