Objects and Classes, Co-Algebraically

The co-algebraic perspective on objects and classes in object-oriented programming is elaborated: classes are described as co-algebras, which may occur as models (implementations) of co-algebraic speciications. These speciications are much like deferred (or virtual) classes with assertions in Eiiel. An object belonging to a class is an element of the state space of the class, as co-algebra. We show how terminal co-algebras of co-algebraic speciications give rise to canonical models (in which all observationally indistinguishable objects are identiied). We further describe operational semantics for objects, with an associated notion of bisimulation (for objects in classes modeling the same speciication), expressing observational indistinguishability.