Formalising Object-Oriented Models in the Object Calculus

This paper identifies how object models, statecharts and interaction diagrams can be given a semantics in the Object Calculus of Fiadeiro and Maibaum. A compositional interpretation of object model and statechart diagrams is developed, with separate theories constructed for object instances, class managers and associations which are then combined using categorical constructions to yield a formal interpretation of complete systems. We use this semantics to identify some problematic features of these notations in the Syntropy method.