Towards a Compositional Interpretation of Object Diagrams

We develop a compositional interpretation of object model and statechart diagrams as used in the “Syntropy” method of Object-Oriented Analysis and Design. Separate theories are constructed for object instances, class managers and associations which are then combined with categorical constructions to yield a formal interpretation of the complete system.We compare the use of state attributes to abstractly interpret history with temporal axioms governing behaviours and contrast the logical notion of locality with object-oriented data encapsulation. We consider the interpretation of statecharts partitioning the overall statespace and defining transitions between partitions and give a formal interpretation to event parameters, filters, preconditions and postconditions. We observe that some features of Syntropy are not amenable to this systematic modular interpretation.