Equational Specification of UML + OCL Static Class Diagrams ?

In this paper we propose an equational specification of UML+OCL static class diagrams that provides a formal foundation for automatically validating UML object diagrams with respect to OCL constraints. Basically, class and object UML diagrams are specified as membership equational theories, and OCL expressions are represented as terms over extensions of those theories. Then, validating object diagrams with respect to invariants is reduced to checking whether the corresponding terms rewrite to true or false. Based on these ideas, we have developed a tool, named ITP/OCL, that provides automatic validation of object diagrams with respect to OCL constraints.