Object-oriented analysis and design methodologies are considered as the most popular software development methods for the 1990s. A common drawback, however, is that they have been developed informally. There is no theoretical framework enabling us to define precisely the object-oriented concepts involved, to solve concurrency problems, and to verify the correctness of the implementation.
We propose a 3-dimensional net structure behind object-oriented software development. This structure consolidates the concepts of classes, inheritance, overloading and message passing through a single model. Inheritance and overloading can be unified with message passing in a 3-dimensional representation, but are physically differentiable by occupying the vertical and horizontal planes, respectively, of the model.
Furthermore, the formal model can be mapped to various object-oriented analysis and design notations. The theoretical framework can thus be adopted for systems validation and verification for existing methodologies. The liveness and consistencies of objects can be verified, and inheritance and interaction coupling can be identified and checked.