The Algebraic Framework for Object-Oriented Systems

Abstract

Category Theory is introduced as the mathematical model for object-oriented systems which are distributed, heterogeneous, real-time, embedded, and open-ended. Each object can be represented as an algebra. A collection of algebras with morphisms form a category if they satisfy some conditions. After a brief introduction of categorical concepts which are needed to formulate the framework for object-oriented systems, they are explicated in terms of objects. Then some system design methodologies such as SADT, JSD, MASCOT 3, OOD, HOOD, MOON, ADM 3, and Petri nets are examined in the categorical framework and classified into four groups: functional, process-based, object-oriented, and net-based. Combining theoretical and practical results, the interactive system design tool OBJ-NET is briefly introduced.