COMPATIBILITY PROBLEMS IN THE DEVELOPMENT OF ALGEBRAIC MODULE SPECIFICATIONS

Algebriac theory provides a framework for the specification and design of modules and modular software systems. Research in this area has focused on the development of "horizontal" operations for building up module and interface specifications. Our previous work also introduced the notion of vertical development steps, where abstract specifications are converted into a more concrete form. In this paper, we study a variety of compatibility problems between structuring operations and development steps and introduce notions of the realization of an interface specification by a module specification. These compatibility problems are studied in a categorical framework where specifications and developments steps are viewed as objects and morphisms in a "development category". We show that compatibility can be expressed as the fact that the structuring operations can be extended to partial functors and give sufficient conditions for this property.