Abstract
The theory of algebraic module specifications with horizontal structuring operations, like composition, actualization and union, is extended by vertical development steps, like refinement, simulation and transformation, and a realization concept of interface by module specifications. Various compatibility results between horizontal operations, vertical steps and realization are explicitly presented and summarized as one compatibility result in a basic development category. Five independent modifications, which are important for practical specification development, are sketched in the paper leading to several other development categories where corresponding compatibility results are true under some additional side conditions.
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