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Integration of categorical frameworks: Rule-based refinement and hierarchical composition for components. (English) Zbl 1147.68055

Summary: The integration of two important categorical frameworks-namely adhesive High-Level Replacement (HLR) systems and the generic component concept-yields a categorical approach to component transformation and refinement. The generic component concept is shown to be an adhesive HLR category, so rules and transformations as well as the corresponding results are available. Moreover, the compatibility with the hierarchical component composition is provided. The extension to rule-based refinement requires additional property-preserving morphisms and yields property-preserving rules and transformations, i.e. refinements where compatibility with the hierarchical component composition again is achieved. The categorical framework is instantiated to typed Algebraic High-Level (AHL) nets and illustrated with an example of AHL net components.

MSC:

68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q42 Grammars and rewriting systems
18A99 General theory of categories and functors
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