A Language for Configuring Multi-level Specifications

This paper shows how systems can be built from their component parts with specified sharing. Its principle contribution is a modular language for configuring systems. A configuration is a description in the new language of how a system is constructed hierarchically from specifications of its component parts. Category theory has been used to represent the composition of specifications that share a component part by constructing colimits of diagrams. We reformulated this application of category theory to view both configured specifications and their diagrams as algebraic presentations of presheaves. The framework of presheaves leads naturally to a configuration language that expresses structuring from instances of specifications, and also incorporates a new notion of instance reduction to extract the component instances from a particular configuration. The language now expresses the hierarchical structuring of multi-level configured specifications. The syntax is simple because it is independent of any specification language; structuring a diagram to represent a configuration is simple because there is no need to calculate a colimit; and combining specifications is simple because structuring is by configuration morphisms with no need to flatten either specifications or their diagrams to calculate colimits

Presheaves as Configured Specifications

The paper addresses a notion of configuring systems, constructing them from specified component parts with stipulated sharing. This notion is independent of any underlying specification language and has been abstractly identified with the taking of colimits in category theory. In particular, Oriat has shown how to use a category of diagrams Diag(C) to express colimits of primitive specifications from a category C. Mathematically it is known that these can equally well be expressed by presheaves over C and the present paper applies this idea to configuration. We develop an algebraic account of presheaves, and show that Oriat's category Diag(C) is equivalent to the category of finitely presented presheaves over C. The presheaf structure is interpreted in terms of instances of specifications and instance reduction and a configuration language is outlined that expresses precisely the finite presentations of presheaves but also describes configuration in a natural way