LOGICAL COMBINATORS FOR SYSTEM CONFIGURATION

System configuration describes the construction of complex engineering systems from their component parts. The configuration language is at a meta-Ievel to a specification language and expresses the horizontal structuring of specifications and modules by extension and parameterization; it also expresses the implementation, of both specifications and modules during the development of a software system. The logic chosen for system configuration is many-sorted first-order logic which possesses the Craig interpolation property. Configuration is expressed precisely within the logical framework by the operation of combinators on recursively defined configured objects of sorts in the set {specification, module}; each configured object is a named theory presentation. Properties of commutativity between the combinators are illustrated by equivalent paths in the three-dimensional development space for configuration. The actual building of configured objects is expressed by constructing diagrams within a categorical workspace that is based on the structure of a KZ-doctrine

Constructing Specifications and Modules in a KZ-Doctrine

Using the structure of a KZ-monad we create a general categorical workspace in which diagrams can be formally constructed. In particular this abstract framework of category theory is shown to provide a precise semantics for constructing the specifications of complex systems from their component parts. 1 Introduction The purely equational 2-dimensional categorical algebra underlying the process of freely completing categories under a given suitable class of colimits is presented by Kock in [8]. A common feature of the category which freely completes another category is that it has diagrams (functors) as its objects. Using properties of adjointness Kock identifies a particular monad which is called either a `monad with the Kock property' or a `KZ-doctrine'. Kock shows that this type of monad, which has structures which are adjoint to units, expresses precisely the properties of free cocompleteness and colimit formation in a category. In this paper the properties of a KZ-doctrine ar..