A Superposition Operator for the Refinement of Algebraic Models

The development of computer languages or software artefacts from basic concepts to the final product is usually a process starting with an abstract model of a key concept and extending this by adding more detailed functionality for extended structural definitions. We will present a refinement approach for the stepwise development of algebraic models. In each step we either add new elements to a model or refine the properties of existing ones. The process of refining elements such that properties of the original element are preserved is called superposition. We will present a categorical framework for refining algebraic structures. Algebras can be used to model a variety of concepts and objects. Language semantics and formal methods are two application areas which use models represented in terms of algebras.