A Superposition Operator for the Refinement of Algebraic Models
Claus Pahl · Electronic Notes in Theoretical Computer Science · 2001
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. We are grateful to the anonymous reviewers who have helped to improve the paper considerably.