Toward a mathematical foundation of software engineering methods

The development of large software systems consists of a sequence of modeling tasks. It requires the modeling and description of the application domain, software requirements, software architecture, software components, their internal structure, and their implementation. Technically, in software engineering, we work with a development method and description techniques with modeling, refinement, and implementation concepts. Today, much of the modeling is carried out by informal text and graphical description techniques. The development is organized in a development process and supported by CASE tools. We show how mathematics can provide a scientific foundation for the modeling aspects, description techniques, and development methods of software engineering. Such a scientific foundation leads to a deeper understanding of the development process and to a basis for a more powerful tool support.