Toward a mathematical foundation of software engineering methods

The development of large software systems consists of a sequence of modelin g 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 engi neering, we work with a development method and description techniques with modeling, refinement, and implementation concepts. Today, much of the model ing is carried out by informal text and graphical description techniques. T he development is organized in a development process and supported by CASE tools. In this paper, we show how mathematics can provide a scientific foun dation for the modeling aspects, description techniques, and development me thods of software engineering. Such a scientific foundation leads to a deep er understanding of the development process and to a basis for a more power ful tool support.