Abstract
This paper tries to contribute to the understanding of the essence of rational systems design and verification. Information technologists and teachers and students of computer science may find the concepts presented here helpful to disentangle complex achievements of computer science and re-use their constituents in other contexts, but also to view their own activities in the light of other disciplines. First a consistent set of notions and a diagram and a formula are introduced, with respect to which important aspects of a rational design process can be understood, together with a proposal for a consistent terminology. Subsequently, formal definitions are provided for basic concepts of formal methods and a mathematical foundation for our formula. They shall illustrate that the rôle of mathematics in development and verification is not limited to useful calculations: Ideally, designing is a creative mathematical activity, which comprises finding a theorem, if necessary strengthening its assumptions until it can be proven. Although for good reasons most systems are designed without use of formal methods it may be a source of useful insight to understand all design as an approximation of such a mathematical activity. This leads amongst others to a taxonomy of design decisions and of fault tolerance. And it may help to relate paradigms, theories, methods, languages, and tools from different areas of computer science to each other to make optimal use of them.
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