The Quest for Correctness

Die Genauigkeit, Kraft und Sicherheit dieses mathematischen] Denkens, die nir-gends im Leben ihresgleichen hat, erf ullte ihm fast mit Schwermut. 1 R. Musil 1952]: Der Mann ohne Eigenschaften. Abstract Modern society has a strong need for reliable Information Technology. To warrant correct designs for hardware and software systems, there is a thorough methodology (speciication, design based on subspecications and composition of components, and correctness proofs). Because of the diculty of making specications and proofs, the success of this method has been only partial, mainly in the area of hardware design. Presently there is emerging a new technology: Computer Mathematics. It consists of the interactive building of deenitions, statements and proofs, such that it can be checked automatically whether the deenitions are well-formed and the proofs are correct. Hereby the human user provides the intelligence and the system does part of the craftsmanship. Some forms of computer mathematics is already of use for the design of hardware systems. After the technology will be mature, it may become a tool for the development of mathematics comparable to systems of computer algebra, but with a scope and strength that is essentially beyond. Moreover, it probably will also be useful for the design of reliable software. 1 The precision, strength and certainty of this mathematical] thinking, that is unequaled in life, almost pervaded him with melancholy. R. Musil: The man without qualities, Ch. 28.