Download Beauty Is Our Business: A Birthday Salute to Edsger W. by W.H.J. Feijen, A.J.M. van Gasteren, David Gries, J. Misra PDF

By W.H.J. Feijen, A.J.M. van Gasteren, David Gries, J. Misra

ISBN-10: 1461244765

ISBN-13: 9781461244769

ISBN-10: 1461287928

ISBN-13: 9781461287926

More than the rest, this ebook is a tribute to Edsger W. Dijkstra, at the get together of his 60th birthday, by way of quite a few of these lucky adequate to be motivated via him and his paintings and to be referred to as his buddy or relation, his grasp, colleague, or scholar. This ebook comprises fifty-four technical contributions in numerous parts of undertaking, even supposing a lot of them take care of a space of specific hindrance to Dijkstra: programming. every one contribution is comparatively brief and will be digested in a single sitting. jointly, they shape a pleasant pass part of the self-discipline of programming firstly of the nineties. whereas many be aware of of Dijkstra's technical contributions, they might not concentrate on his final target, the mastery of complexity in arithmetic and computing technological know-how. He has forcefully argued that good looks and magnificence are necessary to this mastery. The name of this ebook, selected to mirror his final target, comes from a sentence in a piece of writing of his on a few attractive arguments utilizing mathematical induction: "... once we recognize the conflict opposed to chaos, mess, and unmastered complexity as certainly one of computing sci- ence's significant callings, we needs to admit that 'Beauty Is Our Business'."

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Then for all x, th e set P = all p -a parts x has a uniqu e shortest member xs and every element of P is a refinement of xs . Let x s = [Xl, X2, . . , x n ] be some shortest member of P and [YI , Y2,· · . , Yml anot her member of P. It is sufficient to show that ys Proof ys = 41 Richard S. Bird is a refinement of xs. It then follows that if ys is another shortest member of P, then each of xs and ys is a refinement of the other, and so xs = ys. If ys is not a refinement of xs, then some element Yi of ys "spans" some segment Xj , Xj+l, "" Xk, where j

Technical Report CS8916, Department of Mathematics and Computing Science, University of Groningen, 1989. [2] S. MacLane . Categories for the Working Mathematician. Volume 5 of Graduate Texts in Mathematics, Springer-Verlag, 1971. [3] J . C. Reynolds. Towards a theory of type structure. In Programming Symposium, pages 408-425 , Springer-Verlag, 1974. Proceedings, Colloque sur la Programmation, Paris, April 9-111974. [4] J. C. Reynolds . Types , abstraction and parametric polymorphism. E. Mason, editor, IFIP '83, pages 513-523, Elsevier Science Publishers, 1983.

3 Semantics of Quasi-Boolean Expressions A. BijIsma Introduction In deriving programs, it is often useful to consider certain expressions as well-defined although they contain sub expressions to which no value can reasonably be attributed . For instance, one wishes to consider the expression a~ i < nand ali] = a as false when i = n, without worrying whether or not n is in the subscript range of array a. Expressions like these are called quasi-boolean in [3J. 1]. However, cand and cor do not satisfy pleasant algebraic laws: they are not commutative and do not in general distribute over each other.

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