Programming and Mathematical Method

1. Front Matter

   Pages I-VIII

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2. Examples of Derivations

   1. Front Matter

      Pages 1-2

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   2. On the design of a simple proof for Morley’s Theorem

      • Edsger W. Dijkstra

      Pages 3-9

   3. Well-foundedness and the transitive closure

      • A. J. M. van Gasteren, Edsger W. Dijkstra

      Pages 11-15

   4. Designing the proof of Vizing’s Theorem

      • Josyula R. Rao, Edsger W. Dijkstra

      Pages 17-25

   5. Phase Synchronization for two machines

      • Wim H. J. Feijen

      Pages 27-31

   6. The Lexicographic Minimum of a Cyclic Array

      • Wim H. J. Feijen

      Pages 33-42

3. Rules of Programming

   1. Front Matter

      Pages 43-44

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   2. Metalevel Programming in Constructive Type Theory

      • Robert L. Constable

      Pages 45-93

   3. Laws of Programming

      • C. A. R. Hoare, I. J. Hayes, He Jifeng, C. C. Morgan, A. W. Roscoe, J. W. Sanders et al.

      Pages 95-122

   4. Some Applications of Pointer Algebra

      • Bernhard Möller

      Pages 123-155

   5. Some generalizations and applications of Dijkstra’s guarded commands

      • Greg Nelson

      Pages 157-191

4. Refinement and Program Composition

   1. Front Matter

      Pages 193-194

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   2. A Theory of Program Composition

      • K. Mani Chandy

      Pages 195-212

   3. Lectures on Data Refinement

      • David Gries

      Pages 213-244

   4. Refinement algebra proves correctness of compilation

      • C. A. R. Hoare, He Jifeng

      Pages 245-269

5. Distributed Systems

   1. Front Matter

      Pages 271-272

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   2. Process Algebra with Signals and Conditions

      • J. C. M. Baeten, J. A. Bergstra

      Pages 273-323

   3. Functional Specification of Time Sensitive Communicating Systems

      • Manfred Broy

      Pages 325-367

   4. Systematic Derivation of Communicating Programs

      • Ernst-Rüdiger Olderog

      Pages 369-407

The Summer School in Marktoberdorf 1990 had as its overall theme the development of programs as an activity that can be carried out based on and supported by a mathematical method. In particular mathematical methods for the development of programs as parts of distributed systems were included. Mathematical programming methods are a very important topic for which a lot of research in recent years has been carried out. In the Marktoberdorf Summer School outstanding scientists lectured on mathematical programming methods. The lectures centred around logical and functional calculi for the • specification, • refinement, • verification of programs and program systems. Some extremely remarkable examples were given. Looking at these examples it becomes clear that proper research and teaching in the area of program methodology should always show its value by being applied at least to small examples or case studies. It is one of the problems of computing science that examples and case studies have to be short and small to be lJresentable in lectures and papers of moderate size. However, even small examples can tell a lot about the tractability and adequacy of methods and being able to treat small examples does at least prove that the method can be applied in modest ways. Furthermore it demonstrates to some extent the notational and calculational overhead of applying formal methods.

• Programmierung
• Programmverifikation
• Verteilte Systeme
• algorithms
• design
• development
• distributed systems
• functional programming
• logic
• process algebra
• program verification
• programming
• software
• software engineering
• verification

• Institut für Informatik, Technische Universität München, München 2, Germany

  Manfred Broy

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