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.

Inhalt

1. Examples of Derivations.- On the Design of a Simple Proof for Morley's Theorem.- Well-Foundedness and the Transitive Closure.- Designing the Proof of Vizing's Theorem.- Phase Synchronization for Two Machines.- The Lexicographic Minimum of a Cyclic Array.- 2. Rules of Programming.- Metalevel Programming in Constructive Type Theory.- Laws of Programming.- Some Applications of Pointer Algebra.- Some Generalizations and Applications of Dijkstra's Guarded Commands.- 3 Refinement and Program Composition.- A Theoryof Program Composition.- Lectures on Data Refinement.- Refinement Alerebra Proves Correctness of Compilation.- 4 Distributed Svstems.- Process Algebra with Signals and Conditions.- Functional Specification of Time Sensitive Communicating Systems.- Systematic Derivation of Communicating Programs.