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.

In computing science design plays an eminently important role. By now, it is quite clear that the issue of proper design of programs within a formal calculus is one of the most interesting and most difficult parts of computing science. Many demanding problems have to be envisaged here such as notations, rules and calculi, and the study of semantic models. We are 'far away from comprehensive and widely accepted solutions in these areas. Discussions at the summer school have clearly shown that people have quite different perspectives and priorities with respect to these three main areas. There is a general agreement that notation is very important. Here, notation is not so much used in the sense of "syntactic sugar," but rather in the sense of abstract syntax, in the sense of language constructs. Proper notation can significantly improve our understanding of the nature of the objects that we are dealing with and simplify the formal manipulation of these objects. However, influenced by educational background, habits, and schools of thought there are quite different tastes with respect to notation. The papers in these proceedings show very clearly how different those notations can be even when talking about quite similar objects.

The present volume is the third in a series of VDM Symposia Proceedings. VDM, the Vienna Development Method, is a formal method for software engineering, Z refers to Zermelo, a mathematician whose name is associated with set theory. Many computing science, programming and software engineering proceedings are published regularly. The ones by VDM Europe have the distinguished mark that they are concerned with bringing real theory to apply to real programming. In Europe, there is very much interest in methodology, semantics and techniques, that is, in understanding how we build and what it is that we are building. The papers of these proceedings basically fall into four major groups: Applications, Methodology, Formalisations, and Foundations. The Methodology group has been further subdivided into five areas: Specification Methodology, Design Methodology, Modularity, Object Orientedness, and Processes, Concurrency and Distributed Systems.

In a time of multiprocessor machines, message switching networks and process control programming tasks, the foundations of programming distributed systems are among the central challenges for computing sci enti sts. The foundati ons of di stributed programming compri se all the fasci nating questions of computing science: the development of adequate com putational , conceptual and semantic model s for distributed systems, specification methods, verification techniques, transformation rules, the development of suitable representations by programming languages, evaluation and execution of programs describing distributed systems. Being the 7th in a series of ASI Summer Schools at Marktoberdorf, these lectures concentrated on distributed systems. Already during the previous Summer School s at Marktoberdorf aspects of di stributed systems were important periodical topics. The rising interest in distributed systems, their design and implementation led to a considerable amount of research in this area. This is impressively demonstrated by the broad spectrum of the topics of the papers in this vol ume, although they are far from being comprehensive for the work done in the area of distributed systems. Distributed systems are extraordinarily complex and allow many distinct viewpoints. Therefore the literature on distributed systems sometimes may look rather confusing to people not working in the field. Nevertheless there is no reason for resignation: the Summer School was able to show considerable convergence in ideas, approaches and concepts for distributed systems.