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Communicating and Mobile Systems: the π-calculus,

Davide Sangiorgi

2000
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Science of Computer Programming
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The -calculus is a well-known and in uential model of concurrency. It is simplethe grammar that describes the processes has just a few constructs, each with a clear operational intuition -and has an elegant theory, yet it is very powerful. Its amazing expressive power is due to the ability of describing mobile systems. These are concurrent systems whose structure can change, both because processes can be created and can die, and because the linkage structure among existing processes can change.
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... It is remarkable, for instance, that references (in the sense of imperative languages), objects (in the sense of object-oriented languages), and functions can all be described as -calculus processes. The possibility of describing di erent computational models, both sequential and concurrent, and the rich theory make the -calculus an ideal semantic basis for languages and systems that combine features from di erent models, for instance concurrent imperative object-oriented languages. Thorough and intense studies of the -calculus over the past 10 years have allowed us to understand important concepts of concurrency theory -in particular, of mobile systems -such as types and behavioural equivalences. From a marketing point of view, Milner's Communicating and mobile systems: the -calculus is justiÿed by two important reasons: it is the ÿrst textbook on the -calculus; it is a superb introduction to the fundamental principles of concurrency theory. The ÿrst point is just a fact. I should explain, however, the second. In today's information society, concurrency is more and more important. Students should therefore be exposed, already at the undergraduate level, to the basic concepts of its theory. For this, Milner's book stands out as a wonderful instrument. (The book is indeed the outcome of Milner' s lectures to undergraduates in Cambridge.) Undoubtedly, Milner was the right person to endeavour the task of writing such a text. Milner has an extraordinary communication skill, something clear to anybody who has ever read one of his papers or books, or has seated at one of his talks. Furthermore, Milner has been a leading researcher in the area of concurrency theory for the past 30 years. The -calculus, and the earlier calculus of communicating systems (CCS), for instance, are contributions of his [1, 3] .

doi:10.1016/s0167-6423(00)00008-3
fatcat:sxu3sajlvbhzxnvhmjkorz3ozm