Reviews for Communicating and Mobile Systems: The Pi Calculus

1. Marvellous

   Rated 5 out of 5 stars, May 12th, 2007

   The pi-calculus is a beautiful language! Just as the lambda-calculus was invented to model computations, so the pi-calculus was invented to model processes. Milner's earlier work on CCS set the scene, but it only dealt with concurrency; since mobility wasn't included in the primitive operations, it was hard to model things like mobile phone networks, the internet, or network security.
   
   The change from CCS to pi-calculus is as far-reaching as it is straightforward: you simply allow channel names to be passed as messages from process to process. You can literally model any computable function in terms of pi-calculus process interactions.
   
   This book introduces the pi-calculus, and shows you how to model simple systems using it. There are examples of buffers and so forth to set the scene, and readers should learn enough to model real-world systems. However, pi-calculus (like CCS before it) is more than just a language for describing things; it also lets you reason about them. Milner explains some of the basic equivalences on processes, and shows how you can use processes to model data. He also discusses the possibility of adding a type theory to the language.
   
   Pi-calculus is by no means simple, so this book definitely requires some mathematical maturity of its readers. But my experience using it as a course text book is that students find the calculus relatively straightforward provided it's explained well, and you give plenty of examples.
   
   All in all, a great subject, and a great book to learn it from, especially if you couple it with the two online tutorials still available from LFCS (where Milner and his collagues used to work when they invented the calculus). Sangiorgi and Walker's book is better for advanced researchers, but if you want an introductory book that explains the language in non-trivial terms, this is the one for you.

2. best pi-calculus text

   Rated 4 out of 5 stars, September 12th, 2006

   This is the best pi-calculus book to learn and understand this theoretical computer science. This book's author is the author of pi-calculus and it shows in the clarity and logical development of the subject.