This book about process algebra improves on its predecessor, written by Jos Baeten and Peter Weijland almost 20 years ago, by being more comprehensive and by providing far more mathematical detail. In addition the syntax of ACP has been extended by a constant 1 for termination. This modification not only makes the syntax more expressive, it also facilitates a uniform reconstruction of key aspects of CCS, CSP as well as ACP, within a single framework.

After renaming the empty process (∈) into 1 and the inactive process (δ) into 0, the axiom system ACP is redesigned as BCP. This change is both pragmatically justified and conceptually convincing. By using a different acronym instead of ACP, the latter can still be used as a reference to its original meaning, which is both useful and consistent.

Curiously these notational changes may be considered marginal and significant at the same time. In terms of theorems and proofs, or in terms of case studies, protocol formalizations and the design of verification tools, the specific details of notation make no real difference at all. But by providing a fairly definitive and uncompromising typescript a major impact is obtained on what might be called ‘nonfunctional qualities’ of the notational framework. I have no doubt that these nonfunctional qualities are positive and merit being exploited in full detail as has been done by Baeten and his co-authors. Unavoidably, the notational evolution produces a change of perspective. While, for instance, the empty process is merely an add on feature for ACP, it constitutes a conceptual cornerstone for BCP.