Essential Business Process Modeling

The Pi-Calculus

Developed by Scottish mathematician Robin Milner in the 1990s, the pi-calculus is a formal language for defining concurrent, communicating processes, including, but not restricted to, business processes. In its detail, the pi-calculus is a rather advanced algebraic system requiring a senior level of mathematical training. Milner’s presentation of the subject is written in the mathematical idiom of definitions, theorems, and lemmas, inaccessible to most BPM onlookers.^[*] Few business analysts or software developers could survive if required to compose their business processes as lines of pi-calculus code.

But somehow, despite its academic roots and its inherent complexity, the pi-calculus has become one of BPM’s most attention-getting cocktail party terms. Popular BPM literature states boldly that major languages such as XLANG, WSCI, BPML, BPEL, and WS-CDL are based on the pi-calculus. This stunning level of influence, charges leading BPM commentator Wil van der Aalst, is dubious, and surely nothing but hype:

Let the people that advocate BPEL4WS, BPMN, ... and WSCI show the precise relation between the language and some formal foundation. People that cannot do this but still claim strong relationships between their language and e.g., pi-calculus, only cause confusion.^[*]

Whether or not it is hype, the pi-calculus-BPM connection merits a serious look. What, in a nutshell, is the pi-calculus, how does it apply to BPM, and what is the extent and nature of its influence ...