History; other formalisms¶

The $\pi$ -calculus is an example of a process calculus, i.e., a mathematical structure with a set of values and operations on those values in which processes are among the values and parallel composition (“running processes in parallel”) is a commutative and associative operation on processes.
The $\pi$ -calculus was created in 1992 by Robin Milner, Joachim Parrow, and David Walker. Milner (1934-2010) was a famous British computer scientist known for inventing one of the early systems for automatic theorem proving (LCF) and for creating the functional programming language ML, in addition to the $\pi$ -calculus.
The $\pi$ -calculus extends Milner’s earlier process calculus system called CCS (Calculus of Concurrent Systems) [Milner 80].
Another famous British computer scientist, Tony Hoare, created a simlar system called CSP (Communicating Sequential Processes) [Hoare 85], starting about 1978. CSP is the theoretical basis for the Occam language for parallel programming.
A major distinction between the $\pi$ -calculus and predecessor systems is the $\pi$ -calculus’s ability to pass a channels from one process to another, along some other communication channel. This feature enables the system to model mobility, (e.g., cell phones) and changes in process structure.