In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker in 1992, based on ideas by Uffe Engberg and Mogens Nielsen. It can be seen as a continuation of Milner’s work on the process calculus CCS (Calculus of Communicating Systems). The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation.
The π-calculus is elegantly simple yet very expressive. Functional programs can be encoded into the π-calculus, and the encoding emphasises the dialogue nature of computation, drawing connections with game semantics. Extensions of the π-calculus, such as the spi calculus and applied π, have been successful in reasoning about cryptographic protocols. Beside the original use in describing concurrent systems, the π-calculus has also been used to reason about business processes and molecular biology.