Π-calculus

The π-calculus has few terms and is a small, yet expressive language (see § Syntax). 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 through business processes, molecular biology. and autonomous agents in artificial intelligence. The π-calculus belongs to the family of process calculi, mathematical formalisms for describing and analyzing properties of concurrent computation. In fact, the π-calculus, like the λ-calculus, is so minimal that it does not contain primitives such as numbers, Booleans, data structures, variables, functions, or even the usual control flow statements (such as if-then-else, while). Central to the π-calculus is the notion of name. The simplicity of the calculus lies in the dual role that names play as communication channels and variables.