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Process Calculi

A family of formal languages for describing concurrent and distributed systems algebraically. A process calculus fixes a small syntax of process terms (parallel composition, action prefix, restriction, choice) and gives an operational semantics — usually as a labelled transition system — together with a behavioural equivalence such as Bisimulation. Canonical members:

  • CCS (Milner 1980) — fixed-topology synchronisation.
  • CSP (Hoare 1978) — synchronous channel rendezvous; refinement-based equivalences.
  • ACP (Bergstra & Klop 1984) — equational laws as primary; ad-hoc-extensible signature.
  • π-calculus (Milner, Parrow & Walker 1992) — name-passing; mobile communication topology.
  • Mobile Ambients (Cardelli & Gordon 1998) — mobile locations.
  • Join calculus (Fournet & Gonthier 1996) — asynchronous; pattern-matching on joins.
  • Spi calculus (Abadi & Gordon 1997) — π + cryptographic primitives.
  • Applied π-calculus (Abadi & Fournet 2001) — equational theories over terms.

Process calculi supply the formal substrate underneath Session Types, Choreographic Programming, and most modern accounts of distributed-system semantics.

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