The -calculus is a process calculus introduced by Robin Milner, Joachim Parrow, and David Walker in 1992.
Unlike older process calculi, such as CSP or CCS, the -calculus puts the emphasis on mobility of processes. The main technical device by which that is achieved is that of names, and the notions of name generation and scope extrusion.
There are many variations of the basic syntax of -calculus. Here we will work with
There are many variants of this basic syntax. One may:
The asynchronous -calculus arises by replacing the output prefix with a single process
which outputs along , and then stops. Thus, an output action may happen immediately (e.g. by putting the message into a buffer that will be next read when an input on is requested. By the structural congruence, this process can 'float around' to reach its destination.
The asynchronous version of the -calculus was introduced in [Boudol 1992].
Milner, Robin, Joachim Parrow, and David Walker. 1992. ‘A Calculus of Mobile Processes, I’. Information and Computation 100 (1): 1–40. https://doi.org/10.1016/0890-5401(92)90008-4.
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author = {Milner, Robin and Parrow, Joachim and Walker, David},
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Milner, Robin. 1992. ‘Functions as Processes’. Mathematical Structures in Computer Science 2 (2): 119–141. https://doi.org/10.1017/S0960129500001407.
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Milner, Robin. 1999. Communicating and Mobile Systems: The π-Calculus. New York, NY, USA: Cambridge University Press.
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Boudol, Gérard. “Asynchrony and the Pi-Calculus.” Research Report. INRIA, 1992. https://inria.hal.science/inria-00076939.
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Stark, I. “A Fully Abstract Domain Model for the π-Calculus.” In Proceedings 11th Annual IEEE Symposium on Logic in Computer Science, 36–42. IEEE, 1996. https://doi.org/10.1109/LICS.1996.561301.
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Fiore, M.P., E. Moggi, and D. Sangiorgi. “A Fully-Abstract Model for the π-Calculus.” In Proceedings 11th Annual IEEE Symposium on Logic in Computer Science, 43–54, 1996. https://doi.org/10.1109/LICS.1996.561302.
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Fiore, M.P., E. Moggi, and D. Sangiorgi. “A Fully Abstract Model for the π-Calculus.” Information and Computation 179, no. 1 (2002): 76–117. https://doi.org/10.1006/inco.2002.2968.
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