# The Polyadic π-Calculus: a Tutorial

@inproceedings{Milner1993TheP,
title={The Polyadic $\pi$-Calculus: a Tutorial},
author={Robin Milner},
year={1993}
}
The π-calculus is a model of concurrent computation based upon the notion of naming. [...] Key Method Semantics is done in terms of both a reduction system and a version of labelled transitions called commitment; the known algebraic axiomatization of strong bisimilarity is given in the new setting, and so also is a characterization in modal logic. Some theorems about the replication operator are proved.Expand
1,154 Citations
A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions
A formalisation of π-calculus in the Coq system is presented. Based on a de Bruijn notation for names, our implementation exploits the mechanisation of some proof techniques described by Sangiorgi in
A mechanized theory of the π-calculus in HOL
The π-calculus is a process algebra for modelling concurrent systems in which the pattern of communication between processes may change over time. This paper describes the results of preliminary work
From a Concurrent Lambda-Calculus to the Pi-Calculus
• Computer Science
FCT
• 1995
We explore the (dynamic) semantics of a simply typed λ-calculus enriched with parallel composition, dynamic channel generation, and input-output communication primitives. The calculus, called the
A Higher-Order Specification of the pi-Calculus
The rules for type-checking and for evaluation and formalize a proof of type preservation in the Coq system are given and the specification for the pi-calculus formalizes communication by means of function application.
Extended pi-Calculi
• Mathematics, Computer Science
ICALP
• 2008
A general framework for extending the pi-calculus with data terms using a single untyped notion of agent, name and scope, an operational semantics without structural equivalence and a simple definition of bisimilarity is demonstrated.
Explicit substitutions for pi-congruences
• P. Quaglia
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2001
Here the πξ-calculus is extended to characterize late π-congruences, both strong and weak, and a coincidence result with open semantics is proved.
A Translation of the Pi-Calculus Into MONSTR
• Computer Science
• 1996
A translation of the π-calculus into the MONSTR graph rewriting language is described and proved correct, illustrating many features typically encountered in reasoning about graph rewriting systems, and particularly how serialisation techniques can be used to reorder an arbitrary execution into one having stated desirable properties.
The λ-calculus in the π-calculus†
• Mathematics, Computer Science
Mathematical Structures in Computer Science
• 2011
The encoding is proved to preserve and reflect beta reduction, and is shown to be fully abstract with respect to Abramsky's applicative bisimilarity.
Characterizing Bisimulation Congruence in the pi-Calculus (Extended Abstract)
• Xinxin Liu
• Mathematics, Computer Science
CONCUR
• 1994
The characterization supports a bisimulation-like proof technique which avoids explicit case analysis by taking a dynamic point of view of actions a process may perform, thus providing a new way of proving bisimulations congruence.
The Calculus of Explicit Substitutions
• Mathematics
• 1994
The aim of this work is to describe the prototypical mobility expressed by the π-calculus within a CCS-like approach to process algebras. Many versions of π-calculus bisimulation equivalence are

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