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.

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

Sequentiality and the pi-Calculus

The result shows how a typed π-calculus can be used as a descriptive tool for a significant class of programming languages without losing the latter's semantic properties.

A mechanized theory of the π-calculus in HOL

Preliminary work on a definitional formal theory of the π-calculus in higher order logic using the HOL theorem prover is described, with the ultimate goal of providing practical mechanized support for reasoning with the ρ-Calculus about applications.

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

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

A Translation of the Pi-Calculus Into MONSTR

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 Calculus of Explicit Substitutions

The aim of this work is to describe the prototypical mobility expressed by the π-calculus within a CCS-like approach to process algebras by introducing suitable constructors for both the explicit handling of name substitutions and the explicit instantiation of names.

Characterizing Bisimulation Congruence in the pi-Calculus (Extended Abstract)

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.

A Pi-Calculus with Explicit Substitutions

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