The-calculus: Notes on labelled semantics (original) (raw)

The π-calculus [MPW92] is a name-passing calculus that allows the description of distributed systems with a dynamically changing interconnection topology. Name communication, together with the possibility of declaring and exporting local names, gives the calculus a great expressive power. For instance, it was shown that process-passing calculi, which express mobility at higher order, can be encoded naturally in π-calculus [San93a]. Since its inception, the π-calculus has proliferated into a family of calculi differing slightly from one another either in the communication paradigm (polyadic vs monadic, asynchronous vs synchronous) or in the bisimulation semantics (labelled vs unlabelled, late vs early vs open vs barbed vs ...). These short notes present a collection of the labelled strong semantics 3 of the (synchronous monadic) π-calculus. The notes could not possibly replace any of the standard references listed in the Bibliography. They are an attempt to group together, using a uniform notation and the terminology that got assessed over the last years, a few definitions and concepts otherwise scattered throughout the π-calculus literature. I would like to thank James J. Leifer for his careful reading of the manuscript, and the helpful suggestions he provided. 3 The definition of weak late semantics requires some ingenuity. But for this case, the weak corresponding of each of the semantics we present can be easily defined by mimicking the standard CCS-like pattern.

A π-calculus with explicit substitutions: The late semantics

Lecture Notes in Computer Science, 1994

A new formulation of the-calculus, where name instantiation is handled explicitly, is presented. The explicit handling of name instantiation allows us to reduce the-calculus transitional semantics to a standard SOS framework. Hence,-calculus bisimulation models can take fully advantage of the SOS metatheory developed for`static' process calculi. For instance, complete axiomatic characterizations of-calculus bisimulation equivalences can be automatically derived by turning SOS rules into equations. Moreover, this formulation of the-calculus is promising for the development of semantic-based automatic veri cation tools. Here we treat in full detail the Late bisimulation semantics. A nite branching labelled transition system and a complete axiomatic characterization of the Late bisimulation equivalence are obtained.

Final semantics for the π-calculus

Programming Concepts and Methods PROCOMET ’98, 1998

In this paper we discuss nal semantics for the-calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the nal semantics paradigm, originated by Aczel and Rutten for CCS-like languages, can be successfully applied also here. This is achieved by suitably generalizing the standard techniques so as to accommodate the mechanism of name creation and the behaviour of the binding operators peculiar to the-calculus. As a preliminary step, we give a higher order presentation of the-calculus using as metalanguage LF, a logical framework based on typed-calculus. Such a presentation highlights the nature of the binding operators and elucidates the rôle of free and bound channels. The nal semantics is de ned making use of this higher order presentation, within a category of hypersets.

On bisimulations for the asynchronous π-calculus

Theoretical Computer Science, 1998

The asynchronous n-calculus is a variant of the n-calculus where message emission is nonblocking. Honda and Tokoro have studied a semantics for this calculus based on bisimulation. Their bisimulation relies on a modified transition system where, at any moment, a process can perform any input action. In this paper we propose a new notion of bisimulation for the asynchronous n-calculus, defined on top of the standard labelled transition system. We give several characterizations of this equivalence including one in terms of Honda and Tokoro's bisimulation, and one in terms of barbed equivalence. We show that this bisimulation is preserved by name substitutions, hence by input prefix. Finally, we give a complete axiomatization of the (strong) bisimulation for finite terms.

A lexically scoped distributed pi-calculus

2002

We define the syntax, the operational semantics, and a type system for lsd π, an asynchronous and distributed π-calculus with local communication and process migration. The calculus follows a simple model of distribution for mobile calculi, with a lexical scoping mechanism that provides both for remote communication and for process migration, making explicit migration primitives superfluous.

On the expressivity of infinite and local behaviour in fragments of the pi-calculus

The pi-calculus [Miln99] is one the most influential formalisms for modelling and analyzing the behaviour of concurrent systems. This calculus provides a language in which the structure of terms represents the structure of processes together with an operational semantics to represent computational steps. For example, the parallel composition term P | Q, which is built from the terms P and Q, represents the process that results from the parallel execution of the processes P and Q. Similarly, the restriction (\nu x)P represents a process P with local resource x. The replication !P can be thought of as abbreviating the parallel composition P | P | P .... of an unbounded number of P processes. As for other language-based formalisms (e.g., logic, formal grammars and the lambda-calculus) a fundamental part of the research in process calculi involves the study of the expressiveness of fragments or variants of a given process calculus. In this dissertation we shall study the expressiveness ...

Relationally Staged Computations in Calculi of Mobile Processes

Electronic Notes in Theoretical Computer Science, 2004

We apply the recently developed techniques of higher order abstract syntax and functorial operational semantics to give a compositional and fully abstract semantics for the π-calculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of presheaves over subcategories of Set to presheaves over subcategories of Rel. This extra structure is crucial in controlling the renaming of extruded names and in providing a variety of different dynamic allocation operators to model the different binders of the π-calculus.

Pi+-calculus: A calculus for concurrent processes with constraints

1998

The-calculus is a formal model of concurrent computation based on the notion of naming. It has an important role to play in the search for more abstract theories of concurrent and communicating systems. In this paper we augment the-calculus with a constraint store and add the notion of constraint agent to the standard-calculus concept of agent. We call this extension the +-calculus. We also extend the notion of barbed bisimulation to de ne behavioral equivalence for the +-calculus and use it to characterize some equivalent behaviors derived from constraint agents. The paper discusses examples of the extended calculus showing the transparent i n teraction of constraints and communicating processes.

From a Concurrent Lambda-Calculus to the Pi-Calculus

1995

We explore the (dynamic) semantics of a simply typedcalculus enriched with parallel composition, dynamic channel generation, and input-output communication primitives. The calculus, called the kcalculus, can be regarded as the kernel of concurrent-functional languages such as LCS, CML and Facile, and it can be taken as a basis for the definition of abstract machines, the transformation of programs, and the development of modal speci cation languages. The main technical contribution of this paper is the proof of adequacy of a compact translation of the k -calculus into the -calculus.

From a concurrent λ-calculus to the π-calculus

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 λ∥-calculus, can be regarded as the kernel of concurrent-functional languages such as LCS, CML and Facile, and it can be taken as a basis for the definition of abstract machines, the transformation of programs, and the development of modal specification languages. The main technical contribution of this paper is the proof of adequacy of a compact translation of the λ ∥-calculus into the π-calculus.

The weak late π-calculus semantics as observation equivalence

Lecture Notes in Computer Science, 1995

We show that the Weak Late ~r-calcuius semantics can be characterized as ordinary Observation congruence over a specialized transition system where both the instantiation of input placeholders and the name substitutions, clue e.g. to communication, are explicitly handled via suitable constructors. The approach presented here allows to axiomatize the Weak Late lr-calcuhis semantics by simply adding Milner's r-laws to the proof system for the Strong equivalence. Resorting to Observation equivalence provides a framework which is general enough to allow to recover, in straightforward ways, other bisimulation semantics (e.g. Early, both Strong and Weak, and Dynamic and Branching, both Early and Late).

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