Presheaf models for the π-calculus (original) (raw)

Lecture Notes in Computer Science, 1997

In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a built-in notion of bisimulation. We show how presheaf categories, in which traditional models of concurrency are embedded, can be used to deduce congruence properties of bisimulation for the traditional models. A key result is given here; it is shown that the homomorphisms between presheaf categories, i.e., colimit preserving functors, preserve open map bisimulation. We follow up by observing that presheaf categories and colimit preserving functors organise in what can be considered as a category of non-deterministic domains. Presheaf models can be obtained as solutions to recursive domain equations. We investigate properties of models given for a range of concurrent process calculi, including CCS, CCS with value-passing, π-calculus and a form of CCS with linear process passing. Open map bisimilarity is shown to be a congruence for each calculus. These are consequences of general mathematical results like the preservation of open map bisimulation by colimit preserving functors. In all but the case of the higher order calculus, open map bisimulation is proved to coincide with traditional notions of bisimulation for the process terms. In the case of higher order processes, we obtain a finer equivalence than the one one would normally expect, but this helps reveal interesting aspects of the relationship between the presheaf and the operational semantics. For a fragment of the language, corresponding to a form of λ-calculus, open map bisimulation coincides with applicative bisimulation. In developing a suitable general theory of domains, we extend results and notions, such as the limit-colimit coincidence theorem of Smyth and Plotkin, from the orderenriched case to a "fully" 2-categorical situation. Moreover we provide a domain theoretical analysis of (open map) bisimulation in presheaf categories. We present, in fact, induction and coinduction principles for recursive domains as in the works of Pitts and of Hermida and Jacobs and use them to derive a coinduction property based on bisimulation. vii Personal debts can never be adequately acknowledged. I am especially grateful to my supervisor Glynn Winskel. Not only has he taught me how to do research, but he also transmitted his enthusiasm for it. It has always been a pleasure and a source of learning to discuss ideas with him and this thesis owes much to his stimulating guidance. While leaving me the freedom of choosing the problems I wished to work on, he has always been very involved in what I was doing to the point that this thesis can, in fact, be regarded as the result of four years of joint work. I shall also heartily thank him for his friendship. Pino Rosolini gave unstinting support in more ways than one. He guided my first steps as a researcher when I was working on my 'tesi di laurea'. Later, when I decided to go on with postgraduate studies, he put me in contact and warmly suggested that I should study with Glynn. Ever since then he discreetly followed my progresses as a PhD student while always being available whenever I needed his help or advice. Thanks are due to Vladimiro Sassone, Ian Stark and Marcelo Fiore. They all showed me friendship and stimulated my research. Marcelo in particular has been very influential in the development of an important part of this thesis, Chapter 6.

A Fully Abstract Model for the π-calculus

Information and Computation, 2002

This paper provides both a fully abstract (domaintheoretic) model for the π-calculus and a universal (set-theoretic) model for the finite π-calculus with respect to strong late bisimulation and congruence. This is done by: considering categorical models, defining a metalanguage for these models, and translating the π-calculus into the metalanguage. A technical novelty of our approach is an abstract proof of full abstraction: The result on full abstraction for the finite π-calculus in the set-theoretic model is axiomatically extended to the whole π-calculus with respect to the domain-theoretic interpretation. In this proof, a central role is played by the description of nondeterminism as a free construction and by the equational theory of the metalanguage.

A Fully-Abstract Model for the pi-Calculus (Extended Abstract)

Concurrent and Located Synchronizations in π-Calculus

Lecture Notes in Computer Science, 2007

We present two novel semantics for π-calculus. The first allows one to observe on which channel a synchronization is performed, while the second allows concurrent actions, provided that they do not compete for resources. We present both a reduction and a labeled semantics, and show that they induce the same behavioral equivalence. As our main result we show that bisimilarity is a congruence for the concurrent semantics. This important property fails for the standard semantics.

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.

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.

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.

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.

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.

Higher category models of the pi-calculus

2015

We present an approach to modeling computational calculi using higher category theory. Specifically we present a fully abstract semantics for the pi-calculus. The interpretation is consistent with Curry-Howard, interpreting terms as typed morphisms, while simultaneously providing an explicit interpretation of the rewrite rules of standard operational presentations as 2-morphisms. One of the key contributions, inspired by catalysis in chemical reactions, is a method of restricting the application of 2-morphisms interpreting rewrites to specific contexts.

Presheaf models for the π-calculus (original) (raw)

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