On the π-calculus and linear logic

Bellin, Gianluigi; Scott, Philip

doi:10.1016/0304-3975(94)00104-9

Cited by 123 publications

(148 citation statements)

References 9 publications

Supporting

Mentioning

147

Contrasting

Order By: Relevance

“…We could treat all CP processes quotiented by these permutations, but that would presuppose these equivalences, rather than having them induced by the actual behaviour of CP processes. (Bellin and Scott do such an identification in [7], pg. 14, rule (1).)…”

Section: Problems With Wadler's Reduction Semantics For Cpmentioning

confidence: 93%

“…To realise this hope, Abramsky proposed a programme of "Processes as Proofs" [2] in the early nineties. Abramsky [1] and Bellin and Scott [7] interpreted CLL proofs as terms in process calculi, matching (Cut)-reduction to process reduction. However, these correspondences interpret CLL proofs in an extremely restricted set of processes -those which never deadlock and never exhibit racy or nondeterministic behaviour -and so their correspondences could reasonably be criticised as not really capturing concurrency.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

View full text Add to dashboard Cite

Abstract. Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication. We use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences.

show abstract

Section: Problems With Wadler's Reduction Semantics For Cpmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

View full text Add to dashboard Cite

show abstract

“…Bellin and Scott [5] establish a mapping from linear logic proofs to a variant of the π-calculus and some connections between proof reduction and π-calculus reduction. However, this mapping results in complex encodings, so that their system could hardly be considered a type assignment system for processes, which has been achieved in this work.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…", seems to have been a source of inspiration for Milner when introducing replication in the π-calculus [22]. Following the early works of Abramsky [1], several authors have exploited variants of π-calculi to express proof reductions (e.g., [5]) or game semantics (e.g., [19]) in systems of linear logic. In the field of concurrency, many research directions have also drawn inspiration from linear logic for developing type-theoretic analyses of mobile processes, motivated by the works of Kobayashi, Pierce, and Turner [21]; a similar influence is already noticeable in the first publications by Honda on session types [16].…”

Section: Introductionmentioning

confidence: 99%

Session Types as Intuitionistic Linear Propositions

Caires

Pfenning

2010

CONCUR 2010 - Concurrency Theory

257

534

View full text Add to dashboard Cite

Several type disciplines for π-calculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the π-calculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic. Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types. We show that our type discipline is useful from a programming perspective, and ensures session fidelity, absence of deadlocks, and a tight operational correspondence between π-calculus reductions and cut elimination steps.

show abstract

“…

AbstractContinuing a line of work by Abramsky (1994), Bellin and Scott (1994), and Caires and Pfenning (2010), among others, this paper presents CP, a calculus, in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), Honda et al (1998), andVasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and a translation from GV into CP.

…”

mentioning

confidence: 99%

Propositions as sessions

2014

View full text Add to dashboard Cite

Continuing a line of work by Abramsky (1994), Bellin and Scott (1994), and Caires and Pfenning (2010), among others, this paper presents CP, a calculus, in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), Honda et al. (1998), andVasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and a translation from GV into CP. The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yields a language free from races and deadlock, where race and deadlock freedom follows from the correspondence to linear logic. 'The new connectives of linear logic have obvious meanings in terms of parallel computation. [. . . ] Linear logic is the first attempt to solve the problem of parallelism

show abstract

On the π-calculus and linear logic

Cited by 123 publications

References 9 publications

Observed Communication Semantics for Classical Processes

Observed Communication Semantics for Classical Processes

Session Types as Intuitionistic Linear Propositions

Propositions as sessions

Contact Info

Product

Resources

About