Session Types as Intuitionistic Linear Propositions

Caires, Luís; Pfenning, Frank

doi:10.1007/978-3-642-15375-4_16

Cited by 257 publications

(541 citation statements)

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“…Session types were originally proposed by Honda [17] in the context of the π-calculus as a way to ensure that processes conform to a protocol. The linear logic-based study of session types was initiated by Caires and Pfenning [9], who presented an assignment of π-calculus terms to sequent calculus proofs of Intuitionistic Linear Logic (ILL) that interprets the connectives of ILL as session types in the sense of Honda. The fundamental ideas of Caires and Pfenning were later adapted by Wadler to CLL [35,36], yielding a more symmetric system of "Classical Processes" (CP).…”

Section: Introductionmentioning

confidence: 99%

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

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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.

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Section: Introductionmentioning

confidence: 99%

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

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“…Anticipated with some analogies for some time [11,23], session types have recently been placed upon the firm foundation of linear logic via a Curry-Howard interpretation of linear propositions as types, proofs as processes, and cut reduction as communication. Variations apply for both intuitionistic [5,6] and classical [24] linear logic. This has enabled the application of proof-theoretic techniques in this domain, for example, developing logical relations [17], corecursion [22], and parametricity and behavioral polymorphism [4].…”

Section: Introductionmentioning

confidence: 99%

Polarized Substructural Session Types

Pfenning

Griffith

2015

Lecture Notes in Computer Science

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Abstract. The deep connection between session-typed concurrency and linear logic is embodied in the language SILL that integrates functional and message-passing concurrent programming. The exacting nature of linear typing provides strong guarantees, such as global progress, absence of deadlock, and race freedom, but it also requires explicit resource management by the programmer. This burden is alleviated in an affine type system where resources need not be used, relying on a simple form of garbage collection. In this paper we show how to effectively support both linear and affine typing in a single language, in addition to the already present unrestricted (intuitionistic) types. The approach, based on Benton's adjoint construction, suggests that the usual distinction between synchronous and asynchronous communication can be viewed through the lens of modal logic. We show how polarizing the propositions into positive and negative connectives allows us to elegantly express synchronization in the type instead of encoding it by extra-logical means.

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“…[2] uses refinement types for channels to verify authentication in multiparty session protocols, but does not consider multi-session properties. The work [7] investigates a relationship between a dual intuitionistic linear logic and binary session types, and shows that the former defines a proof system for a session calculus which can automatically characterise and guarantee a session fidelity and global progress. None of the above works treat either virtual states or logical specifications for interleaved multiparty sessions.…”

Section: Related Work and Further Topicsmentioning

confidence: 99%

A Multiparty Multi-session Logic

Bocchi

Demangeon

Yoshida

2013

Trustworthy Global Computing

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Abstract. Recent work on the enhancement of typing techniques for multiparty sessions with logical annotations enables, not only the validation of structural properties of the conversations and on the sorts of the messages, but also properties on the actual values exchanged. However, specification and verification of mutual effects of multiple cross-session interactions are still an open problem. We introduce a multiparty logical proof system with virtual states that enables the tractable specification and validation of fine-grained inter-session correctness properties of processes participating in several interleaved sessions. We present a sound and relatively complete static verification method.

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Session Types as Intuitionistic Linear Propositions

Cited by 257 publications

References 25 publications

Observed Communication Semantics for Classical Processes

Observed Communication Semantics for Classical Processes

Polarized Substructural Session Types

A Multiparty Multi-session Logic

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