Propositions as sessions

Wadler, Philip

doi:10.1017/s095679681400001x

Cited by 146 publications

(261 citation statements)

References 42 publications

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“…and End ? from Wadler's GV calculus [Wadler 2012]. Unlike GV, the LSST calculus is not free of deadlock.…”

Section: Binary Session Typesmentioning

confidence: 99%

“…Then send M is a function from A to S, which must be used once (because it is closed over the channel endpoint). We flip the arguments for send with respect to other presentations in the literature Igarashi et al 2017;Lindley and Morris 2016;Wadler 2012], while aligning with those of Padovani [2017b]. The rule GV NEW for creating channels prescribes that new returns a pair of channel endpoints with dual session types.…”

Section: Binary Session Typesmentioning

confidence: 99%

“…Their approach enables viewing π -calculus reductions as proof transformations in the logic. Wadler [2012] proposed a foundation based on classical linear logic.…”

Section: Related Workmentioning

confidence: 99%

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Label-dependent session types

Thiemann

Vasconcelos

2019

Proc. ACM Program. Lang.

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Session types have emerged as a typing discipline for communication protocols. Existing calculi with session types come equipped with many different primitives that combine communication with the introduction or elimination of the transmitted value.We present a foundational session type calculus with a lightweight operational semantics. It fully decouples communication from the introduction and elimination of data and thus features a single communication reduction, which acts as a rendezvous between senders and receivers. We achieve this decoupling by introducing label-dependent session types, a minimalist value-dependent session type system with subtyping. The system is sufficiently powerful to simulate existing functional session type systems. Compared to such systems, label-dependent session types place fewer restrictions on the code. We further introduce primitive recursion over natural numbers at the type level, thus allowing to describe protocols whose behaviour depends on numbers exchanged in messages. An algorithmic type checking system is introduced and proved equivalent to its declarative counterpart. The new calculus showcases a novel lightweight integration of dependent types and linear typing, with has uses beyond session type systems.

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“…and End ? from Wadler's GV calculus [Wadler 2012]. Unlike GV, the LSST calculus is not free of deadlock.…”

Section: Binary Session Typesmentioning

confidence: 99%

Section: Binary Session Typesmentioning

confidence: 99%

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Label-dependent session types

Thiemann

Vasconcelos

2019

Proc. ACM Program. Lang.

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“…Generally, session types are inspired by linear type systems and systems with typestate as channels change their type at each communication operation and must thus be handled linearly. Some variants are directly connected to linear logic via the Curry-Howard correspondence [Caires and Pfenning 2010;Toninho et al 2013;Wadler 2012].…”

Section: Introductionmentioning

confidence: 99%

Intrinsically-Typed Mechanized Semantics for Session Types

Thiemann

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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Session types have emerged as a powerful paradigm for structuring communication-based programs. They guarantee type soundness and session fidelity for concurrent programs with sophisticated communication protocols. As type soundness proofs for languages with session types are tedious and technically involved, it is rare to see mechanized soundness proofs for these systems.We present an executable intrinsically typed small-step semantics for a realistic functional session type calculus. The calculus includes linearity, recursion, and recursive sessions with subtyping. Asynchronous communication is modeled with an encoding.The semantics is implemented in Agda as an intrinsically typed, interruptible CEK machine. This implementation proves type preservation and a particular notion of progress by construction. CCS CONCEPTS• Software and its engineering → Concurrent programming structures; Semantics; • Theory of computation → Process calculi.

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“…In L. Caires and F. Pfenning [10] and in P. Wadler [32], π-calculus-like processes are typed with linear types regarded as session types and occur in the framework of a more standard system of functional programming. We remark that here too the context is intuitionistic, or polarized; however it is beyond the limits of this paper to examine these interesting new ideas in detail.…”

Section: Introductionmentioning

confidence: 99%

On the π-calculus and Co-intuitionistic Logic. Notes on Logic for Concurrency and λP Systems

Bellin

Menti

2014

Fundamenta Informaticae

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We reconsider work by Bellin and Scott in the 1990s on R. Milner and S. Abramsky's encoding of linear logic in the π-calculus and give an account of efforts to establish a tight connection between the structure of proofs and of the cut elimination process in multiplicative linear logic, on one hand, and the input-output behaviour of the processes that represent them, on the other, resulting in a proof-theoretic account of (a variant of) Chu's construction. But Milner's encoding of the linear lambda calculus suggests consideration of multiplicative co-intuitionistic linear logic: we provide a term assignment for it, a calculus of coroutines which presents features of concurrent and distributed computing. Finally, as a test case of its adequacy as a logic for distributed computation, we represent our term assignment as a λP system. We argue that translations of typed functional languages in concurrent and distributed systems (such as π-calculi or λP systems) are best typed with co-intuitionistic logic, where some features of computations match the logical properties in a natural way. * We thank Phil Scott and Tristan Crolard for their cooperation over the years on the topics of this paper. We had useful conversations with 1 In 1991-2 Gianluigi Bellin and Philip Scott were in Edinburgh, learning the π-calculus from Robin Milner; also they were well aware of the work by Samson Abramsky, who gave a lecture on it in Edinburgh in 1992. 22 G. Bellin and A. Menti / Intuitionistic Duality, π Calculus and λP SystemsThe π-calculus is meant as a paradigmatic language for concurrent and distributed computing in the same way as the λ-calculus is paradigmatic for functional programming; since the fundamental role of the typed λ-calculus is confirmed by the Curry-Howard correspondence with propositions of intuitionistic logic and proofs in natural deduction, so there was the expectation that linear logic might provide a meaningful type system for the π-calculus and normalization of proofs in linear logic might correspond to the behaviour of concurrent processes of the π-calculus in a natural way. The need for conceptual clarity in the foundations of concurrent and distributed computing is even more evident today, not only because, as Philip Wadler puts it, "with the advent of multicores, mobile phones, and server farms, we have all become concurrent programmers" [32], but also because our understanding of information processing in basic biological entities takes the form of distributed computing.Linear logic [14] appeared as a good candidate for a type system for concurrent logical computations: Girard himself had presented the representation of derivations in classical linear logic in the system of proof nets as a way to realize a "parallelization of the syntax"; in [14] this goal was regarded as already achieved for the multiplicative fragment of linear logic and was proposed as a research project for larger parts of the system. Therefore the encodings in the π-calculus of linear logic proofs, and in particular of proof-nets, a...

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Propositions as sessions

Cited by 146 publications

References 42 publications

Label-dependent session types

Label-dependent session types

Intrinsically-Typed Mechanized Semantics for Session Types

On the π-calculus and Co-intuitionistic Logic. Notes on Logic for Concurrency and λP Systems

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