Better late than never: a fully-abstract semantics for classical processes

Kokke, Wen; Montesi, Fabrizio; Peressotti, Marco

doi:10.1145/3290337

Cited by 25 publications

(51 citation statements)

References 31 publications

(50 reference statements)

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“…Following that, in ğ3 we introduce a process calculus with strong coexponentials, which we call CSLL (Client-Server Linear Logic). This new system is in the style of Kokke et al [2019a], which replaces the one-sided sequents with hypersequents. It is argued that coexponentials enable the collection of an arbitrary number of clients following session into a client pool, which communicates on a channel that follows session £ .…”

Section: Roadmapmentioning

confidence: 99%

Client-server sessions in linear logic

Qian

Kavvos

Birkedal

2021

Proc. ACM Program. Lang.

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We introduce coexponentials, a new set of modalities for Classical Linear Logic. As duals to exponentials, the coexponentials codify a distributed form of the structural rules of weakening and contraction. This makes them a suitable logical device for encapsulating the pattern of a server receiving requests from an arbitrary number of clients on a single channel. Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is suited to modelling client-server interactions. We also present a session-typed functional programming language for client-server programming, which we translate to our system of coexponentials.

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Section: Roadmapmentioning

confidence: 99%

Client-server sessions in linear logic

Qian

Kavvos

Birkedal

2021

Proc. ACM Program. Lang.

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“…As a consequence of adopting linear sequent calculus, the session typings of [9,32,18] do not support directly functional computation. Several approaches have been developed to overcome this intrinsic limitation.…”

Section: λ`And Other Typed Concurrent λ-Calculimentioning

confidence: 99%

Par means parallel: multiplicative linear logic proofs as concurrent functional programs

Aschieri¹,

Genco

2019

Proc. ACM Program. Lang.

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Along the lines of the Abramsky "Proofs-as-Processes" program, we present an interpretation of multiplicative linear logic as typing system for concurrent functional programming. In particular, we study a linear multiple-conclusion natural deduction system and show it is isomorphic to a simple and natural extension of λ-calculus with parallelism and communication primitives, called λ`. We shall prove that λ`satisfies all the desirable properties for a typed programming language: subject reduction, progress, strong normalization and confluence. * Funded by FWF grant P32080-N31. † Funded by ANR JCJC project Intuitions Bolzaniennes. linking proofs to programs, propositions to types, proof normalization to computation. Soon after, Wadler [32] introduced the session typed π-calculus CP, shown to tightly correspond to classical linear logic. LimitationsThis important research notwithstanding, it appears that there is still ground to cover toward canonical and firm foundations for concurrent computation. First of all, asynchronous communication does not appear to rest on solid foundations. Yet this communication style is easier to implement and more practical than the purely synchronous paradigm, so it is widespread and asynchronous typed process calculi have been already investigated (see [13]). Unfortunately, linear logic has not so far provided via Curry-Howard a logical account of asynchronous communication. The reason is that there is a glaring discrepancy between full cut-elimination and π-calculus reduction which has not so far been addressed. On one hand, as we shall see, linear logic does support asynchronous communication, but only through the full process of cut-elimination, which indeed makes essential use of asynchronous communication. On the other hand, the π-calculus of [9] only mimics a partial cut-elimination process that only eliminates top-level cuts. Indeed, by comparison with its type system, the π-calculus lacks some necessary computational reduction rules. Some of the missing reductions, corresponding to commuting conversions, were provided in Wadler's CP. The congruence rules that allow the extra reductions to mirror full cut-elimination, however, were rejected: in Wadler's [32] own words, "such rules do not correspond well to our notion of computation on processes, so we omit them". A set of reductions similar to that rejected by Wadler is regarded in [27] as sound relatively to a notion of "typed context bisimilarity". The notion, however, only ensures that two "bisimilar" processes have the same input/output behaviour along their main communication channel; the internal synchronization among the parallel components of the two processes is not captured and may differ significantly. Thus, the extensional flavor of the bisimilarity notion prevents it to detect the intensionally different behaviour of the related processes, that is, how differently they communicate and compute.

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“…Kokke et al [12] introduced Hypersequent Classical Processes (HCP), which addresses this mismatch. The key insight is to register parallelism in the typing judgements using hypersequents [2], a technique from logic which generalises judgements from one sequent to many.…”

Section: Introductionmentioning

confidence: 99%

Taking Linear Logic Apart

Kokke

Montesi

Peressotti

2019

Electron. Proc. Theor. Comput. Sci.

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Process calculi based on logic, such as πDILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of the π-calculus: the fundamental operator for parallel composition does not correspond to any rule of linear logic.Kokke et al. [12] introduced Hypersequent Classical Processes (HCP), which addresses this mismatch using hypersequents (collections of sequents) to register parallelism in the typing judgements. However, the step from CP to HCP is a big one. As of yet, HCP does not have reduction semantics, and the addition of delayed actions means that CP processes interpreted as HCP processes do not behave as they would in CP.We introduce HCP − , a variant of HCP with reduction semantics and without delayed actions. We prove progress, preservation, and termination, and show that HCP − supports the same communication protocols as CP.

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Better late than never: a fully-abstract semantics for classical processes

Cited by 25 publications

References 31 publications

Client-server sessions in linear logic

Client-server sessions in linear logic

Par means parallel: multiplicative linear logic proofs as concurrent functional programs

Taking Linear Logic Apart

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