Functions as Session-Typed Processes

Toninho, Bernardo; Caires, Luís; Pfenning, Frank

doi:10.1007/978-3-642-28729-9_23

Cited by 38 publications

(50 citation statements)

References 19 publications

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“…Pfenning et al (2011) extended that system to support proof-carrying code and proof irrelevance. Toninho et al (2012) explore encodings of λ -calculus into πDILL. Pérez et al (2012) introduce logical relations on linear-typed processes to prove termination and contextual equivalences.…”

Section: Deadlock Freedommentioning

confidence: 99%

Propositions as sessions

2014

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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

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Section: Deadlock Freedommentioning

confidence: 99%

Propositions as sessions

2014

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“…Lemma 3 shows a forwarding (link) agent corresponds to the identity process (cf. [7,51]), which is ensured by the linearity of session types.…”

Section: Definition 13 (Reduction-closed Barbed Congruence)mentioning

confidence: 99%

“…Since the metalanguage style for effects separates more clearly in the type system what is definitely pure from what is potentially effectful, we could combine existing typed encodings of the pure λ-calculus (such as that of [51]) with an encoding for the effectful parts (let and unit above). The encoding of (let) above would be the same as the encoding for let x = M in N shown at the start of Section 3.…”

Section: Monadic Metalanguage For Effectsmentioning

confidence: 99%

“…The encoding for (unit) is similar to values in our calculus (variables and constants) with M ei,eo r = ei?(c).eo! c | M r where M r is any other (sound) typed encoding of PCF, perhaps building on the many possible encodings in the literature (e.g., [33,49,51], with various trade-offs).…”

Section: Monadic Metalanguage For Effectsmentioning

confidence: 99%

“…Such embeddings are applied for type-based analyses of programming languages for, e.g., concurrent abstract data types [45], a tail-call optimisation of functions [31], secrecy [24] and termination [56]. Recently Toninho et al [51] showed that simply typed λ-terms are encodable more tightly into session-typed processes via a CurryHoward interpretation, providing a new logical explanation of sharing and copying parallel λ-evaluation strategies.…”

Section: Introductionmentioning

confidence: 99%

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Effects as sessions, sessions as effects

OrchardDominic¹,

Yoshida²

2016

SIGPLAN Not.

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Effect and session type systems are two expressive behavioural type systems. The former is usually developed in the context of the lambda-calculus and its variants, the latter for the pi-calculus. In this paper we explore their relative expressive power. Firstly, we give an embedding from PCF, augmented with a parameterised effect system, into a session-typed pi-calculus (session calculus), showing that session types are powerful enough to express effects. Secondly, we give a reverse embedding, from the session calculus back into PCF, by instantiating PCF with concurrency primitives and its effect system with a session-like effect algebra; effect systems are powerful enough to express sessions. The embedding of session types into an effect system is leveraged to give a new implementation of session types in Haskell, via an effect system encoding. The correctness of this implementation follows from the second embedding result. We also discuss various extensions to our embeddings.

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A Categorical Model of an $$\mathbf {i/o}$$ -typed $$\pi $$ -calculus

Sakayori

Tsukada

2019

Programming Languages and Systems

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This paper introduces a new categorical structure that is a model of a variant of the i/o-typed π-calculus, in the same way that a cartesian closed category is a model of the λ-calculus. To the best of our knowledge, no categorical model has been given for the i/o-typed πcalculus, in contrast to session-typed calculi, to which corresponding logic and categorical structure were given. The categorical structure introduced in this paper has a simple definition, combining two well-known structures, namely, closed Freyd category and compact closed category. The former is a model of effectful computation in a general setting, and the latter describes connections via channels, which cause the effect we focus on in this paper. To demonstrate the relevance of the categorical model, we show by a semantic consideration that the π-calculus is equivalent to a core calculus of Concurrent ML.

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Functions as Session-Typed Processes

Cited by 38 publications

References 19 publications

Propositions as sessions

Propositions as sessions

Effects as sessions, sessions as effects

A Categorical Model of an $$\mathbf {i/o}$$ -typed $$\pi $$ -calculus

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