Polarized Substructural Session Types

Griffith, Dennis E.

doi:10.2172/1562827

Cited by 18 publications

(19 citation statements)

References 52 publications

(80 reference statements)

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“…We abbreviate the sum of these features simply as nested types [3]. Prior work has restricted itself to parametric polymorphism either: in prenex form without nested types [26,45]; with explicit higher-rank quantifiers [6,38] (including bounded ones [24]) but without general recursion; or in specialized form for iteration at the type level [46]. None of these allow a free, nested use of polymorphic type constructors combined with prenex polymorphism.…”

Section: Introductionmentioning

confidence: 99%

Nested Session Types

Das

DeYoung

Mordido

et al. 2021

Programming Languages and Systems

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Session types statically describe communication protocols between concurrent message-passing processes. Unfortunately, parametric polymorphism even in its restricted prenex form is not fully understood in the context of session types. In this paper, we present the metatheory of session types extended with prenex polymorphism and, as a result, nested recursive datatypes. Remarkably, we prove that type equality is decidable by exhibiting a reduction to trace equivalence of deterministic first-order grammars. Recognizing the high theoretical complexity of the latter, we also propose a novel type equality algorithm and prove its soundness. We observe that the algorithm is surprisingly efficient and, despite its incompleteness, sufficient for all our examples. We have implemented our ideas by extending the Rast programming language with nested session types. We conclude with several examples illustrating the expressivity of our enhanced type system.

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Section: Introductionmentioning

confidence: 99%

Nested Session Types

Das

DeYoung

Mordido

et al. 2021

Programming Languages and Systems

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“…Links [LM16b, LM17, FLMD19] is a language aimed at developing web applications. While based on a different foundations, it is related to SILL [TCP13,Gri16] in that both integrate traditional functional types with linear session types. As such, they can express many (nonlinear) programs that Rast cannot, but they support neither arithmetic refinements nor ergometric or temporal types.…”

Section: Methodsmentioning

confidence: 99%

Rast: A Language for Resource-Aware Session Types

Das¹,

Pfenning²

2022

Logical Methods in Computer Science

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Traditional session types prescribe bidirectional communication protocols for concurrent computations, where well-typed programs are guaranteed to adhere to the protocols. However, simple session types cannot capture properties beyond the basic type of the exchanged messages. In response, recent work has extended session types with refinements from linear arithmetic, capturing intrinsic attributes of processes and data. These refinements then play a central role in describing sequential and parallel complexity bounds on session-typed programs. The Rast language provides an open-source implementation of session-typed concurrent programs extended with arithmetic refinements as well as ergometric and temporal types to capture work and span of program execution. To further support generic programming, Rast also enhances arithmetically refined session types with recently developed nested parametric polymorphism. Type checking relies on Cooper's algorithm for quantifier elimination in Presburger arithmetic with a few significant optimizations, and a heuristic extension to nonlinear constraints. Rast furthermore includes a reconstruction engine so that most program constructs pertaining the layers of refinements and resources are inserted automatically. We provide a variety of examples to demonstrate the expressivity of the language.

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“…This is because of the nature of our system which essentially requires the type checker to verify a fixed point rather than infer the least one. This has proven highly beneficial for providing good error messages even in the simpler case of pure subtyping, without intersections and unions [16].…”

Section: Stdmentioning

confidence: 99%

Intersections and Unions of Session Types

Acay

Pfenning

2017

Electron. Proc. Theor. Comput. Sci.

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Prior work has extended the deep, logical connection between the linear sequent calculus and sessiontyped message-passing concurrent computation with equi-recursive types and a natural notion of subtyping. In this paper, we extend this further by intersection and union types in order to express multiple behavioral properties of processes in a single type. We prove session fidelity and absence of deadlock and illustrate the expressive power of our system with some simple examples. We observe that we can represent internal and external choice by intersection and union, respectively, which was previously suggested in [6,18] for a different language of session types motivated by operational rather than logical concerns.

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Polarized Substructural Session Types

Cited by 18 publications

References 52 publications

Nested Session Types

Nested Session Types

Rast: A Language for Resource-Aware Session Types

Intersections and Unions of Session Types

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