Nested Session Types

Das, Ankush; DeYoung, Henry; Mordido, Andreia; Pfenning, Frank

doi:10.1007/978-3-030-72019-3_7

Cited by 11 publications

(12 citation statements)

References 47 publications

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“…On the other-hand, from the work of Korenjak and Hopcroft [27] we know that the language L 3 = {l n a r n a | n ≥ 0} ∪ {l n b r n b | n ≥ 0} is deterministic context-free but cannot be accepted by a DPDA with a single state. This was used by Das et al [10] to argue that context-free session types cannot express language L 3 . However, we can use 1-counter types to express this language, i.e., define the type T KH as X z with equations…”

Section: Results For Context-free and Nested Session Typesmentioning

confidence: 99%

“…Type checking is known to be decidable for finite types, recursive, context-free and nested session types. Given that type checking for nested session types is incorporated in the RAST language [10], a natural first step would be to investigate how to translate 1-counter and pushdown processes into that language.…”

Section: Discussionmentioning

confidence: 99%

“…Dependent session types have been studied in several forms, for binary session types [43,44], for multi-party session types [13,32,48] and for polymorphic, nested session types [10]. Although our parameterised type definitions have some similarities with definitions in some dependently typed systems, we do not support the connection between values in messages and parameters in types, and we have not yet studied how the types that can be expressed in dependent systems fit into our hierarchy.…”

Section: Related Workmentioning

confidence: 98%

“…Nested session types A class of types that turns out to be equivalent to pushdown types was recently proposed by Das et al [10]. The main idea is to have type constructors that are applied not to natural numbers or to sequences of symbols but to types themselves; and to let type constructors take a variable (but fixed) number of parameters.…”

Section: Stringsmentioning

confidence: 99%

“…!bool.Y , quit : end} which offers a choice between go and quit operations, each with its own protocol. A natural observation is that session types look like finite-state automata, but some systems from the literature go beyond the finite-state format: for example, context-free session types [42] and nested session types [10,11], as well as label-dependent session types [43] and value-dependent session types [44].…”

Section: Introductionmentioning

confidence: 99%

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The Different Shades of Infinite Session Types

Gay¹,

Poças²,

Vasconcelos³

2022

Preprint

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Many type systems include infinite types. In session type systems, which are the focus of this paper, infinite types are important because they allow the specification of communication protocols that are unbounded in time. Usually infinite session types are introduced as simple finite-state expressions rec X.T or by non-parametric equational definitions X . = T . Alternatively, some systems of label-or value-dependent session types go beyond simple recursive types. However, leaving dependent types aside, there is a much richer world of infinite session types, ranging through various forms of parametric equational definitions, all the way to arbitrary infinite types in a coinductively defined space. We study infinite session types across a spectrum of shades of grey on the way to the bright light of general infinite types. We identify four points on the spectrum, characterised by different styles of equational definitions, and show that they form a strict hierarchy by establishing bidirectional correspondences with classes of automata: finite-state, 1-counter, pushdown and 2-counter. This allows us to establish decidability and undecidability results for the problems of type formation, type equivalence and duality in each class of types. We also consider previous work on context-free session types (and extend it to higher-order) and nested session types, and locate them on our spectrum of infinite types.

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Section: Results For Context-free and Nested Session Typesmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 98%

Section: Stringsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Different Shades of Infinite Session Types

Gay¹,

Poças²,

Vasconcelos³

2022

Preprint

View full text Add to dashboard Cite

show abstract

The Different Shades of Infinite Session Types

Gay

Poças

Vasconcelos

2022

Lecture Notes in Computer Science

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Many type systems include infinite types. In session type systems, infinite types are important because they specify communication protocols that are unbounded in time. Usually infinite session types are introduced as simple finite-state expressions "Equation missing" or by non-parametric equational definitions "Equation missing". Alternatively, some systems of label- or value-dependent session types go beyond simple recursive types. However, leaving dependent types aside, there is a much richer world of infinite session types, ranging through various forms of parametric equational definitions, to arbitrary infinite types in a coinductively defined space. We study infinite session types across a spectrum of shades of grey on the way to the bright light of general infinite types. We identify four points on the spectrum, characterised by different styles of equational definitions, and show that they form a strict hierarchy by establishing bidirectional correspondences with classes of automata: finite-state, 1-counter, pushdown and 2-counter. This allows us to establish decidability and undecidability results for type formation, type equivalence and duality in each class of types. We also consider previous work on context-free session types (and extend it to higher-order) and nested session types, and locate them on our spectrum of infinite types.

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Polarized Subtyping

Lakhani

Das

DeYoung

et al. 2022

Lecture Notes in Computer Science

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Polarization of types in call-by-push-value naturally leads to the separation of inductively defined observable values (classified by positive types), and coinductively defined computations (classified by negative types), with adjoint modalities mediating between them. Taking this separation as a starting point, we develop a semantic characterization of typing with step indexing to capture observation depth of recursive computations. This semantics justifies a rich set of subtyping rules for an equirecursive variant of call-by-push-value, including variant and lazy records. We further present a bidirectional syntactic typing system for both values and computations that elegantly and pragmatically circumvents difficulties of type inference in the presence of width and depth subtyping for variant and lazy records. We demonstrate the flexibility of our system by systematically deriving related systems of subtyping for (a) isorecursive types, (b) call-by-name, and (c) call-by-value, all using a structural rather than a nominal interpretation of types.

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Nested Session Types

Cited by 11 publications

References 47 publications

The Different Shades of Infinite Session Types

The Different Shades of Infinite Session Types

The Different Shades of Infinite Session Types

Polarized Subtyping

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