Value-Dependent Session Design in a Dependently Typed Language

Muijnck-Hughes, Jan de; Brady, Edwin; Vanderbauwhede, Wim

doi:10.4204/eptcs.291.5

Cited by 8 publications

(6 citation statements)

References 33 publications

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“…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: 99%

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: Related Workmentioning

confidence: 99%

The Different Shades of Infinite Session Types

Gay¹,

Poças²,

Vasconcelos³

2022

Preprint

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“…Thus, the embedding gives us label-dependent session types [43] with no additional cost. Previous work in exploring value-dependent sessions in a dependently typed language [15] is directly expressible using linearity in Idris 2. We have not yet explored further extensions to session types, however, such as multiparty session types [22], dealing with exceptions during protocol execution [18] or dealing with errors in transmission in distributed systems.…”

Section: Session Typesmentioning

confidence: 99%

Idris 2: Quantitative Type Theory in Practice

Brady¹

2021

Preprint

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Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run. This is promising, because it suggests the ability to design and reason about resource usage protocols, such as we might find in distributed and concurrent programming, where the state of a communication channel changes throughout program execution. As yet, however, there has not been a full-scale programming language with which to experiment with these ideas. Idris 2 is a new version of the dependently typed language Idris, with a new core language based on QTT, supporting linear and dependent types. In this paper, we introduce Idris 2, and describe how QTT has influenced its design. We give examples of the benefits of QTT in practice including: expressing which data is erased at run time, at the type level; and, resource tracking in the type system leading to type-safe concurrent programming with session types.

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“…By choice, Idris accumulates much of best practices in implementing dependently-typed theories. To the best of our knowledge Idris is not restricted to value-dependency, although it appears to be possible to enforce such restrictions [de Muijnck-Hughes et al 2019]. Nishimura [1998] introduces a calculus for objects where messages (a method name and parameters) are first-class constructs.…”

Section: Related Workmentioning

confidence: 99%

Label dependent lambda calculus and gradual typing

Krause

Thiemann

2021

Proc. ACM Program. Lang.

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Dependently-typed programming languages are gaining importance, because they can guarantee a wide range of properties at compile time. Their use in practice is often hampered because programmers have to provide very precise types. Gradual typing is a means to vary the level of typing precision between program fragments and to transition smoothly towards more precisely typed programs. The combination of gradual typing and dependent types seems promising to promote the widespread use of dependent types. We investigate a gradual version of a minimalist value-dependent lambda calculus. Compile-time calculations and thus dependencies are restricted to labels, drawn from a generic enumeration type. The calculus supports the usual Pi and Sigma types as well as singleton types and subtyping. It is sufficiently powerful to provide flexible encodings of variant and record types with first-class labels. We provide type checking algorithms for the underlying label-dependent lambda calculus and its gradual extension. The gradual type checker drives the translation into a cast calculus, which extends the original language. The cast calculus comes with several innovations: refined typing for casts in the presence of singletons, type reduction in casts, and fully dependent Sigma types. Besides standard metatheoretical results, we establish the gradual guarantee for the gradual language.

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Value-Dependent Session Design in a Dependently Typed Language

Cited by 8 publications

References 33 publications

The Different Shades of Infinite Session Types

The Different Shades of Infinite Session Types

Idris 2: Quantitative Type Theory in Practice

Label dependent lambda calculus and gradual typing

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