Deciding the Bisimilarity of Context-Free Session Types

Almeida, Bernardo Pinto de; Mordido, Andreia; Vasconcelos, Vasco T.

doi:10.1007/978-3-030-45237-7_3

Cited by 18 publications

(36 citation statements)

References 24 publications

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“…Since the simulation creates a large number of equations, we will only show an initial fragment of the unfolding steps, and a subset of relevant equations as we go along. In our example there are four type constructors X (1) (arity 3), X (2) (arity 2) and X (3) (arity 0). Therefore, the maximum arity is n = 3.…”

Section: Proof Of Theorem 8 (Equivalence Of Pushdown and Nested Sessi...mentioning

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: Proof Of Theorem 8 (Equivalence Of Pushdown and Nested Sessi...mentioning

confidence: 99%

The Different Shades of Infinite Session Types

Gay¹,

Poças²,

Vasconcelos³

2022

Preprint

Self Cite

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“…this implementation of queues. In Figure 1, the initial queue (of size 1) consists of an empty process that provides along c 1 : queue A [0] (indicated by • between empty and c 1 ) and does not use any channels, and an elem process that uses c 1 : queue A [0], and an element of type A (not shown) and provides c 2 : queue A [1]. The ins message is first received on c 2 , then passed on to c 1 , which spawns a new empty process offering on c 0 : queue A [0].…”

Section: Overview Of Refined Session Typesmentioning

confidence: 99%

“…However, even in the presence of recursive types, the kinds of protocols that can be specified are limited, which has led to a number of extensions, such as context-free session types [1,28], label-dependent session types [29], and general dependent session types [17,24,30,31]. In prior work, we have proposed arithmetically refined session types [12] and have investigated their properties independently of any specific programming language.…”

Section: Introductionmentioning

confidence: 99%

Verified Linear Session-Typed Concurrent Programming

Das

Pfenning

2020

Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming

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We present a system of linear session types that integrates several features aimed at verification of different properties of concurrent programs, specifically types indexed with arithmetic expressions, linear constraints and quantification. We prove the standard type safety properties of session fidelity and deadlock freedom. In order to control the verbosity of programs we introduce implicit syntax and an algorithm for reconstruction, which is complete under some mild assumptions on the structure of types. We then illustrate the expressive power of our language (called Rast) with a variety of examples, including normalization for the linear λ-calculus, balanced ternary arithmetic, binary counters and tries. CCS CONCEPTS • Theory of computation → Linear logic; Type theory; • Computing methodologies → Concurrent programming languages.

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“…The origin of mixed sessions Mixed sessions dawned on us when looking into an algorithm to decide the equivalence of context-free session types [1,42]. The algorithm translates types into (simple) context-free grammars.…”

Section: Related Workmentioning

confidence: 99%

Mixed Sessions

Vasconcelos

Casal

Almeida

et al. 2020

Lecture Notes in Computer Science

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Session types describe patterns of interaction on communicating channels. Traditional session types include a form of choice whereby servers offer a collection of options, of which each client picks exactly one. This sort of choice constitutes a particular case of separated choice: offering on one side, selecting on the other. We introduce mixed choices in the context of session types and argue that they increase the flexibility of program development at the same time that they reduce the number of synchronisation primitives to exactly one. We present a type system incorporating subtyping and prove preservation and absence of runtime errors for well-typed processes. We further show that classical (conventional) sessions can be faithfully and tightly embedded in mixed choices. Finally, we discuss algorithmic type checking and a runtime system built on top of a conventional (choice-less) message-passing architecture.

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Deciding the Bisimilarity of Context-Free Session Types

Cited by 18 publications

References 24 publications

The Different Shades of Infinite Session Types

The Different Shades of Infinite Session Types

Verified Linear Session-Typed Concurrent Programming

Mixed Sessions

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