Polymorphic lambda calculus with context-free session types

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

doi:10.1016/j.ic.2022.104948

Cited by 13 publications

(13 citation statements)

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“…This section briefly introduces the notions of kinds, types and expressions; we refer the interested reader to previous work for details [1]. FREEST relies on a base set for type variables (denoted by a, b, c) and another for labels (denoted by k, ℓ).…”

Section: The Syntax Of Kinds Types and Expressionsmentioning

confidence: 99%

Kind Inference for the FreeST Programming Language

Almeida

Mordido

Vasconcelos

2023

Electron. Proc. Theor. Comput. Sci.

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We present a kind inference algorithm for the FREEST programming language. The input to the algorithm is FREEST source code with (possibly part of) kind annotations replaced by kind variables. The algorithm infers concrete kinds for all kind variables. We ran the algorithm on the FREEST test suite by first replacing kind annotation on all type variables by fresh kind variables, and concluded that the algorithm correctly infers all kinds. Non surprisingly, we found out that programmers do not choose the most general kind in 20% of the cases.

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Section: The Syntax Of Kinds Types and Expressionsmentioning

confidence: 99%

Kind Inference for the FreeST Programming Language

Almeida

Mordido

Vasconcelos

2023

Electron. Proc. Theor. Comput. Sci.

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“…Traditional recursive session types are limited to tail recursion, thus failing to capture all protocols whose traces cannot be characterized by regular languages. Context-free session types overcome this limitation by extending types with a notion of sequential composition, T ; U [2,68]. The set of types together with the ; binary operation constitutes a monoid, for which a new type, Skip, acts as the neutral element and End acts as an absorbing element.…”

Section: Introductionmentioning

confidence: 99%

“…In either case, once the whole tree is received, the channel must be closed, as witnessed by the final End. Beyond first-order context-free session types (where only basic types are exchanged) [2,68] we may be interested in higher-order session types capable of exchanging values of complex types [19]. A goal of this paper is the integration of higher-order context-free session types into system F µ ω .…”

Section: Introductionmentioning

confidence: 99%

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System $$F^\mu _\omega $$ with Context-free Session Types

Poças

Costa

Mordido

et al. 2023

Lecture Notes in Computer Science

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We study increasingly expressive type systems, from $$F^\mu $$ F μ —an extension of the polymorphic lambda calculus with equirecursive types—to $$F^{\mu ;}_\omega $$ F ω μ ; —the higher-order polymorphic lambda calculus with equirecursive types and context-free session types. Type equivalence is given by a standard bisimulation defined over a novel labelled transition system for types. Our system subsumes the contractive fragment of $$F^\mu _\omega $$ F ω μ as studied in the literature. Decidability results for type equivalence of the various type languages are obtained from the translation of types into objects of an appropriate computational model: finite-state automata, simple grammars and deterministic pushdown automata. We show that type equivalence is decidable for a significant fragment of the type language. We further propose a message-passing, concurrent functional language equipped with the expressive type language and show that it enjoys preservation and absence of runtime errors for typable processes.

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“…}; Chan → ∃ • . { : }; Unit (2) Quantification over session types, as in ∀( : Session), has been considered and analyzed in other recent work [Almeida et al 2022;Lindley and Morris 2017].…”

Section: Introductionmentioning

confidence: 99%

Polymorphic Typestate for Session Types

Saffrich¹,

Thiemann²

2022

Preprint

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Session types provide a principled approach to typed communication protocols that guarantee type safety and protocol fidelity. Formalizations of session-typed communication are typically based on process calculi, concurrent lambda calculi, or linear logic. An alternative model based on context-sensitive typing and typestate has not received much attention due to its apparent restrictions. However, this model is attractive because it does not force programmers into particular patterns like continuation-passing style or channel-passing style, but rather enables them to treat communication channels like mutable variables.Polymorphic typestate is the key that enables a full treatment of session-typed communication. Previous work in this direction was hampered by its setting in a simply-typed lambda calculus. We show that higherorder polymorphism and existential types enable us to lift the restrictions imposed by the previous work, thus bringing the expressivity of the typestate-based approach on par with the competition. On this basis, we define PolyVGR, the system of polymorphic typestate for session types, establish its basic metatheory, type preservation and progress, and present a prototype implementation.

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Polymorphic lambda calculus with context-free session types

Cited by 13 publications

References 60 publications

Kind Inference for the FreeST Programming Language

Kind Inference for the FreeST Programming Language

System $$F^\mu _\omega $$ with Context-free Session Types

Polymorphic Typestate for Session Types

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