Gradual typing: a new perspective

Castagna, Giuseppe; Lanvin, Victor; Petrucciani, Tommaso; Siek, Jeremy G.

doi:10.1145/3290329

Cited by 29 publications

(20 citation statements)

References 52 publications

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“…In [23] set-theoretic types are combined with polymorphic gradual typing by means of a single typing rule which prescribes where casts must be added. A significant problem is that a direct set-theoretic interpretation of the constructor "?"…”

Section: Semantic Subtypingmentioning

confidence: 99%

A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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Intersection types have come a long way since their introduction in the Seventies. They have been exploited for characterising behaviours of λ-terms and π-calculus processes, building λ-models, verifying properties of higher-order programs, synthesising code, and enriching the expressivity of programming languages. This paper is a light overview of intersection types and some of their applications. CCS Concepts: • Theory of computation → Type theory.

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Section: Semantic Subtypingmentioning

confidence: 99%

A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…Researchers have explored many interpretations and extensions of gradual types. Future work could pursue type migration that supports subtyping [Garcia et al 2016;Siek and Taha 2007;Vitousek et al 2014], refinement types [Lehmann and Éric Tanter 2017], monotonic references [Siek et al 2015b], and polymorphism and set theoretic types [Castagna et al 2019]. In particular, future work can consider our decision problems for those richer type systems.…”

Section: Related Workmentioning

confidence: 99%

What is decidable about gradual types?

Migeed

Palsberg

2019

Proc. ACM Program. Lang.

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Programmers can use gradual types to migrate programs to have more precise type annotations and thereby improve their readability, efficiency, and safety. Such migration requires an exploration of the migration space and can benefit from tool support, as shown in previous work. Our goal is to provide a foundation for better tool support by settling decidability questions about migration with gradual types. We present three algorithms and a hardness result for deciding key properties and we explain how they can be useful during an exploration. In particular, we show how to decide whether the migration space is finite, whether it has a top element, and whether it is a singleton. We also show that deciding whether it has a maximal element is NP-hard. Our implementation of our algorithms worked as expected on a suite of microbenchmarks.We can use those properties to classify programs into five increasingly larger sets. Figure 1 illustrates both how those sets are nested (top half) and the migration possibilities (bottom half). Each of (a)ś(e) shows the original program as a circle and, above it, possible migrations; maximal migrations are shown as bold circles.Our contributions. We present algorithms (with names in bold below) and a hardness result for deciding the four questions above for the gradually typed λ-calculus [Siek and Taha 2006]. Singleton problem:decidable in O(n 2 ) time (Theorem 3.5) Singleton Checker Top-choice problem: decidable in EXPTIME (Theorem 5.3) Top-Choice Checker Finiteness problem: decidable in EXPTIME (Theorem 4.11) Finiteness Checker Maximality problem: NP-hard (Theorem 6.1).

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“…A gradual treatment of record types may be found in the paper on Abstract Gradual Typing (AGT) (Garcia et al, 2016). Variant types have proved elusive, but union types have been considered (Siek & Tobin-Hochstadt, 2016) along with intersection types and polymorphism as part of a set-theoretical reevaluation of gradual principles (Castagna et al, 2019).…”

Section: Gradual Typingmentioning

confidence: 99%

Gradual session types

Igarashi¹,

Thiemann²,

Tsuda³

et al. 2019

J. Funct. Prog.

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Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages, with type disciplines in a spectrum between static and dynamic typing. Gradual session types address this mixed setting by providing a framework which grants seamless transition between statically typed handling of sessions and any required degree of dynamic typing.We propose Gradual GV as a gradually typed extension of the functional session type system GV. Following a standard framework of gradual typing, Gradual GV consists of an external language, which relaxes the type system of GV using dynamic types, and an internal language with casts, for which operational semantics is given, and a cast-insertion translation from the former to the latter. We demonstrate type and communication safety as well as blame safety, thus extending previous results to functional languages with session-based communication. The interplay of linearity and dynamic types requires a novel approach to specifying the dynamics of the language.

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Gradual typing: a new perspective

Cited by 29 publications

References 52 publications

A tale of intersection types

A tale of intersection types

What is decidable about gradual types?

Gradual session types

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