Automatically generating the dynamic semantics of gradually typed languages

Cimini, Matteo; Siek, Jeremy G.

doi:10.1145/3009837.3009863

Cited by 19 publications

(8 citation statements)

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“…Frameworks for Gradual Typing. There are two recent proposals for a more general theory of gradual typing: Abstracting Gradual Typing (AGT) [12] and the Gradualizer [4]. Broadly, their systems and ours are similar in that type dynamism and graduality are central and a gradually typed language is constructed from a statically typed language.…”

Section: Contracts As Coreflectionsmentioning

confidence: 99%

Gradual type theory

New

Licata

Ahmed

2019

Proc. ACM Program. Lang.

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We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism. These dynamism judgments build on prior work in blame calculi and on the "gradual guarantee" theorem of gradual typing. Combined with the ordinary extensionality (η) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs. This construction is a semantic analogue of the interpretation of gradual typing using contracts, and use it to build some concrete domain-theoretic models of gradual typing. CC Creative Commons 7:2 M.S. New and D.R. Licata Vol. 16:1"strictly less than", and similarly for other terms such as "greater than", "more dynamic", etc. 7:4 M.S. New and D.R. Licata Vol. 16:1 7:6 M.S. New and D.R. Licata Vol. 16:1 7:8 M.S. New and D.R. Licata Vol. 16:1 2.2. PTT Signatures. While gradual type theory proves that most operational rules of gradual typing are equivalences, some must be added as axioms. Compare Moggi's monadic metalanguage [22]: since it is a general theory of monads, it is not provable that an effect is 7:12 M.S. New and D.R. Licata Vol. 16:1

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Section: Contracts As Coreflectionsmentioning

confidence: 99%

Gradual type theory

New

Licata

Ahmed

2019

Proc. ACM Program. Lang.

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“…As a consequence, gradual typing could be used to evolve a process into a more and more statically typed version over time without disrupting the workflow of the programmer. We expect this property to be challenging, as it has been proven challenging in several contexts [21,11,6].…”

Section: Properties (Not Addressed In This Preliminary Work)mentioning

confidence: 99%

Towards Gradually Typed Capabilities in the Pi-Calculus

Cimini

2019

Electron. Proc. Theor. Comput. Sci.

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Gradual typing is an approach to integrating static and dynamic typing within the same language, and puts the programmer in control of which regions of code are type checked at compile-time and which are type checked at run-time.In this paper, we focus on the π-calculus equipped with types for the modeling of input-output capabilities of channels. We present our preliminary work towards a gradually typed version of this calculus. We present a type system, a cast insertion procedure that automatically inserts run-time checks, and an operational semantics of a π-calculus that handles casts on channels. Although we do not claim any theoretical results on our formulations, we demonstrate our calculus with an example and discuss our future plans.

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“…In order to ensure that these assumptions are upheld during the reduction of a program, formal gradual languages do not define reduction directly on the gradual calculus, and instead convert gradual terms into a term in a cast calculus instead. (Cimini and Siek 2017). To be well-typed, the body of the cast must satisfy the source type, and the source and target types must be consistent.…”

Section: Castsmentioning

confidence: 99%

“…In further work, inference for gradual types is explored by the 𝜆 ?𝛼 → calculus of Siek and Vachharajani (2008) and the inference algorithm of Rastogi, Chaudhuri, and Hosmer (2012), as well as the investigation of Garcia and Cimini (2015) into the potential meaning of omitting a type annotation in a gradually typed language, ultimately subsuming the earlier work on gradual inference. Recent developments have investigated generating gradually typed languages directly from existing statically-typed languages (Cimini and Siek 2016;Garcia, Clark, and Tanter 2016;Cimini and Siek 2017)…”

Section: Castsmentioning

confidence: 99%

“…One aspect that is missing from the design for casts is a system for blame tracking. Consider a hypothetical design for blame: casts labelled with blame labels ℓ as in the cast calculi of Wadler and Findler (2009) or Cimini and Siek (2017). The relevant blame label is attached to a raise generated by a coercion to indicate which cast was to blame for a run-time type error:…”

Section: Blamementioning

confidence: 99%

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Classless Object Semantics

Jones¹

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<p>Objects have been categorised into classes that declare and implement their behaviour ever since the paradigm of object-orientation in programming languages was first conceived. Classes have an integral role in the design and theory of object-oriented languages, and often appear alongside objects as a foundational concept of the paradigm in many theoretical models. A number of object-oriented languages have attempted to remove classes as a core component of the language design and rebuild their functionality purely in terms of objects, to varying success. Much of the formal theory of objects that eschews classes as a fundamental construct has difficulty encoding the variety of behaviours possible in programs from class-based languages. This dissertation investigates the foundational nature of the class in the object-oriented paradigm from the perspective of an ‘objects-first’, classless language. Using the design of theoretical models and practical implementations of these designs as extensions of the Grace programming language, we demonstrate how objects can be used to emulate the functionality of classes, and the necessary trade-offs of this approach. We present Graceless, our theory of objects without classes, and use this language to explore what class functionality is difficult to encode using only objects. We consider the role of classes in the types and static analysis of object-oriented languages, and present both a practical design of brand objects and a corresponding extension of our theory that simulates the discipline of nominal typing. We also modify our theory to investigate the semantics of many different kinds of implementation reuse in the form of inheritance between both objects and classes, and compare the consequences of these different approaches.</p>

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Automatically generating the dynamic semantics of gradually typed languages

Cited by 19 publications

References 23 publications

Gradual type theory

Gradual type theory

Towards Gradually Typed Capabilities in the Pi-Calculus

Classless Object Semantics

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