Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism

Dunfield, Jana; Krishnaswami, Neelakantan R.

doi:10.48550/arxiv.1306.6032

Cited by 7 publications

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“…(It may be possible to design a more complicated system in which λx. e does synthesize, as Dunfield and Krishnaswami (2013) did for a different type system. )…”

Section: From Type Assignment Rules To Bidirectional Rulesmentioning

confidence: 86%

“…We solve all of these problems via a bidirectional version of the system. In many settings, bidirectional typing has been chosen to overcome fundamental limitations of type inference, such as undecidability of inference for object-oriented subtyping (Pierce and Turner 1998), dependent types (Xi and Pfenning 1999;Pientka and Dunfield 2010) and first-class polymorphism (Dunfield and Krishnaswami 2013). It can also be motivated by better localization of type error messages.…”

Section: Bidirectional Source Typingmentioning

confidence: 99%

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Sums of uncertainty: refinements go gradual

Jafery

Dunfield

2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with refinements passes type checking, pattern-matching failures become impossible. Unfortunately, refinement is a monolithic property of a type, exacerbating the difficulty of adding refinement types to nontrivial programs.Gradual typing has explored how to incrementally move between static typing and dynamic typing. We develop a type system of gradual sums that combines refinement with imprecision. Then, we develop a bidirectional version of the type system, which rules out excessive imprecision, and give a type-directed translation to a target language with explicit casts. We prove that the static sublanguage cannot have match failures, that a well-typed program remains well-typed if its type annotations are made less precise, and that making annotations less precise causes target programs to fail later. Several of these results correspond to criteria for gradual typing given by Siek et al. (2015).

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“…(It may be possible to design a more complicated system in which λx. e does synthesize, as Dunfield and Krishnaswami (2013) did for a different type system. )…”

Section: From Type Assignment Rules To Bidirectional Rulesmentioning

confidence: 86%

Section: Bidirectional Source Typingmentioning

confidence: 99%

Sums of uncertainty: refinements go gradual

Jafery

Dunfield

2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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“…We linger on this point partly to highlight an irony: our widely used technique for bidirectional polymorphism [Dunfield and Krishnaswami 2013] was inspired by a technique of Cardelli [1993] for a system with subtyping as a central feature-but Cardelli's technique works by pretending there is no subtyping and hoping for the best.…”

Section: Polymorphismmentioning

confidence: 99%

Bidirectional Typing

Dunfield,

Krishnaswami

2019

Preprint

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Bidirectional typing combines two modes of typing: type checking, which checks that a program satisfies a known type, and type synthesis, which determines a type from the program. Using checking enables bidirectional typing to break the decidability barrier of Damas-Milner approaches; using synthesis enables bidirectional typing to avoid the large annotation burden of explicitly typed languages. In addition, bidirectional typing improves error locality. We highlight the design principles that underlie bidirectional type systems, survey the development of bidirectional typing from the prehistoric period before Pierce and Turner's local type inference to the present day, and provide guidance for future investigations.

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“…However, the idea was popularized only more recently by Pierce and Turner [38]. The technique has shown great applicability-it has been used for dependent types [17], indexed refinement types [44,45], intersection and union types [21,25], higher-rank polymorphism [23,24,35], contextual modal types [37], algebraic effect handlers [30] and gradual typing [42]. Our approach is inspired by many of these papers, in particular DML [44,45], but departs in the technical design of the algorithmic type system due to new challenges offered by relational and modal types, and costs.…”

Section: Constraint Solvingmentioning

confidence: 99%

Bidirectional Type Checking for Relational Properties

Çiçek,

Qu,

Barthe

et al. 2018

Preprint

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Relational type systems have been designed for several applications including information flow, differential privacy, and cost analysis. In order to achieve the best results, these systems often use relational refinements and relational effects to maximally exploit the similarity in the structure of the two programs being compared. Relational type systems are appealing for relational properties because they deliver simpler and more precise verification than what could be derived from typing the two programs separately. However, relational type systems do not yet achieve the practical appeal of their non-relational counterpart, in part because of the lack of a general foundations for implementing them.In this paper, we take a step in this direction by developing bidirectional relational type checking for systems with relational refinements and effects. Our approach achieves the benefits of bidirectional type checking, in a relational setting. In particular, it significantly reduces the need for typing annotations through the combination of type checking and type inference. In order to highlight the foundational nature of our approach, we develop bidirectional versions of several relational type systems which incrementally combine many different components needed for expressive relational analysis.

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Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism

Cited by 7 publications

References 0 publications

Sums of uncertainty: refinements go gradual

Sums of uncertainty: refinements go gradual

Bidirectional Typing

Bidirectional Type Checking for Relational Properties

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