Branching Types

Wells, J. B.; Haack, Christian

doi:10.1007/3-540-45927-8_9

Cited by 19 publications

(19 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But with intersection types, such a completeness property does not hold for the usual notion of type annotation (e : A) (as previously noted [16,6,23]), a problem exacerbated by scoping issues arising from quantified types. We therefore extend the notion of type annotation to contextual typing annotation, (e : Γ 1 A 1 , .…”

Section: Introductionmentioning

confidence: 99%

Tridirectional typechecking

Dunfield

Pfenning

2004

SIGPLAN Not.

View full text Add to dashboard Cite

In prior work we introduced a pure type assignment system that encompasses a rich set of property types, including intersections, unions, and universally and existentially quantified dependent types. This system was shown sound with respect to a call-by-value operational semantics with effects, yet is inherently undecidable.In this paper we provide a decidable formulation for this system based on bidirectional checking, combining type synthesis and analysis following logical principles. The presence of unions and existential quantification requires the additional ability to visit subterms in evaluation position before the context in which they occur, leading to a tridirectional type system. While soundness with respect to the type assignment system is immediate, completeness requires the novel concept of contextual type annotations, introducing a notion from the study of principal typings into the source program.

show abstract

Section: Introductionmentioning

confidence: 99%

Tridirectional typechecking

Dunfield

Pfenning

2004

SIGPLAN Not.

View full text Add to dashboard Cite

show abstract

“…(Our semantics already has them.). Following the work of Wells and Haack (2002) on branching types, it would then be interesting to have intersection types as branching typings.…”

Section: Extensions and Variationsmentioning

confidence: 99%

System F with coercion constraints

Cretin

Rémy

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

View full text Add to dashboard Cite

We present a second-order λ-calculus with coercion constraints that generalizes a previous extension of System F with parametric coercion abstractions by allowing multiple but simultaneous type and coercion abstractions, as well as recursive coercions and equi-recursive types. This enables a uniform presentation of several type system features that had previously been studied separately: type containment, bounded and instance-bounded polymorphism, which are already encodable with parametric coercion abstraction, and ML-style subtyping constraints. Our framework allows for a clear separation of language constructs with and without computational content. We also distinguish coherent coercions that are fully erasable from potentially incoherent coercions that suspend the evaluation-and enable the encoding of GADTs.Technically, type coercions that witness subtyping relations between types are replaced by a more expressive notion of typing coercions that witness subsumption relations between typings, e.g. pairs composed of a typing environment and a type. Our calculus is equipped with full reduction that allows reduction under abstractions-but we also introduce a form of weak reduction as reduction cannot proceed under incoherent type abstractions. Type soundness is proved by adapting the step-indexed semantics technique to full reduction, moving indices inside terms so as to control the reduction steps internally-but this is only detailed in the extended version.

show abstract

“…The typed languages proposed in [12] and [11] are not complete with respect to the type assignment, the ones in [4], [13] and [16] do not satisfy requirement 1, while the language in [17] does not satisfy requirement 2.…”

Section: Introductionmentioning

confidence: 97%