Type Assignment for Intersections and Unions in Call-by-Value Languages

Dunfield, Joshua; Pfenning, Frank

doi:10.1007/3-540-36576-1_16

Cited by 40 publications

(48 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The intersection type in this paper is commutative (A ∧ B = B ∧ A) and idempotent (A ∧ A = A), following several seminal papers on intersection types (Pottinger 1980;Coppo et al 1981) and more recent work with refinement intersections (Freeman and Pfenning 1991;Davies and Pfenning 2000;Dunfield and Pfenning 2003). Other lines of research have worked with nonlinear and/or ordered intersections, e.g.…”

Section: Intersection Typesmentioning

confidence: 99%

See 1 more Smart Citation

Elaborating intersection and union types

Dunfield¹

2014

J. Funct. Prog.

Self Cite

View full text Add to dashboard Cite

Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide general mechanisms that subsume many different features.In modern type systems, parametric polymorphism is fundamental, but intersection polymorphism has gained little traction in programming languages. Most practical intersection type systems have supported only refinement intersections, which increase the expressiveness of types (more precise properties can be checked) without altering the expressiveness of terms; refinement intersections can simply be erased during compilation. In contrast, unrestricted intersections increase the expressiveness of terms, and can be used to encode diverse language features, promising an economy of both theory and implementation.We describe a foundation for compiling unrestricted intersection and union types: an elaboration type system that generates ordinary λ-calculus terms. The key feature is a Forsythe-like merge construct. With this construct, not all reductions of the source program preserve types; however, we prove that ordinary call-byvalue evaluation of the elaborated program corresponds to a typepreserving evaluation of the source program.We also describe a prototype implementation and applications of unrestricted intersections and unions: records, operator overloading, and simulating dynamic typing.

show abstract

Section: Intersection Typesmentioning

confidence: 99%

“…The logic of the subtyping rules ( Figure 4, top) is taken straight from Dunfield and Pfenning (2003), so we only briefly give some intuition. Roughly, A ≤ B is sound if every value of type A can be treated as having type B.…”

Section: (Source) Subtypingmentioning

confidence: 99%

Elaborating intersection and union types

Dunfield¹

2014

J. Funct. Prog.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note the stratification: terms have types, indices have index sorts; terms and indices are distinct. The proof of safety in [9] requires that | = be a consequence relation, that . = be an equivalence relation, that · | = ⊥, and that | = and have expected substitution and weakening properties [8].…”

Section: Refined Datatypesmentioning

confidence: 99%

“…A sound formulation of the elimination rule in a type assignment form [9] without a syntactic marker 2 requires an evaluation context E around the subterm of union type.…”

Section: Indefinite Property Typesmentioning

confidence: 99%

“…Section 5 restricts the tridirectional rules and compensates by introducing left rules to yield a left tridirectional system. We prove soundness and completeness with respect to the simple tridirectional system, prove decidability, and use the results in [9] to prove type safety. Finally, we discuss related work (Section 6) and conclude (Section 7).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tridirectional typechecking

Dunfield

Pfenning

2004

Proceedings of the 31st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Self Cite

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

Set Constraints, Pattern Match Analysis, and SMT

Eremondi

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Type Assignment for Intersections and Unions in Call-by-Value Languages

Cited by 40 publications

References 17 publications

Elaborating intersection and union types

Elaborating intersection and union types

Tridirectional typechecking

Set Constraints, Pattern Match Analysis, and SMT

Contact Info

Product

Resources

About