Intersection and Union Types: Syntax and Semantics

Barbanera, Franco; Dezani‐Ciancaglini, Mariangiola; de’Liguoro, Ugo

doi:10.1006/inco.1995.1086

Cited by 146 publications

(174 citation statements)

References 30 publications

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“…Our subtype system is closely related to the functional programming language with intersection and union types presented by Barbanera et al [2]. Our subtype system without properties coincides with the subtype system of Barbanera et al without implication.…”

Section: Yago:sovietcomputerscientists ≤ Dbp:personsupporting

confidence: 72%

“…1 performs subsumption, which allows a weaker type for a resource to be inferred, by using the rdfs:subClassOf relation. Subsumption is a common feature of subtype systems [10,34,2] -an observation key to the formal system developed in the body of this work. The remaining rules rdfs2 and rdfs3 formalise that if the given URI is used as a property in a triple then the object of the triple, respectively the subject of the triple, has the type indicated.…”

Section: W3c Recommended Rdf Schema Inferencementioning

confidence: 99%

“…Implication corresponds to fully fledged function types, which, of course, is much more expressive than our property types. Properties can be encoded using implication, so our system is a restriction of the system presented in [2]. However, the system of Barbanera et al types all terminating functions; hence is undecidable, and therefore inappropriate to use directly.…”

Section: Yago:sovietcomputerscientists ≤ Dbp:personmentioning

confidence: 99%

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A descriptive type foundation for RDF Schema

Ciobanu

Horne

Sassone

2016

Journal of Logical and Algebraic Methods in Programming

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This paper provides a type theoretic foundation for descriptive types that appear in Linked Data. Linked Data is data published on the Web according to principles and standards supported by the W3C. Such Linked Data is inherently messy: this is due to the fact that instead of being assigned a strict a priori schema, the schema is inferred a posteriori. Moreover, such a posteriori schema consists of opaque names that guide programmers, without prescribing structure. We employ what we call a descriptive type system for Linked Data. This descriptive type system differs from a traditional type system in that it provides hints or warnings rather than errors and evolves to describe the data while Linked Data is discovered at runtime. We explain how our descriptive type system allows RDF Schema inference mechanisms to be tightly coupled with domain specific scripting languages for Linked Data, enabling an interactive feedback to Web developers.

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Section: Yago:sovietcomputerscientists ≤ Dbp:personsupporting

confidence: 72%

Section: W3c Recommended Rdf Schema Inferencementioning

confidence: 99%

Section: Yago:sovietcomputerscientists ≤ Dbp:personmentioning

confidence: 99%

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A descriptive type foundation for RDF Schema

Ciobanu

Horne

Sassone

2016

Journal of Logical and Algebraic Methods in Programming

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“…Work on union types began later (MacQueen et al 1986); Barbanera et al (1995) is a key paper on type assignment for unions.…”

Section: Related Workmentioning

confidence: 99%

Elaborating intersection and union types

Dunfield¹

2014

J. Funct. Prog.

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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.

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“…We address the problem of designing a λ-calculus à la Church corresponding to Curry-style type assignment to an untyped λ-calculus with intersection and union types [MPS86,BDCD95]. In particular, we define a typed language such that its relationship with the intersection-union type assignment system fulfills the following desiderata: (i) typed and type assignment derivations are isomorphic, i.e., the application of an erasing function on all typed terms and contexts (in a typed derivation judgment) produces a derivable type assignment derivation with the same structure, and every type assignment derivation is obtained from a typed one with the same structure by applying the same erasure; (ii) type checking and type reconstruction are decidable; (iii) reduction on typed terms has the same fundamental nice properties of reduction on terms receiving a type in the type-assignment system, namely confluence, preservation of typing under reduction, and strong normalization of terms typable without the universal type ω.…”

Section: Introductionmentioning

confidence: 99%

Logic and Computation in a Lambda Calculus with Intersection and Union Types

Dougherty

Liquori

2010

Logic for Programming, Artificial Intelligence, and Reasoning

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We present an explicitly typed lambda calculus "à la Church" based on the union and intersection types discipline; this system is the counterpart of the standard type assignment calculus "à la Curry." Our typed calculus enjoys Subject Reduction and confluence, and typed terms are strongly normalizing when the universal type is omitted. Moreover both type checking and type reconstruction are decidable. In contrast to other typed calculi, a system with union types will fail to be "coherent" in the sense of Tannen, Coquand, Gunter, and Scedrov: different proofs of the same typing judgment will not necessarily have the same meaning. In response, we introduce a decidable notion of equality on type-assignment derivations inspired by the equational theory of bicartesian-closed categories.

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Intersection and Union Types: Syntax and Semantics

Cited by 146 publications

References 30 publications

A descriptive type foundation for RDF Schema

A descriptive type foundation for RDF Schema

Elaborating intersection and union types

Logic and Computation in a Lambda Calculus with Intersection and Union Types

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