NDLI: Disjoint intersection types

Content Provider	ACM Digital Library
Author	Alpuim, João Oliveira, Bruno C. d. S. Shi, Zhiyuan
Abstract	Dunfield showed that a simply typed core calculus with intersection types and a merge operator is able to capture various programming language features. While his calculus is type-safe, it is not coherent: different derivations for the same expression can elaborate to expressions that evaluate to different values. The lack of coherence is an important disadvantage for adoption of his core calculus in implementations of programming languages, as the semantics of the programming language becomes implementation-dependent. This paper presents λ_i: a coherent and type-safe calculus with a form of intersection types and a merge operator. Coherence is achieved by ensuring that intersection types are disjoint and programs are sufficiently annotated to avoid type ambiguity. We propose a definition of disjointness where two types A and B are disjoint only if certain set of types are common supertypes of A and B. We investigate three different variants of λ_i, with three variants of disjointness. In the simplest variant, which does not allow ⊤ types, two types are disjoint if they do not share any common supertypes at all. The other two variants introduce ⊤ types and refine the notion of disjointness to allow two types to be disjoint when the only the set of common supertypes are top-like. The difference between the two variants with ⊤ types is on the definition of top-like types, which has an impact on which types are allowed on intersections. We present a type system that prevents intersection types that are not disjoint, as well as an algorithmic specifications to determine whether two types are disjoint for all three variants.
Starting Page	364
Ending Page	377
Page Count	14
File Format	PDF
ISSN	03621340 15581160
DOI	10.1145/3022670.2951945
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	51
Issue Number	9
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Intersection types Type system
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Tridirectional typechecking

Elaborating intersection and union types

Intersection type calculi of bounded dimension

Dependent types from counterexamples

Subtyping and intersection types revisited

Intersection types and computational effects

Types, potency, and idempotency:why nonlinearity and amnesia make a type system work

Elaborating evaluation-order polymorphism

Polymorphic Functions with Set-Theoretic Types:Part 2: Local Type Inference and Type Reconstruction

Disjoint intersection types

Similar Documents

Tridirectional typechecking

Elaborating intersection and union types

Intersection type calculi of bounded dimension

Dependent types from counterexamples

Subtyping and intersection types revisited

Intersection types and computational effects

Types, potency, and idempotency:why nonlinearity and amnesia make a type system work

Elaborating evaluation-order polymorphism

Polymorphic Functions with Set-Theoretic Types:Part 2: Local Type Inference and Type Reconstruction

Disjoint intersection types