A theory of higher-order subtyping with type intervals
Artikel i vetenskaplig tidskrift, 2021

The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose F··ω, a rigorous theoretical foundation for Scala's higher-kinded types. F··ω extends F<:ω with interval kinds, which afford a unified treatment of important type- and kind-level abstraction mechanisms found in Scala, such as bounded quantification, bounded operator abstractions, translucent type definitions and first-class subtyping constraints. The result is a flexible and general theory of higher-order subtyping. We prove type and kind safety of F··ω, as well as weak normalization of types and undecidability of subtyping. All our proofs are mechanized in Agda using a fully syntactic approach based on hereditary substitution.

higher-kinded types

bounded type operators

singleton kinds

type intervals

dependent kinds

bounded polymorphism


hereditary substitution



Sandro Stucki

Chalmers, Data- och informationsteknik, Informationssäkerhet

Paolo G. Giarrusso

BedRock Systems Inc.

Proceedings of the ACM on Programming Languages

24751421 (eISSN)

Vol. 5 ICFP 3473574




Matematisk analys



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