A theory of higher-order subtyping with type intervals
Journal article, 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, Computer Science and Engineering (Chalmers), Information Security

Paolo G. Giarrusso

BedRock Systems Inc.

Proceedings of the ACM on Programming Languages

24751421 (eISSN)

Vol. 5 ICFP 3473574

Subject Categories


Computational Mathematics

Mathematical Analysis



More information

Latest update