A case for DOT: Theoretical Foundations for Objects With Pattern Matching and GADT-style Reasoning

TL;DR

This paper introduces cDOT, a formal calculus based on Dependent Object Types, to provide a theoretical foundation for subtyping reconstruction in pattern matching on objects, addressing type errors in modern OO languages.

Contribution

The paper presents cDOT, a new calculus that formalizes subtyping reconstruction, enabling better handling of pattern matching on generic class hierarchies in object-oriented languages.

Findings

cDOT can encode advanced OO features like generics and recursive modules.

Subtyping reconstruction in cDOT subsumes GADTs.

Encoding of GADT calculus into cDOT demonstrates its expressiveness.

Abstract

Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic class hierarchies currently results in puzzling type errors in most of these languages. Yet this combination of features occurs naturally in many scenarios, such as when manipulating typed ASTs. To support it properly, compilers need to implement a form of subtyping reconstruction: the ability to reconstruct subtyping information uncovered at runtime during pattern matching. We introduce cDOT, a new calculus in the family of Dependent Object Types (DOT) intended to serve as a formal foundation for subtyping reconstruction. Being descended from pDOT, itself a formal foundation for Scala, cDOT can be used to encode advanced object-oriented features such as generic inheritance, type constructor variance, F-bounded polymorphism, and first-class recursive modules. We demonstrate that subtyping reconstruction subsumes GADTs by encoding $\lambda_{2,G\mu}$, a classical constraint-based GADT calculus, into cDOT.