A case for DOT: theoretical foundations for objects with pattern matching and GADT-style reasoning

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