The metatheory of Scala's core type system - the Dependent Object Types (DOT) calculus - is hard to extend, like the metatheory of other type systems combining subtyping and dependent types. Soundness of important Scala features therefore remains an open problem in theory and in practice. To address some of these problems, we use a semantics-first approach to develop a logical relations model for a new version of DOT, called guarded DOT (gDOT). Our logical relations model makes use of an abstract form of step-indexing, as supported by the Iris framework, to model various forms of recursion in gDOT. To demonstrate the expressiveness of gDOT, we show that it handles Scala examples that could not be handled by previous versions of DOT, and prove using our logical relations model that gDOT provides the desired data abstraction. The gDOT type system, its semantic model, its soundness proofs, and all examples in the paper have been mechanized in Coq.

Every newly created object goes through several initialization states: starting from a state where all fields are uninitialized until all of them are assigned. Any operation on the object during its initialization process, which usually happens in the constructor via this, has to observe the initialization states of the object for correctness, i.e. only initialized fields may be used. Checking safe usage of this statically, without manual annotation of initialization states in the source code, is a challenge, due to aliasing and virtual method calls on this. Mainstream languages either do not check initialization errors, such as Java, C++, Scala, or they defend against them by not supporting useful initialization patterns, such as Swift. In parallel, past research has shown that safe initialization can be achieved for varying degrees of expressiveness but by sacrificing syntactic simplicity. We approach the problem by upholding local reasoning about initialization which avoids whole-program analysis, and we achieve typestate polymorphism via subtyping. On this basis, we put forward a novel type-and-effect system that can effectively ensure initialization safety while allowing flexible initialization patterns. We implement an initialization checker in the Scala 3 compiler and evaluate on several real-world projects.

Generalized algebraic data types (GADT) have been notoriously difficult to implement correctly in Scala. Both major Scala compilers, Scalac and Dotty, are currently known to have type soundness holes related to them. In particular, covariant GADTs have exposed paradoxes due to Scala's inheritance model. We informally explore foundations for GADTs within Scala's core type system, to guide a principled understanding and implementation of GADTs in Scala.