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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.

If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A derivative maps changes in the program's input directly to changes in the program's output, without reexecuting the original program. We present a program transformation taking programs to their derivatives, which is fully static and automatic, supports first-class functions, and produces derivatives amenable to standard optimization. We prove the program transformation correct in Agda for a family of simply-typed ��-calculi, parameterized by base types and primitives. A precise interface specifies what is required to incrementalize the chosen primitives. We investigate performance by a case study: We implement in Scala the program transformation, a plugin and improve performance of a nontrivial program by orders of magnitude., 11 pages; unpublished preprint, under submission

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 \emph{this}, has to observe the initialization states of the object for correctness, i.e.~only initialized fields may be used. Checking safe usage of \emph{this} statically, without manual annotation of initialization states in the source code, is a challenge, due to aliasing and virtual method calls on \emph{this}. Mainstream languages either do not check initialization errors, like 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 \emph{local reasoning} about initialization which avoids whole-program analysis, and we achieve \emph{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.

Accessing uninitialized data during object initialization is a common and subtle programming error. This error is either not prevented by mainstream languages, like in Java, C++, Scala, or it is prevented by greatly restricting initialization patterns, like in Swift. In this paper, we propose a model called _Celsius_ for safe and modular initialization of objects, and prove its soundness. We extend the model and implement a prototype in Scala. The experiments on several real-world Scala projects show that the design requires few programmer annotations.