Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly challenging, and existing proofs are complicated, and reason about multiple concepts at the same time (e.g. types, values, evaluation). To serve as a core calculus for Scala, DOT should be easy to experiment with and extend, and therefore its soundness proof needs to be easy to modify.
This paper presents a simple and modular proof strategy for reasoning in DOT. The strategy separates reasoning about types from other concerns. It is centred around a theorem that connects the full DOT type system to a restricted variant in which the challenges and paradoxes caused by abstract type members are eliminated. Almost all reasoning in the proof is done in the intuitive world of this restricted type system. Once we have the necessary results about types, we observe that the other aspects of DOT are mostly standard and can be incorporated into a soundness proof using familiar techniques known from other calculi.
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|SAVI Objects: Sharing and Virtuality Incorporated|
Izzat El Hajj University of Illinois at Urbana-Champaign, USA, Thomas B. Jablin University of Illinois at Urbana-Champaign, USA / Multicoreware, USA, Dejan Milojicic Hewlett Packard Labs, USA, Wen-mei Hwu University of Illinois at Urbana-Champaign, USADOI
|A Simple Soundness Proof for Dependent Object Types|
Marianna Rapoport University of Waterloo, Canada, Ifaz Kabir University of Waterloo, Canada, Paul He University of Waterloo, Canada, Ondřej Lhoták University of Waterloo, CanadaDOI
|Unifying Typing and Subtyping|
Avik Chaudhuri Facebook, USA, Panagiotis Vekris University of California at San Diego, USA, Sam Goldman Facebook, USA, Marshall Roch Facebook, USA, Gabriel Levi Facebook, USADOI