Integrating Nominal and Structural Subtyping

Nominal and structural subtyping each have their own strengths and weaknesses. Nominal subtyping allows programmers to explicitly express design intent, and, when types are associated with run time tags, enables run-time type tests and external method dispatch. On the other hand, structural subtyping is flexible and compositional, allowing unanticipated reuse. To date, nearly all object-oriented languages fully support one subtyping paradigm or the other. In this paper, we describe a core calculus for a language that integrates the key aspects of nominal and structural subtyping in a unified framework. We have also merged the flexibility of structural subtyping with statically typechecked external methods, a novel combination. We prove type safety for this language and illustrate its practical utility through examples that are not easily expressed in other languages. Our work provides a clean foundation for the design of future languages that enjoy the benefits of both nominal and structural subtyping. This research was supported in part by the U.S. Department of Defense, Army Research Office grant number DAAD1902-1-0389 entitled “Perpetually Available and Secure Information Systems,” and NSF CAREER award CCF-0546550.