Decidable subtyping of existential types for the Julia language

Abstract

Julia is a dynamic, high-performance programming language for scientific computing. To encourage a high level of code reuse and extensibility, Julia is designed around symmetric multiple dynamic dispatch, which allows functions to have multiple implementations tailored to different argument types. To resolve multiple dispatch, Julia relies on a subtype relation over a complex language of run-time types and type annotations, which include set-theoretic unions, distributive tuples, parametric invariant types, and impredicative existential types. Notably, subtyping in Julia is undecidable, which manifests with a run-time stack-overflow error when program execution encounters a subtyping query that causes the subtype checker to loop.In this dissertation, I propose a decidable subtype relation for a restricted language of Julia types where existential types inside invariant constructors are limited to ones expressible with use-site variance. To estimate migration effort that would be required for switching to the restricted type language, I analyze type annotations in the corpus of 9K registered Julia packages. Out of 2M statically identifiable type annotations in the corpus, 99.99% satisfy the restriction, making it a viable candidate for evolving Julia towards decidable subtyping.iii acknowledgements I would not be able to do this without plenty of luck and so many good people who helped me along the way. C O N T E N T S Acknowledgements iii Contents iv List of Figures vi List of Tables viii viii 1.1 subtyping in juliaFor example, X implements Comparable<X> in Java.