Julia Subtyping: a Rational Reconstruction

F. Zappa Nardelli, J. Belyakova, A. Pelenitsyn, B. Chung, J. Bezanson, J. Vitek.

In OOPSLA 2018.


Programming languages that support multiple dispatch rely on an expressive notion of subtyping to specify method applicability. In these languages, type annotations on method declarations are used to select, out of a potentially large set of methods, the one that is most appropriate for a particular tuple of arguments. Julia is a language for scientific computing built around multiple dispatch and an expressive subtyping relation. This paper provides the first formal definition of Julia's subtype relation and motivates its design. We validate our specification empirically with an implementation of our definition that we compare against the existing Julia implementation on a collection of real-world programs. Our subtype implementation differs on 122 subtype tests out of 6014476. The first 120 differences are due to a bug in Julia that was fixed once reported; the remaining 2 are under discussion.


  • Julia Subtyping: a Rational Reconstruction [.pdf]
  • Detailed results of validation of traces of widely used packages
    • Validation methodology and results [.pdf]
    • Statistics about rule usage [.pdf]
  • Full statistics on type annotations in real-world [.pdf]
  • Issues reported to Julia developers [.pdf]
  • Note on how the diagonal rule is implemented in C♯ [.pdf]


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