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			     S E M I N A I R E
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			     I N R I A - Paris
                 2 rue Simone Iff (ou: 41 rue du Charolais)
                          Salle Lions 1, bâtiment C

                          Lundi 25 septembre, 10h30

                           ------------------------
                           Francesco Zappa Nardelli
                           ------------------------

                                 Inria Paris

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                        Julia Subtyping Reconstructed
                        =============================

Julia is a programming language designed to support the needs of the
scientific community. In the five years since its release it has grown
in popularity to reach over 6,000 Julia projects hosted on
GitHub. Julia occupies a unique position in the design landscape, it
is a dynamic language with no type system, yet it has a surprisingly
rich set of types and type annotations used to specify multimethod
dispatch. The types that can be expressed in function signatures
include parametric union types, covariant tuple types, parametric
user-defined types with single inheritance, invariant type
application, and finally types and values can be reified to appear in
signatures.  Subtyping plays a central role in Julia as it is used to
determine the order of applicability of variants of a function, and to
ascertain if a particular tuple of values matches the type
specification of the function. While subtyping is based on simple
intuitions, designing an algorithm to compute the subtype relation is
surprisingly complex.

In this talk I will offer empirical evidence that users appeal to all
the features provided by Julia and I will present a specification of
the Julia subtyping algorithm. The specification is validated by a
reference implementation tested against the subtype traces recorded
while executing the regression tests bundled with Julia and 34 widely
used packages from GitHub.

This is joint work with Artem Pelenytsin, Benjamin Chung, Jeff Bezanson,
Jan Vitek.