# Sources for the Zappa Nardelli et al. subtyping implementation?

**URL:** <https://discourse.julialang.org/t/sources-for-the-zappa-nardelli-et-al-subtyping-implementation/108531>\
**Category:** Internals & Design\
**Tags:** question, git, type\
**Created:** [January 8, 2024, 6:53pm UTC](https://discourse.julialang.org/t/sources-for-the-zappa-nardelli-et-al-subtyping-implementation/108531 "2024-01-08T18:53:30Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![nsajko](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nsajko/32/221187_2.png) [@nsajko](https://discourse.julialang.org/u/nsajko)\
**Post date:** [January 8, 2024, 6:53pm UTC](https://discourse.julialang.org/t/sources-for-the-zappa-nardelli-et-al-subtyping-implementation/108531/1 "2024-01-08T18:53:30Z")

</div>

> Francesco Zappa Nardelli, Julia Belyakova, Artem Pelenitsyn, Benjamin Chung, Jeff Bezanson, et al… Julia Subtyping: A Rational Reconstruction. Proceedings of the ACM on Programming Languages, 2018, 27, ⟨10.1145/3276483⟩. ⟨hal-01882137⟩

The authors of the above [paper](https://inria.hal.science/hal-01882137) re-implemented Julia’s subtype relation, `<:`. I’d like to try it out, where can I find the source? @fzn @julbinb @ulysses @ckfinite

If sharing the sources is not an option, I’m particularly interested in the following: [`Vector{<:Int} <: Union{Vector{Int},Vector{Union{}}}`](https://github.com/JuliaLang/julia/issues/52818).

---

<div class="post-metadata">

**Author:** ![nsajko](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nsajko/32/221187_2.png) [@nsajko](https://discourse.julialang.org/u/nsajko)\
**Post date:** [January 8, 2024, 7:14pm UTC](https://discourse.julialang.org/t/sources-for-the-zappa-nardelli-et-al-subtyping-implementation/108531/2 "2024-01-08T19:14:26Z")

</div>

It seems all the data I want is here (although there’s no Git repo, sadly): [Julia Subtyping: a Rational Reconstruction](https://fzn.fr/projects/lambdajulia/)