There is no such thing as “submodule” or “child module” in Elixir. Foo.Bar, despite it shares the first part of the name with Foo is absolutely not related to Foo by any means.

If you meant “to check whether a module shares a namespace,” that’d be easy to achieve with Module.split/1 and List.starts_with?/2, like

{m1, m2} = {Foo.Bar.Baz, Foo.Bar}

[m2, m1] |> Enum.map(&Module.split/1) |> Enum.reduce(&List.starts_with?/2)
#⇒ true
[m1, m2] |> Enum.map(&Module.split/1) |> Enum.reduce(&List.starts_with?/2)     
#⇒ false

There are no private modules, only private functions. It might be possible to do something of the sort with macro / metaprogramming trickery, but there is no standard feature for it. There is a library called Boundary that provides some guarantees to prevent using modules you shouldn’t.

I made the change to the topic and set the solution as requested.