in reply to "use" inheritance

You're missing the import.

use actually does two things:

  1. require the module file
  2. call the import class method from the package of the module

In order for perl to recognize your "imported" sub Bar in Foo, it needs to be imported into Foo! And by not use'ing Bar inside Foo, you not only skip the (indeed not strictly necessary) use, but also the import!

There's noting wrong with using Bar twice. The require will be called only once, but then, Bar would indeed be imported both into main::, and into Foo::. Just like you want it.

Or you could use fully qualified names. I'd go for the double import.