The most consistent solution with the least ceremony. Now it is a module, not a type though.

You can create first-class values of this module type, and since values have types, "it" is a type. Specifically, my_foobar has type (module FOOBAR).

Actually getting values out of such a module-typed structure does involve some ceremony, however:

    let f =
      let module M = (val my_foobar) in
      M.foo