Most of the dissonance in these discussions come with the disagreement of what a private function means. To me, a private function is an implementation detail. I don’t care how it is named, I don’t care about the argument it receives. If I refactor my private functions and a test breaks, I have a bad test. This is also how the compiler is designed. A private function may not exist at all after the code is compiled.

That’s also why Elixir makes a distinction between code comments and documentation. Code comments are for those reading the source code.

In any case, if a private function has complexity to the point you feel you need to test it and/or document it, then it is most likely worth its own module. And you can still do so while keeping it private and using doctests. To provide an actual example, let’s see how the code above could be rewritten.

Let’s assume @polypush135’s code looks like this:

  defmodule User.Invitation do
    def find_invite!(invite_token) do
      Repo.get_by!(User, invite_token: encrypt_token(invite_token))
    end

    defp encrypt_token(token) do
      :crypto.hmac(:sha256, BeffectWeb.Endpoint.config(:secret_key_base), token)
      |> Base.encode16(case: :lower)
    end
  end

I would rewrite it to:

defmodule User.Invitation do
  defmodule Token do
    @moduledoc false

    @doc """
    Now I can doctest this too!
    """
    def encrypt(token) do
      :crypto.hmac(:sha256, BeffectWeb.Endpoint.config(:secret_key_base), token)
      |> Base.encode16(case: :lower)
    end
  end

  def find_invite!(invite_token) do
    Repo.get_by!(User, invite_token: Token.encrypt(invite_token))
  end
end

This way you keep everything in the same file, you provide a logical place for grouping all of the token functionality, you can write tests and doctests and you still don’t expose it to your “final” users.

PS: Note ex_doc now allows custom groups, so you can even have modules targeting different audiences and you can use the grouping functionality to break those apart in the UI.

I mostly disagree with this. In my experience private functions are mostly internal details of the implementation, and the main reason of their existence is to organize the module internal code and make it easier to follow.

The API of the module is what the module guarantees, and this is IMO the only thing that should be tested.

In such cases, I find that there’s usually potential to split the module, and move complex internal functions as public functions of the new module, so they can be properly documented and tested.

Occasionally I do see the need to explain some private function, in which case I simply use a comment.

Finally, it’s worth noting that in Elixir, functions which are public but not meant to be invoked directly, should be marked with @doc false. This should indicate that a function is internal (even though marked public), and the clients should not depend on it directly. Such function will not appear in the generated doc, and the users will be unaware of its existence. People who read the code will see the function, but they will also see that it is marked with @doc false, and hence not meant to be invoked directly.

It’s less about private vs public but also about separating dependencies. Having a own module to do the encoding does allow you to test the encoding in isolation as well as being able to inject an mock for the encryption module on your user handling. In other words find_invite should not really be concerned with how your token is created, it just needs to be able to match tokens.

@eahanson already pointed out that you can now have bugs that won’t be caught in tests. It is worth mentioning that @compile :export_all emits warnings from OTP 20 on:

warning: export_all flag enabled - all functions will be exported
  lib/elixir/test/elixir/code_formatter/general_test.exs:3

FWIW, the warning and functionality comes from the Erlang compiler, Elixir has nothing to do with it.

Extract that function to its own module and make it public?

You can even test the implementation of encrypt_token function that way if you want.