How to make erlang see that an atom is a PID - concurrency

Question

I have the following code:
-module(circle).
-export([proc/1,mother/0,chain/1]).
-spec mother() -> none().
mother() ->
register(mother,self()).
-spec proc(pid()) -> none().
proc(Next) when is_pid(Next) ->
receive
{_, Msg} -> Next ! {self(), Msg}
end.
-spec chain(integer()) -> pid().
chain(0) -> mother;
chain(N) when is_integer(N) ->
spawn(circle,proc,chain(N-1)).
It compiles as expected however whenever I run, it throws a bad argument error when the chain reaches the 0 argument. This is because erlang treats the mother as an atom however I have previously called the mother function which should've registered mother as a pid.
I initially thought the mother does not get registered however after having called this in the console:
-> circle:mother().
-> mother ! {abc}.
abc
I was able to deduce from here that mother does get treated like a Pid. How can I make the code work? How can I make erlang see that mother is a PID?
What I'm trying to achieve is to build N processes in a circle.

Answer 1

Registered process name doesn't turn into pid.
Here is type specification of destination in erlang:send/2 which is the same as ! operator:
dst() = pid()
| port()
| (RegName :: atom())
| {RegName :: atom(), Node :: node()}
As you see send takes many types as destination.
You don't need to care about that, so just remove that guard; make another clause for atom case or append to guard orelse is_atom(Next).
-spec proc(pid() | atom()) -> none().
proc(Next) ->
receive
{_, Msg} -> Next ! {self(), Msg}
end.
You have one error in spawn(circle,proc,chain(N-1)).
spawn/3 takes list of arguments as third argument:
spawn(circle,proc,[chain(N-1)]).
I don't see any benefit from registering a root process. If closing a circle was problematic with pids only, here is how you can do it:
chain(N) ->
chain(N, self()).
chain(0, Mother) -> Mother;
chain(N, Mother) when is_integer(N) ->
spawn(circle,proc,[chain(N-1, Mother)]).

Answer 2

If you want to invoke mother/0 in the chain(0) clause you must correct the clause so that it reads:
chain(0) -> mother();
As it currently stands you are simply returning an atom, since all you have in the body of the function clause is an atom, and not the invocation of a function. Example:
something() -> fun_name. %=> returns `fun_name`
something() -> fun_name(). %=> invokes `fun_name/0` and returns the result of the call.