To sum up:
Functions are named by their atom name and their arity. There is no such thing as an arity-less function. There is such a thing as an atom-less function, those are anonymous functions, notice it still has an arity however. Thus every function always absolutely has an arity. Now considering that a default argument actually creates two function of one with the full arity and one of less that just calls the one with more, and considering function pointers only reference a single function and not multiple, that means it can’t encode both, just not possible.
