addition.ex

defprotocol Addition do
  @fallback_to_any true
  def a + b
end

defimpl Addition, for: Any do
  def a + b do
    Kernel.+(a, b)
  end
end


defmodule Complex do
  defstruct re: 0, im: 0
end

defimpl Addition, for: Complex do
  def %Complex{re: re1, im: im1} + %Complex{re: re2, im: im2} do
    %Complex{re: Kernel.+(re1, re2), im: Kernel.+(im1, im2)}
  end
end

sample

iex(1)> Addition.+(3, 4)
7

iex(2)> c1 = %Complex{re: 1, im: 2}
%Complex{im: 2, re: 1}

iex(3)> c2 = %Complex{re: 3, im: 4}
%Complex{im: 4, re: 3}

iex(4)> Addition.+(c1, c2)
%Complex{im: 6, re: 4}

iex(5)> import Kernel, except: [+: 2]
nil

iex(6)> import Addition
nil

iex(7)> 5 + 6
11

iex(8)> c1 + c2
%Complex{im: 6, re: 4}