Depth-wise tree walk and execute a function

tree walk.ex

defmodule Treewalk do
  @type tree :: {:node, integer(), tree(), tree()} | nil

  def depth({:node, value, nil, nil}, _fun) do
    value
  end

  def depth({:node, value, nil, right}, fun) do
    fun.(value, depth(right, fun), nil)
  end

  def depth({:node, value, left, nil}, fun) do
    fun.(value, depth(left, fun), nil)
  end

  def depth({:node, value, left, right}, fun) do
    fun.(value, depth(left, fun), depth(right, fun))
  end

  # The function to be run on each
  # node of the tree which is passed
  # the current value, the result of
  # running the funciton on the left
  # branch and the result of running
  # the function on the right branch
  def adder(a, b, nil) do
    a + b
  end

  def adder(a, b, c) do
    a + b + c
  end

  # Test tess
  def tree do
    {:node,
      1,
      {:node, 2,
        {:node, 4, nil, nil},
        nil
      },
      {:node, 3,
        nil,
        {:node, 4, nil, nil}
      }
    }
  end

  # run a test, returns 14
  def test do
    depth(tree(), &adder/3)
  end
end