Levenshtein in elixir

leven.ex

defmodule Levenshtein do
  def first_letter_check(one_letter, two_letter) do
    case one_letter == two_letter do
      true -> 0
      false -> 1
    end
  end

  def distance(string_1, string_1), do: 0
  def distance(string, ''), do: :string.len(string)
  def distance('', string), do: :string.len(string)
  def distance([h1|rest1], [h2|rest2]) do
    cost = first_letter_check(h1, h2)

    :lists.min([
              distance(rest1, [h2|rest2]) + 1,
              distance([h1|rest1], rest2) + 1,
              distance(rest1, rest2) + cost
              ])
  end
end

IO.inspect :timer.tc(Levenshtein, :distance, ['kitten', 'sitting'])
IO.inspect :timer.tc(Levenshtein, :distance, ['space balls', 'base spalls'])

leven_memo.ex

defmodule Levenshtein do
  def distance(string_1, string_2) do
    {list, _} = distance(string_1, string_2, :dict.new)
    list
  end

  def distance(string_1, []=string_2, cache) do
    length = :string.len string_1
    {length, :dict.store({string_1,string_2}, length, cache)}
  end

  def distance([]=string_1, string_2, cache) do
    length = :string.len string_2
    {length, :dict.store({string_1,string_2}, length, cache)}
  end

  def distance([x|rest1], [x|rest2], cache) do
    distance(rest1, rest2, cache)
  end

  def distance([_|rest1]=string_1, [_|rest2]=string_2, cache) do
    case :dict.is_key({string_1, string_2}, cache) do
      true -> {:dict.fetch({string_1, string_2}, cache), cache}
      false ->
        {l1, c1} = distance(string_1, rest2, cache)
        {l2, c2} = distance(rest1, string_2, c1)
        {l3, c3} = distance(rest1, rest2, c2)

        min = :lists.min([l1, l2, l3]) + 1
        {min, :dict.store({string_1,string_2}, min, c3)}
    end
  end
end

IO.inspect :timer.tc(Levenshtein, :distance, ['kitten', 'sitting'])
IO.inspect :timer.tc(Levenshtein, :distance, ['space balls', 'base spalls'])