livebook/lib/live_book/delta/transformation.ex

defmodule LiveBook.Delta.Transformation do
  @moduledoc false

  # Implementation of the Operational Transformation concept for deltas.
  #
  # The transformation allows for conflict resolution in concurrent editing.
  # Consider delta `Oa` and delta `Ob` that occurred at the same time against the same text state `S`.
  # The resulting new text states are `S ∘ Oa` and `S ∘ Ob` respectively.
  # Now for each text state we would like to apply the other delta,
  # so that both texts converge to the same state, i.e.:
  #
  # `S ∘ Oa ∘ transform(Oa, Ob) = S ∘ Ob ∘ transform(Ob, Oa)`
  #
  # That's the high-level idea.
  # To actually achieve convergence we have to introduce a linear order of operations.
  # This way we can resolve conflicts - e.g. if two deltas insert a text at the same
  # position, we have to unambiguously determine which takes precedence.
  # A reasonable solution is to have a server process where all
  # the clients send deltas, as it naturally imposes the necessary ordering.

  alias LiveBook.Delta
  alias LiveBook.Delta.Operation

  @type priority :: :left | :right

  @doc """
  Transforms `right` delta against the `left` delta.

  Assuming both deltas represent changes applied to the same
  document state, this operation results in modified `right` delta
  that represents effectively the same changes (preserved intent),
  but works on the document with `left` delta already applied.

  The `priority` indicates which delta is considered to have
  happened first and is used for conflict resolution.
  """
  @spec transform(Delta.t(), Delta.t(), priority()) :: Delta.t()
  def transform(left, right, priority) do
    do_transform(left.ops, right.ops, priority, Delta.new())
    |> Delta.trim()
  end

  defp do_transform(_ops_a, [] = _ops_b, _priority, result) do
    result
  end

  defp do_transform([], ops_b, _priority, result) do
    Enum.reduce(ops_b, result, &Delta.append(&2, &1))
  end

  defp do_transform([{:insert, _} | _] = ops_a, [{:insert, _} | _] = ops_b, :left, result) do
    [ins_a | remainder_a] = ops_a
    retain = make_retain(ins_a)
    do_transform(remainder_a, ops_b, :left, Delta.append(result, retain))
  end

  defp do_transform([{:insert, _} | _] = ops_a, [{:insert, _} | _] = ops_b, :right, result) do
    [ins_b | remainder_b] = ops_b
    do_transform(ops_a, remainder_b, :right, Delta.append(result, ins_b))
  end

  defp do_transform([{:insert, _} | _] = ops_a, [{:retain, _} | _] = ops_b, priority, result) do
    [ins_a | remainder_a] = ops_a
    retain = make_retain(ins_a)
    do_transform(remainder_a, ops_b, priority, Delta.append(result, retain))
  end

  defp do_transform([{:insert, _} | _] = ops_a, [{:delete, _} | _] = ops_b, priority, result) do
    [ins_a | remainder_a] = ops_a
    retain = make_retain(ins_a)
    do_transform(remainder_a, ops_b, priority, Delta.append(result, retain))
  end

  defp do_transform([{:delete, _} | _] = ops_a, [{:insert, _} | _] = ops_b, priority, result) do
    [ins_b | remainder_b] = ops_b
    do_transform(ops_a, remainder_b, priority, Delta.append(result, ins_b))
  end

  defp do_transform([{:delete, _} | _] = ops_a, [{:retain, _} | _] = ops_b, priority, result) do
    {[_del_a | remainder_a], [_ret_b | remainder_b]} = Operation.align_heads(ops_a, ops_b)
    do_transform(remainder_a, remainder_b, priority, result)
  end

  defp do_transform([{:delete, _} | _] = ops_a, [{:delete, _} | _] = ops_b, priority, result) do
    {[_del_a | remainder_a], [_del_b | remainder_b]} = Operation.align_heads(ops_a, ops_b)
    do_transform(remainder_a, remainder_b, priority, result)
  end

  defp do_transform([{:retain, _} | _] = ops_a, [{:insert, _} | _] = ops_b, priority, result) do
    [ins_b | remainder_b] = ops_b
    do_transform(ops_a, remainder_b, priority, Delta.append(result, ins_b))
  end

  defp do_transform([{:retain, _} | _] = ops_a, [{:retain, _} | _] = ops_b, priority, result) do
    {[ret | remainder_a], [ret | remainder_b]} = Operation.align_heads(ops_a, ops_b)
    do_transform(remainder_a, remainder_b, priority, Delta.append(result, ret))
  end

  defp do_transform([{:retain, _} | _] = ops_a, [{:delete, _} | _] = ops_b, priority, result) do
    {[_ret_a | remainder_a], [del_b | remainder_b]} = Operation.align_heads(ops_a, ops_b)
    do_transform(remainder_a, remainder_b, priority, Delta.append(result, del_b))
  end

  defp make_retain(op) do
    op
    |> Operation.length()
    |> Operation.retain()
  end
end