defprotocol Applicative do
  @moduledoc """
  Applicative functors, or applicatives for short, are like functors, except
  they can apply more than one parameter. They do so by currying the function,
  and applying one parameter at a time (see `Curry`).

  Applicatives must also follow four laws: identity, composition,
  homomorphism, and interchange (see `Applicative.Law`).
  """

  @fallback_to_any true

  @doc """
  Takes an applicative holding a function and an applicative holding value and
  returns an applicative.

  (applicative<(b -> c)>, applicative<b>) -> applicative<c>
  """
  @spec apply(t, t) :: t
  def apply(value, fun)
end

defimpl Applicative, for: List do
  def apply(list, list_fun) do
    Monad.bind(list_fun, &Functor.fmap(list, &1))
  end
end

defimpl Applicative, for: Function do
  def apply(rhs_fun, lhs_fun) do
    &(&1 |> rhs_fun.() |> lhs_fun.())
  end
end

defimpl Applicative, for: Any do
  def apply(value, fun) do
    Monad.bind(fun, &Functor.fmap(value, &1))
  end
end