package sbt

	import Types._
	import Classes.Applicative

/** Heterogeneous list with each element having type M[T] for some type T.*/
sealed trait KList[+M[_]]
{
	type Transform[N[_]] <: KList[N]

	/** Apply the natural transformation `f` to each element. */
	def transform[N[_]](f: M ~> N): Transform[N]

	/** Folds this list using a function that operates on the homogeneous type of the elements of this list. */
	def foldr[T](f: (M[_], T) => T, init: T): T = init // had trouble defining it in KNil

	/** Applies `f` to the elements of this list in the applicative functor defined by `ap`. */
	def apply[N[x] >: M[x], Z](f: Transform[Id] => Z)(implicit ap: Applicative[N]): N[Z]

	/** Equivalent to `transform(f) . apply(x => x)`, this is the essence of the iterator at the level of natural transformations.*/
	def traverse[N[_], P[_]](f: M ~> (N ∙ P)#l)(implicit np: Applicative[N]): N[Transform[P]]

	/** Discards the heterogeneous type information and constructs a plain List from this KList's elements. */
	def toList: List[M[_]]
}
final case class KCons[H, +T <: KList[M], +M[_]](head: M[H], tail: T) extends KList[M]
{
	final type Transform[N[_]] = KCons[H, tail.Transform[N], N]

	def transform[N[_]](f: M ~> N) = KCons(f(head), tail.transform(f))
	def toList: List[M[_]] = head :: tail.toList
	def apply[N[x] >: M[x], Z](f: Transform[Id] => Z)(implicit ap: Applicative[N]): N[Z] =
	{
		val g = (t: tail.Transform[Id]) => (h: H) =>f( KCons[H, tail.Transform[Id], Id](h, t) )
		ap.apply( tail.apply[N, H => Z](g), head )
	}
	def traverse[N[_], P[_]](f: M ~> (N ∙ P)#l)(implicit np: Applicative[N]): N[Transform[P]] =
	{
		val tt: N[tail.Transform[P]] = tail.traverse[N,P](f)
		val g = (t: tail.Transform[P]) => (h: P[H]) => KCons(h, t)
		np.apply(np.map(g, tt), f(head))
	}
	def :^:[A,N[x] >: M[x]](h: N[A]) = KCons(h, this)
	override def foldr[T](f: (M[_], T) => T, init: T): T = f(head, tail.foldr(f, init))
}
sealed abstract class KNil extends KList[Nothing]
{
	final type Transform[N[_]] = KNil
	final def transform[N[_]](f: Nothing ~> N): Transform[N] = KNil
	final def toList = Nil
	final def apply[N[x], Z](f: KNil => Z)(implicit ap: Applicative[N]): N[Z] = ap.pure(f(KNil))
	final def traverse[N[_], P[_]](f: Nothing ~> (N ∙ P)#l)(implicit np: Applicative[N]): N[KNil] = np.pure(KNil)
}
case object KNil extends KNil {
	def :^:[M[_], H](h: M[H]): KCons[H, KNil, M] = KCons(h, this)
}
