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recursion schemes for cats; to iterate is human, to recurse, divine
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package higherkindness.droste
package data
package stream

import cats.Monad
import cats.Monoid
import cats.syntax.applicative._
import cats.syntax.functor._
import java.util.{Iterator => JavaIterator}
import scala.annotation.tailrec
import list._

object `package` {
  type Stream[A] = Nu[ListF[A, *]]
}

object Stream extends StreamInstances {

  def forever[A](a: A): Stream[A] =
    Nu(Coalgebra[ListF[A, *], A](aa => ConsF(aa, aa)), a)

  def pure[A](a: A): Stream[A] = Nu(ConsF(a, empty))

  def cons[A](fa: Stream[A])(a: A): Stream[A] = Nu(ConsF(a, fa))

  def empty[A]: Stream[A] = Nu(NilF: ListF[A, Nu[ListF[A, *]]])

  def map[A, B](fa: Stream[A])(f: A => B): Stream[B] =
    Nu(
      Coalgebra(fa.unfold.run andThen (_ match {
        case ConsF(head, tail) => ConsF(f(head), tail)
        case NilF              => NilF
      })),
      fa.a
    )

  def flatMap[A, B](fa: Stream[A])(f: A => Stream[B]): Stream[B] = {
    type S = Either[fa.A, (Stream[B], fa.A)]

    lazy val inner: fa.A => ListF[B, S] =
      fa.unfold(_) match {
        case ConsF(h, t) =>
          Nu.un(f(h)) match {
            case ConsF(hh, tt) => ConsF(hh, Right((tt, t)))
            case NilF          => inner(t)
          }
        case NilF => NilF
      }

    val outer: S => ListF[B, S] = _ match {
      case Left(seed) => inner(seed)
      case Right(cont) =>
        Nu.un(cont._1) match {
          case ConsF(h, t) => ConsF(h, Right((t, cont._2)))
          case NilF        => inner(cont._2)
        }
    }

    Nu(Coalgebra(outer), Left(fa.a))
  }

  object coalgebras {
    def increment: Coalgebra[ListF[Int, *], Int] =
      Coalgebra(n => ConsF(n, n + 1))
  }

  def naturalNumbers: Stream[Int] =
    Nu(coalgebras.increment, 1)

  def take[A](fa: Stream[A])(n: Int): Stream[A] =
    Nu(
      Coalgebra[ListF[A, *], (Int, fa.A)](ia =>
        if (ia._1 <= 0) NilF
        else
          fa.unfold(ia._2) match {
            case ConsF(head, tail) => ConsF(head, (ia._1 - 1, tail))
            case NilF              => NilF
          }
      ),
      (n, fa.a)
    )

  def fromJavaIterator[A](it0: => JavaIterator[A]): Stream[A] =
    Nu(
      Coalgebra((it: JavaIterator[A]) =>
        if (it.hasNext) ConsF(it.next(), it) else NilF
      ),
      it0
    )

  def fromIterator[A](it0: => Iterator[A]): Stream[A] =
    Nu(
      Coalgebra((it: Iterator[A]) =>
        if (it.hasNext) ConsF(it.next(), it) else NilF
      ),
      it0
    )

  def fromList[A](l0: List[A]): Stream[A] =
    Nu(
      Coalgebra((l: List[A]) =>
        l match {
          case head :: tail => ConsF(head, tail)
          case Nil          => NilF
        }
      ),
      l0
    )

  def foldLeft[A, B](fa: Stream[A])(z: B)(f: (B, A) => B): B = {
    @tailrec def kernel(in: Stream[A], out: B): B = Nu.un(in) match {
      case ConsF(head, tail) => kernel(tail, f(out, head))
      case NilF              => out
    }
    kernel(fa, z)
  }

  def toList[A](fa: Stream[A]): List[A] =
    foldLeft(fa)(List.empty[A])((acc, a) => a :: acc).reverse

  final class StreamOps[A](val fa: Stream[A]) extends AnyVal {
    def map[B](f: A => B): Stream[B]             = Stream.map(fa)(f)
    def flatMap[B](f: A => Stream[B]): Stream[B] = Stream.flatMap(fa)(f)
    def take(n: Int): Stream[A]                  = Stream.take(fa)(n)
    def toList: List[A]                          = Stream.toList(fa)
  }

  object implicits {
    implicit def toStreamOps[A](fa: Stream[A]): StreamOps[A] =
      new StreamOps[A](fa)
  }

}

private[stream] sealed trait StreamInstances {

  implicit val drosteMonadForStream: Monad[Stream] = new Monad[Stream] {
    def pure[A](a: A): Stream[A] = Stream.pure(a)
    def flatMap[A, B](fa: Stream[A])(f: A => Stream[B]): Stream[B] =
      Stream.flatMap(fa)(f)
    def tailRecM[A, B](a: A)(f: A => Stream[Either[A, B]]): Stream[B] = ???
  }

  implicit def drosteMonoidForStream[A]: Monoid[Stream[A]] =
    new Monoid[Stream[A]] {
      def empty: Stream[A] = Stream.empty
      def combine(x: Stream[A], y: Stream[A]): Stream[A] =
        Stream.flatMap(Stream.cons(Stream.pure(y))(x))(identity)
    }
}