Flatten.scala

import cats.instances.list._
import Flatten.Level.Aux

import scala.language.higherKinds

object Flatten {
  import cats.Monad
  import cats.syntax.flatMap._

  trait Level {
    type From[_[_], _]
    type To[_[_], _]
    def convert[U, M[_]: Monad](f: From[M, U]): To[M, U]
  }

  object Level {
    type Aux[FFrom[_[_], _], TTo[_[_], _]] = Level {
      type From[M[_], T] = FFrom[M, T]
      type To[M[_], T]   = TTo[M, T]
    }
  }

  def flatten[L <: Level](implicit levelAux: Level.Aux[L#From, L#To]): Aux[L#From, L#To] = levelAux

  trait Two extends Level {
    type From[M[_], T] = M[M[M[T]]]
    type To[M[_], U]   = M[U]

    override def convert[U, M[_]: Monad](f: M[M[M[U]]]): M[U] = f.flatten.flatten
  }

  trait One extends Level {
    override type From[M[_], T] = M[M[T]]
    override type To[M[_], T]   = M[T]

    override def convert[U, M[_]: Monad](f: M[M[U]]): M[U] = f.flatten
  }

  implicit object Two extends Two
  implicit object One extends One

  val ints: List[List[List[Int]]] = List(List(List(5), List(10)))

  //these types can be inferred automatically
  val once: List[List[Int]] = flatten[One].convert(ints)
  val twice: List[Int]      = flatten[One].convert(once)
  val twice3: List[Int]     = flatten[Two].convert(ints)
}