Some Tree Ideas

tree.scala

//Haven't even checked if this compiles
//Just an idea

trait TreeLike[A, This <: IterableLike[TreeLike[A, This], This]]{
  def root: A
  def children: This

  def map[B, That](f: A => B): TreeLike[A, That] = over(this, f).run

  protected def over[B, That](tree: TreeLike[A, This], f: A => B): Trampoline[TreeLike[B, That]] = 
    if(tree.children.isEmpty) done(build(f(tree.root))
    else for{
      childs <- step(tree.children, f)
    } yield build(f(tree.root), childs)

  protected def step[B, That](forest: This, f: A => B, acc: That): Trampoline[That] =
    if(forest.isEmpty) done(acc)
    else for{
      item <- suspend(over(forest.head, f))
      remainder <- suspend(step(forest.tail, f, acc))
    } yield remainder :+ item