Bidirectional reference with case classes

Question

Is it possible to implement a bi-directional tree in a case class. This seems like it should be easy, but I'm getting stumped

case class Node(name:String, parent:Option[Node], children:List[Node])

I want to add a child (and get a new root) -- something like

def addChild(n:String):Node = {
  Node(name, parent, Node(n, Some(this), Nil)::children)
}

But that won't work because the "parent" in the child will no longer refer to the Node which lists the child as a child. Is this possible with immutable lists and case classes?

Based on answer given below

case class Node(name: String, parent: () => Option[Node], children: List[Node]) {
  def makeChild(name: String) = {
    lazy val newParent:Node = Node(this.name, this.parent, kid :: this.children)
    lazy val kid:Node = Node(name, () => Some(newParent), Nil)
    newParent
  }
}

Answer 1

I asked the same question to @jamesiry on Twitter recently :-).

His answer:

sealed abstract class Tree[T]
case class Node[T](left : Tree[T], right : Tree[T]) extends Tree[T]
case class Leaf[T](value : T, parent : () => Tree[T]) extends Tree[T]

def make = {
   lazy val root = Node(left, right)
   lazy val left : Leaf[Int] = Leaf(1, () => root)
   lazy val right : Leaf[Int] = Leaf(2, () => root)
   root
}