 Solution

Read and advance the cursor only when the iterator is asked for its next value:

def asIter[T](cur: Cursor[T]): Iter[T] = new Iter[T] {
  def hasNext: Boolean = cur.hasCurrent
  def next(): T = {
    require(cur.hasCurrent, "empty iterator")
    val answer = cur.current
    cur.next()
    answer
  }
}

The two abstract sequences are identical. A next call returns the old head and removes it, while hasNext only queries availability. No element is read at construction or during an availability test, and no later element is read while returning the current one. Thus the adapter is not too eager. The source's Cursor.current clause needs the implicit precondition that its sequence is nonempty; taking the head of an empty sequence is undefined. The checks above satisfy that requirement even without relying on the client convention.