Store characters in a mutable dynamic array. Its length is maintained by the collection, giving constant-time size.
class DocImpl extends Doc {
  private val text = scala.collection.mutable.ArrayBuffer.empty[Char]
  def insert(x: Char, pos: Int): Unit = {
    require(0 <= pos && pos <= text.length)
    text.insert(pos, x)
  }
  def delete(pos: Int): Char = {
    require(0 <= pos && pos < text.length)
    text.remove(pos)
  }
  def read(pos: Int): Char = {
    require(0 <= pos && pos < text.length)
    text(pos)
  }
  def size: Int = text.length
}
The representation invariant requires a nonnull private dynamic array containing a finite sequence of characters, with its internal collection invariant maintained by the library. The abstraction function is
(1)
Insertion allows the end position and shifts the suffix right; deletion returns exactly the removed character and shifts the suffix left. read leaves the abstract state unchanged. size equals the abstract sequence length in time complexity. Indexed reads are also constant time; insertion and deletion may take linear time, which the question permits.

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