LongAddition.scala

type Digit = Int

def toDigits(i: Int) = i.toString.map(_.asDigit).reverse
def fromDigits(digits: Seq[Digit]) = digits.reverse.dropWhile(_ == 0).map(_.toString).reduce(_ + _).toInt

case class FullAdder(inCarry: Digit, i: Digit, j: Digit) {
  val asDigits = toDigits(inCarry + i + j)
  def sum() = asDigits(0)
  def carry() = if(asDigits.length > 1) asDigits(1) else 0
}

def longAddition(x: Int, y: Int) = {
  val xDigits = toDigits(x) ++ Seq(0)
  val yDigits = toDigits(y) ++ Seq(0)

  val zipped = xDigits.zipAll(yDigits, 0, 0)
  
  val adders = zipped.scanLeft(FullAdder(0, 0, 0)) { case (acc, (i, j)) => FullAdder(acc.carry(), i, j)}.tail
  fromDigits(adders.map(_.sum()))
}

val x = 145678
val y = 7865
val res = longAddition(x, y)

println("res is " + res + ", res equals x + y is " + (x + y == res))