example.scala

trait Semigroup[A] {
  def op(a1: A, a2: A): A
}

trait Monoid[A] extends Semigroup[A] {
  def zero: A
}

trait Group[A] extends Monoid[A] {
  // Override one or both
  def inverse(a1: A): A = minus(zero, v)
  def minus(l: A, r: A): A = op(l, inverse(r))
}

def stringConcatMonoid = new Monoid[String] { 
  def op(a1: String, a2: String) = a1 + a2
  val zero = ""
}

def listConcatMonoid[A] = new Monoid[List[A]] {
  def op(a1: List[A], a2: List[A]) = a1 ++ a2
  val zero = Nil
}

def intSum = new Group[Int] {
  def op(a1: Int, a2: Int) = a1 + a2
  def inverse(a: Int) = -a
  val zero = 0
}