Formal definition of a Monad

A monad it a parametric type with two functions defined, $flatMap$ and $unit$.

trait Monad[T] {
  def flatMap[U](f: T => Monad[U]): Monad[U]
}

def unit[T](t: T): Monad[T]

Monads must satisfy the following three laws:

Associativity law: $$ m.flatMap(f).flatMap(g) = m.flatMap ( x => f(x).flatmap(g)) $$

Left unit law:  $$ unit(x).flatMap(f) = f(x) $$

Right unit law: $$ m.flatMap(unit) = m $$