Functional Definitions: Monoid, Functor, Monad

Monoid

	trait Monoid[A] {
	// a monoid comprises an associative binary operator ...
	def op(a1: A, a2: A): A
	// ... and a 'zero' value such that op(x, zero) == x
	// and op(zero, x) = x
	def zero: A
	}
	Object Monoid {
	// integer addition is monoidal
	val intAddition: Monoid[Int] = new Monoid[Int] {
	def op(x: Int, y: Int) = x + y
	val zero = 0
	}
	}

view raw MonoidDefinition.scala hosted with ❤ by GitHub

Functor

	trait Functor[F[_]] {
	// a functor is just a thing with a map function
	def map[A, B](a: F[A])(f: A => B): F[B]
	}

view raw FunctorDefinition.scala hosted with ❤ by GitHub

Monad