Semigroupoid in scala

README.md

https://groups.google.com/d/msg/scala-user/Z54ncnC7XKA/AKfUwF5qDk0J

Semigroupoid.scala

trait Functor[F[_]] {
  def fmap[A, B](f: A => B): F[A] => F[B] 
}

trait FlatMap[F[_]] extends Functor[F] {
  def flatMap[A, B](f: A => F[B]): F[A] => F[B]
}

trait Semigroupoid[~>[_, _]] {
  def compose[A, B, C]: (A ~> B) => (B ~> C) => (A ~> C)
}

case class Kleisli[A, F[_], B](k: A => F[B]) 

def KleisliSemigroupoid[F[_]: FlatMap]: Semigroupoid[({ type lam[a, b]=Kleisli[a, F, b] })#lam]
  = new Semigroupoid[({ type lam[a, b]=Kleisli[a, F, b] })#lam] {
    def compose[A, B, C] = f => g => Kleisli(a => implicitly[FlatMap[F]].flatMap(g.k)(f k a)) 
  }