Bi-Kleiseli on Scala

BiKleisli.scala

package com.github.everpeace

import scalaz._
import Scalaz._

/**
 * BiKleisli arrow
 * W: comonad
 * M: monad
 */
trait BiKleisli[W[_],M[_],A,B]{
  def apply(wa:W[A]):M[B]

  import BiKleislis.{bikleisli,bikleisliFn}

  // bikleisli arrow composition (f ## g = cojoin;W(f);t;M(g);join)
  def ##[C] (g:BiKleisli[W,M,B,C])(implicit w:Comonad[W],m:Monad[M],t:Distributes[W,M]):BiKleisli[W,M,A,C] = bikleisli((wa:W[A]) => t(wa =>> this) >>= g) //m.bind(t(w.fmap(w.cojoin(wa),this)),g)
}

object BiKleislis{
  // constructor
  def bikleisli[W[_],M[_],A,B](f:W[A]=>M[B])(implicit w:Comonad[W],m:Monad[M],t:Distributes[W,M]):BiKleisli[W,M,A,B] = new BiKleisli[W,M,A,B]{
    def apply(wa: W[A]) = f(wa)
  }

  // implicit conversion: bikleisli to function
  implicit def bikleisliFn[W[_],M[_],A,B](bk:BiKleisli[W,M,A,B]):W[A]=>M[B] = bk(_)

  // implicit conversion: bikleisli to scalaz.MAB
  implicit def bikleislimab[W[_],M[_],A,B](bk:BiKleisli[W,M,A,B]) = mab[({type λ[α,β]=BiKleisli[W,M,α,β]})#λ,A,B](bk)

  // implicit bikleisli category (for scalaz.MAB methods)
  implicit def BiKleisliCategory[W[_],M[_]](implicit w:Comonad[W],m:Monad[M],t:Distributes[W,M]):Category[({type λ[α,β]=BiKleisli[W,M,α,β]})#λ] = new Category[({type λ[α,β]=BiKleisli[W,M,α,β]})#λ] {
    // id = η○ε
    def id[A] = bikleisli((wa:W[A]) => m.pure(w.copure(wa)))
    // compose(f,g) = g ## f
    def compose[A,B,C](f: BiKleisli[W,M,B,C], g: BiKleisli[W,M,A,B]) = g ## f
  }
}