arrow-derivation.scala

import scalaz.{Alt, Apply, ApplicativePlus, Arrow, Choice, Decidable, Divide, Semigroup}

object Derive {
  implicit def ArrowInstanceCovariant[F[_, _], From](implicit A: Arrow[F]): Apply[F[From, ?]] = new Apply[F[From, ?]] {
    def map[A, B](fa: F[From, A])(f: A => B): F[From, B] = A.compose(A.arr(f), fa)
    def ap[A,B](fa: => F[From, A])(f: => F[From, A => B]): F[From, B] =
      A.mapsnd(A.combine(f, fa))(t => t._1(t._2))
  }

  implicit def ArrowChoiceInstance[F[_, _], To](implicit A: Arrow[F], C: Choice[F]): Decidable[F[?, To]] = new Decidable[F[?, To]] {
    def choose2[Z, A1, A2](a1: =>F[A1, To], a2: =>F[A2, To])(f: Z => (A1 \/ A2)): F[Z, To] =
      A.mapfst(C.choice(a1, a2))(f)
  }

  implicit def ArrowInstance[F[_, _], To](A: Arrow[F], S: Semigroup[To]): Divide[F[?, To]] = new Divide[F[?, To]] {
    def contramap[A, B](r: F[A, To])(f: B => A): F[B, To] = A.mapfst(r)(f)
    def divide2[A1, A2, Z](a1: =>F[A1, To], a2: =>F[A2, To])(f: Z => (A1, A2)): F[Z, To] =
      A.compose(A.arr((t: (To, To)) => S.append(t._1, t._2)), A.compose(A.splitA(a1, a2), A.arr(f)))
  }

  implicit def altPlus[F[_]](implicit AP: ApplicativePlus[F]): Alt[F] = new Alt[F] {
    def point[A](a: => A): F[A] = AP.point(a)
    def ap[A, B](fa: => F[A])(f: => F[A => B]): F[B] = AP.ap(fa)(f)
    def alt[A](a1: =>F[A], a2: =>F[A]): F[A] = AP.plus(a1, a2)
  }
}