trait HFunctor[F[_]] {
def ffmap[G[_]: Functor, A, B](f: A => B): F[G[A]] => F[G[B]]
def hfmap[G[_], H[_]](t: G ~> H): ({type λ[α] = F[G[α]]})#λ ~> ({type λ[α] = F[H[α]]})#λ
}
trait Functor[F[_]] { self =>
def fmap[A, B](f: A => B): F[A] => F[B]
def map[A, B](x: F[A])(f: A => B): F[B] = fmap(f)(x)
def strengthL[A, B]: A => F[B] => F[(A, B)] = a => f => fmap((x: B) => (a, x))(f)
def strengthR[A, B]: F[A] => B => F[(A, B)] = f => b => fmap((x: A) => (x, b))(f)
def compose[G[_]](implicit e: Functor[G]): Functor[({ type λ[α] = F[G[α]]})#λ] =
new Functor[({ type λ[α] = F[G[α]]})#λ] {
def F = self;
def G = e
def fmap[A, B](f: A => B) = F.fmap(G.fmap(f))
}
}
object Functor {
@inline def apply[F[_]: Functor]: Functor[F] = iev
}
trait Coyoneda[F[_], A] { co =>
type I
def fi: F[I]
def k: I => A
final def run(implicit F: Functor[F]): F[A] = F.fmap(k)(fi)
final def map[B](f: A => B): Coyoneda.Aux[F, B, I] =
Coyoneda(fi)(f compose k)
final def trans[G[_]](phi: F ~> G): Coyoneda[G, A] =
Coyoneda(phi(fi))(k)
}
object Coyoneda {
type Aux[F[_], A, B] = Coyoneda[F, A] { type I = B }
def apply[F[_], B, A](x: F[B])(f: B => A): Aux[F, A, B] =
new Coyoneda[F, A] {
type I = B
val fi = x
val k = f
}
implicit def coyonedaFunctor[F[_]]: Functor[({ type λ[α] = Coyoneda[F, α] })#λ] =
new Functor[({ type λ[α] = Coyoneda[F, α] })#λ] {
def fmap[A, B](f: A => B): Coyoneda[F, A] => Coyoneda[F, B] =
x => apply(x.fi)(f compose x.k)
}
implicit def coyonedaHFunctor: HFunctor[({ type λ[F[_]] = ({ type λ[α] = Coyoneda[F, α] })#λ })#λ] =
new HFunctor[({ type λ[F[_]] = ({ type λ[α] = Coyoneda[F, α] })#λ })#λ] {
def ffmap[G[_]: Functor, A, B](f: A => B): Coyoneda[G, A] => Coyoneda[G, B] = _.map(f)
def hfmap[F[_], G[_]](t: F ~> G): (({ type λ[α] = Coyoneda[F, α] })#λ ~> ({ type λ[α] = Coyoneda[G, α] })#λ) =
new (({ type λ[α] = Coyoneda[F, α] })#λ ~> ({ type λ[α] = Coyoneda[G, α] })#λ) {
def apply[A](x: Coyoneda[F, A]) = x.trans(t)
}
}
def liftCoyoneda[F[_], A](fa: F[A]): Coyoneda[F, A] = apply(fa)(x => x)
def lowerCoyoneda[F[_]: Functor, A](c: Coyoneda[F, A]): F[A] = c.run
}
distribute
不是Functor
上的方法 - 它是自己的类型类:http://hackage.haskell.org/package/distributive-0.1.2/docs/Data-Distributive.html - dyross