适用于猫的逆变函子，适用，Monad等？

Question

我具有以下特征...

import cats._
import cats.implicits._

trait Preference[-A] {
  self =>

  def compare(a1: A, a2: A): Int

  final def ordering[A1 <: A]: Ordering[A1] = {
    new Ordering[A1] {
      def compare(a1: A1, a2: A1): Int = {
        self.compare(a1, a2)
      }
    }
  }

}


object Preference {

  implicit val contravariant: Contravariant[Preference] = {
    new Contravariant[Preference] {
      def contramap[A, B](fa: Preference[A])(f: B => A): Preference[B] = {
        new Preference[B] {
          def compare(b1: B, b2: B): Int = {
            fa.compare(f(b1), f(b2))
          }
        }
      }
    }
  }
}

我想为此特性定义Apply，Applicative，甚至可能定义Monad实例，但是所有这些类型类都是Functor的扩展。这些类型类的版本在Cats中是否存在逆函子？

Answer 1

Haskell中wpdb的对等等效项是Divisible和Applicative allows to define both of its methods (divide is contramap2, conquer is trivial)。不过，我不确定是否可以肯定cats.ContravariantMonoidal是猫的Divisible。

对于Monoidal，Kmett说

  

There is no contravariant Monad-like. You need C -> C, not C -> C^op. The twist denies you the ability to build nice structure.

也Are there contravariant monads?。