Cows go Muuu

Mu.scala

package cohomolo.gy.generalized

import scalaz.Prelude.{<~<, IsCovariant}
import scalaz.data.{As, Identity, ~>, ∀}

//final case class Mu[F[_]](unMu: Algebra[F, ?] ~> Identity)

trait MuModule {
  type Mu[F[_]]

  def   mu[F[_]](f: F[Mu[F]]):   Mu[F]
  def unMu[F[_]](f:   Mu[F] )(implicit ev: Algebra[F, ?]): Algebra[F, ?] ~> Identity

  def subst[G[_[_[_]]]](g: G[λ[α[_] => α[Mu[α]]]]): G[Mu]

  def liftLiskov[F[_], G[_]](ev: ∀[λ[α => F[α] <~< G[α]]])(implicit F: IsCovariant[F]): Mu[F] <~< Mu[G]
}

private[generalized] object MuImpl extends MuModule {
  type Mu[F[_]] = F[Mu[F]]

  def   mu[F[_]](f: F[Mu[F]]):   Mu[F]  = f
  def unMu[F[_]](f:   Mu[F] )(implicit ev: Algebra[F, ?] ~> Identity): Algebra[F, ?] ~> Identity = ev

  def subst[G[_[_[_]]]](g: G[λ[α[_] => α[Mu[α]]]]): G[Mu] = g

  def liftLiskov[F[_], G[_]](ev: ∀[λ[α => F[α] <~< G[α]]])(implicit F: IsCovariant[F]): Mu[F] <~< Mu[G] =
    As.unsafeForce
}