Lift or unlift type from shapeless' hlist element type

LiftUnliftType.scala

object UnliftType {
  def apply[L <: HList, M[_]](implicit unlift: UnliftType[L, M]) = unlift
  type Aux[L <: HList, M[_], R <: HList] = UnliftType[L, M] { type Out = R }

  implicit def unliftType[H, L <: HList, R <: HList, M[_]]
    (implicit ev: Aux[L, M, R]) :
    Aux[M[H] :: L, M, H :: R] =
      new UnliftType[M[H] :: L, M] { type Out = H :: R }

  implicit def unliftNoType[H, L <: HList, R <: HList, M[_]]
    (implicit ev: Aux[L, M, R], e: H =:!= M[T] forSome { type T }) :
    Aux[H :: L, M, H :: R] =
      new UnliftType[H :: L, M] { type Out = H :: R }

  implicit def unliftNil[M[_]]: Aux[HNil, M, HNil] =
    new UnliftType[HNil, M] { type Out = HNil }
}

trait LiftType[-L <: HList, M[_]] {
  type Out <: HList
}
object LiftType {
  type Aux[L <: HList, M[_], R <: HList] = LiftType[L, M] { type Out = R }
  def apply[L <: HList, M[_]](implicit lift: LiftType[L, M]) = lift

  implicit def liftType[H, L <: HList, R <: HList, M[_]]
    (implicit ev: Aux[L, M, R], ev2: H =:!= M[T] forSome { type T }):
    Aux[H::L, M, M[H] :: R] =
      new LiftType[H :: L, M] { type Out = M[H] :: R}

  implicit def liftNil[M[_]]: Aux[HNil, M, HNil] = new LiftType[HNil, M] { type Out = HNil }
}