Lifting Monoid over arbitrary arity type constructors

gistfile1.scala

object MonoidExamples {
  import shapeless._
  import HList._
  
  trait Monoid[T]
  
  // Boilerplate ...
  trait HListed[S, L <: HList]
  implicit def hl1[S[_], A] = new HListed[S[A], A :: HNil] {}
  implicit def hl2[S[_, _], A, B] = new HListed[S[A, B], A :: B :: HNil] {}
  implicit def hl3[S[_, _, _], A, B, C] = new HListed[S[A, B, C], A :: B :: C :: HNil] {}
  implicit def hl4[S[_, _, _, _], A, B, C, D] = new HListed[S[A, B, C, D], A :: B :: C :: D :: HNil] {}
  implicit def hl5[S[_, _, _, _, _], A, B, C, D, Etc] = new HListed[S[A, B, C, D, Etc], A :: B :: C :: D :: Etc :: HNil] {}
  // Rinse and repeat ...
  // End of boilerplate.
  
  trait Monoids[L <: HList]
  implicit def hnilMonoids = new Monoids[HNil] {}
  implicit def hlistMonoids[H, T <: HList](implicit mh : Monoid[H], mt : Monoids[T]) = new Monoids[H :: T] {}
  
  implicit def hlistMonoid[S, L <: HList](implicit hl : HListed[S, L], ms : Monoids[L]) = new Monoid[S] {}
  
  trait A
  trait B
  trait C
  trait D
  trait Etc

  implicit def aMonoid = new Monoid[A] {}
  implicit def bMonoid = new Monoid[B] {}
  implicit def cMonoid = new Monoid[C] {}
  implicit def dMonoid = new Monoid[D] {}
  implicit def etcMonoid = new Monoid[Etc] {}
  
  trait NotMonoid
  //implicitly[Monoid[NotMonoid]]
  
  trait TC1[A]
  implicitly[Monoid[TC1[A]]]
  //implicitly[Monoid[TC1[NotMonoid]]] // Doesn't compile
  
  trait TC2[A, B]
  implicitly[Monoid[TC2[A, B]]]
  //implicitly[Monoid[TC2[A, NotMonoid]]] // Doesn't compile
  
  trait TC3[A, B, C]
  implicitly[Monoid[TC3[A, B, C]]]
  //implicitly[Monoid[TC3[A, B, NotMonoid]]] // Doesn't compile
  
  trait TC4[A, B, C, D]
  implicitly[Monoid[TC4[A, B, C, D]]]
  //implicitly[Monoid[TC4[A, B, C, NotMonoid]]] // Doesn't compile

  trait TC5[A, B, C, D, E]
  implicitly[Monoid[TC5[A, B, C, D, Etc]]]
  //implicitly[Monoid[TC5[A, B, C, D, NotMonoid]]] // Doesn't compile
}