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Scala: Typelevel unboxed compile time dimensional analysis over tagged types. Intellij Idea compatible 100%
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package superquants


import shapeless.{HList, Nat, Succ, ::, HNil}

trait PowSum[Powed, Tail <: HList, LeftZnak <: PowZnak, Left <: Nat, RightZnak <: PowZnak, Right <: Nat] {
  type OutZnak <: PowZnak
  type Out <: Nat
  type OutList <: HList
}
object PowSum extends PowSumLowPriority {

  implicit def tsum0[Powed, Tail <: HList, Left <: Nat](implicit minat:ExplicitNat[Left])
  :Aux[Powed, Tail, PowPlus, Left, PowPlus, Nat._0, PowPlus, minat.Out, Pow[Long, Powed, PowPlus, minat.Out] :: Tail] = tsumDummy

  implicit def tsum1[Powed, Tail <: HList, Left <: Nat, Right <: Nat]
  (implicit next:PowSum[Powed, Tail, PowPlus, Succ[Left], PowPlus, Right])
  :Aux[Powed, Tail, PowPlus, Left, PowPlus, Succ[Right], PowPlus, next.Out, Pow[Long, Powed, PowPlus, next.Out] :: Tail] = tsumDummy




  implicit def tsumMinusMinus0[Powed, Tail <: HList, Left <: Nat](implicit minat:ExplicitNat[Left])
  :Aux[Powed, Tail, PowMinus, Left, PowMinus, Nat._0, PowMinus, minat.Out, Pow[Long, Powed, PowMinus, minat.Out] :: Tail] = tsumDummy

  implicit def tsumMinusMinusRecur[Powed, Tail <: HList, Left <: Nat, Right <: Nat]
  (implicit next:PowSum[Powed, Tail, PowMinus, Succ[Left], PowMinus, Right])
  :Aux[Powed, Tail, PowMinus, Left, PowMinus, Succ[Right], PowMinus, next.Out, Pow[Long, Powed, PowMinus, next.Out] :: Tail] = tsumDummy






  implicit def tsumPlusMinus000[Powed, Tail <: HList]
  :Aux[Powed, Tail, PowPlus, Nat._0, PowMinus, Nat._0, PowPlus, Nat._0, Pow[Long, Powed, PowPlus, Nat._0] :: Tail] = tsumDummy

  implicit def tsumPlusMinus00[Powed, Tail <: HList, Left <: Nat](implicit minat:ExplicitNat[Left])
  :Aux[Powed, Tail, PowPlus, Left, PowMinus, Nat._0, PowPlus, minat.Out, Pow[Long, Powed, PowPlus, minat.Out] :: Tail] = tsumDummy

  implicit def tsumPlusMinus01[Powed, Tail <: HList, Right <: Nat](implicit minat:ExplicitNat[Right])
  :Aux[Powed, Tail, PowPlus, Nat._0, PowMinus, Right, PowMinus, minat.Out, Pow[Long, Powed, PowMinus, minat.Out] :: Tail] = tsumDummy

  //recur in LowPriority

  implicit def tsumPlusMinusSame[Powed, Tail <: HList, N <: Nat]
  :Aux[Powed, Tail, PowPlus, N, PowMinus, N, PowPlus, Nat._0, Tail] = tsumDummy




  implicit def tsumMinusPlus000[Powed, Tail <: HList]
  :Aux[Powed, Tail, PowMinus, Nat._0, PowPlus, Nat._0, PowMinus, Nat._0, Pow[Long, Powed, PowMinus, Nat._0] :: Tail] = tsumDummy

  implicit def tsumMinusPlus00[Powed, Tail <: HList, Left <: Nat](implicit minat:ExplicitNat[Left])
  :Aux[Powed, Tail, PowMinus, Left, PowPlus, Nat._0, PowMinus, minat.Out, Pow[Long, Powed, PowMinus, minat.Out] :: Tail] = tsumDummy

  implicit def tsumMinusPlus01[Powed, Tail <: HList, Right <: Nat](implicit minat:ExplicitNat[Right])
  :Aux[Powed, Tail, PowMinus, Nat._0, PowPlus, Right, PowPlus, minat.Out, Pow[Long, Powed, PowPlus, minat.Out] :: Tail] = tsumDummy

  //recur in LowPriority

  implicit def tsumMinusPlusSame[Powed, Tail <: HList, N <: Nat]
  :Aux[Powed, Tail, PowMinus, N, PowPlus, N, PowMinus, Nat._0, Tail] = tsumDummy

}


trait PowSumLowPriority {
  type Aux[Powed, Tail <: HList, LeftZnak <: PowZnak, Left <: Nat, RightZnak <: PowZnak, Right <: Nat, OutZnak0 <: PowZnak, Out0 <: Nat, OutList0 <: HList] =
    PowSum[Powed, Tail, LeftZnak, Left, RightZnak, Right]{ type OutZnak = OutZnak0 ; type Out = Out0; type OutList = OutList0 }

  val tsumStub = new PowSum[Nothing,Nothing,Nothing,Nothing,Nothing,Nothing]{}
  def tsumDummy[T]:T = tsumStub.asInstanceOf[T]



  implicit def tsumPlusMinusRecur[Powed, Tail <: HList, Left <: Nat, Right <: Nat]
  (implicit next:PowSum[Powed, Tail, PowPlus, Left, PowMinus, Right])
  :Aux[Powed, Tail, PowPlus, Succ[Left], PowMinus, Succ[Right], next.OutZnak, next.Out, Pow[Long, Powed, next.OutZnak, next.Out] :: Tail] = tsumDummy


  implicit def tsumMinusPlusRecur[Powed, Tail <: HList, Left <: Nat, Right <: Nat]
  (implicit next:PowSum[Powed, Tail, PowMinus, Left, PowPlus, Right])
  :Aux[Powed, Tail, PowMinus, Succ[Left], PowPlus, Succ[Right], next.OutZnak, next.Out, Pow[Long, Powed, next.OutZnak, next.Out] :: Tail] = tsumDummy


}