Intersection.Aux[Int :: HNil, Int :: HNil, HNil]

[aryairani]

There seems to be a problem with Intersection:

scala> implicitly[Intersection.Aux[Int :: HNil, Int :: HNil, Int :: HNil]]
res27: Intersection.Aux[Int :: HNil, Int :: HNil, Int :: HNil] = shapeless.ops.hlist$Intersection$$anon$58@342165b9

This correctly witnesses that { Int } ∩ { Int } = { Int }

scala> implicitly[Intersection.Aux[Int :: HNil, Int :: HNil, HNil]]
res25: Intersection.Aux[Int :: HNil, Int :: HNil, HNil] = shapeless.ops.hlist$LowPriorityIntersection$$anon$56@50fc9b74

This incorrectly witnesses that { Int } ∩ { Int } = ∅
😞

[aryairani]

scala> reify { implicitly[Intersection.Aux[Int::HNil,Int::HNil,HNil]] }
res29: $r.intp.global.Expr[shapeless.ops.hlist.Intersection.Aux[shapeless.::[Int,shapeless.HNil],shapeless.::[Int,shapeless.HNil],shapeless.HNil]] = Expr[shapeless.ops.hlist.Intersection.Aux[shapeless.::[Int,shapeless.HNil],shapeless.::[Int,shapeless.HNil],shapeless.HNil]](Predef.implicitly[hlist.Intersection.Aux[::[Int, HNil], ::[Int, HNil], HNil]](hlist.this.Intersection.hlistIntersection1(hlist.this.Intersection.hnilIntersection)))

simplifies to

Intersection.hlistIntersection1(Intersection.hnilIntersection))

implicit def hnilIntersection[M <: HList]: Aux[HNil, M, HNil] =
  new Intersection[HNil, M] {
    type Out = HNil
    def apply(l: HNil): Out = HNil
  }

implicit def hlistIntersection1[H, T <: HList, M <: HList]
  (implicit i: Intersection[T, M]): Aux[H :: T, M, i.Out] =
    new Intersection[H :: T, M] {
      type Out = i.Out
      def apply(l: H :: T): Out = i(l.tail)
    }

Yes. hnilIntersection says ∅ ∩ M = ∅, which is good.
But hlistIntersection1 says (H :: T) ∩ M = T ∩ M (which is false if H ∈ M)
i.e. { H } ∩ M = ∅ ∩ M = ∅

[aryairani]

There's an equivalent bug in Union:

import shapeless._, ops.hlist.Union
implicitly[Union.Aux[Int :: HNil, Int :: HNil, Int :: Int :: HNil]]

compiles as well, witnessing that { Int } ∪ { Int } = { Int, Int }
😭