A ClassCastException is thrown due to incorrect LUB type

[Atry]

Welcome to Scala 2.13.0 (Java HotSpot(TM) 64-Bit Server VM, Java 1.8.0_202-ea).
Type in expressions for evaluation. Or try :help.

scala> object O {
     |     trait Base {
     |         private[O] type Output
     |         private[O] def output: Output
     |     }
     |     class IntOutput(val output: Int) extends Base {
     |         private[O] type Output = Int
     |     }
     |     class StringOutput1(private[O] val output: String) extends Base {
     |         private[O] type Output = String
     |     }
     |     class StringOutput2(private[O] val output: String) extends Base{
     |         private[O] type Output = String
     |     }
     |     def f: Base { type Output = String } => Int = _.output.length
     |     def f2: (StringOutput1 => Int) with (StringOutput2 => Int) = f
     | }
defined object O

scala> O.f2(new O.IntOutput(3))
java.lang.ClassCastException: java.lang.Integer cannot be cast to java.lang.String
  at O$.$anonfun$f$1(<console>:15)
  at O$.$anonfun$f$1$adapted(<console>:15)
  ... 28 elided

I think O.f2(new O.IntOutput(3)) should not compile, because IntOutput is neither StringOutput1 nor StringOutput2.

[NthPortal]

should StringOutput1 and StringOutput2 not LUB to Base? although not Base { type Output = String }, defining it as f should fail to compile due to being the wrong type.

I suppose StringOutput1 and StringOutput2 could LUB to Base { type Output = String } (in which case O.f2(new O.IntOutput(3)) shouldn't compile), but it's not my impression that such type refinements are usually inferred.

[Atry]

The accessor private[O] prevents LUB from creating refinement type.

BTW, Dotty LUB to StringOutput1 | StringOutput2, which sounds better.