For an object X, X$ should be =:= to X.type

[smarter]

This works in scalac but not in dotty:

case object X

object Test {
  val Alias = X

  val x: X.type = Alias
}

error: type mismatch:
 found   : X(Test.Alias)
 required: X.type
  val x: X.type = Alias
                  ^

Logging shows the issue:

[log frontend] ==> isSubType X$(Test.Alias) <:< X.type class dotty.tools.dotc.core.Types$TermRefWithSignature, class dotty.tools.dotc.core.Types$TermRefWithSignature?
[log frontend]   ==> isSubType X$ <:< X.type class dotty.tools.dotc.core.Types$CachedTypeRef, class dotty.tools.dotc.core.Types$TermRefWithSignature?
[log frontend]   <== isSubType X$ <:< X.type class dotty.tools.dotc.core.Types$CachedTypeRef, class dotty.tools.dotc.core.Types$TermRefWithSignature = false
[log frontend] <== isSubType X$(Test.Alias) <:< X.type class dotty.tools.dotc.core.Types$TermRefWithSignature, class dotty.tools.dotc.core.Types$TermRefWithSignature = false

[sjrd]

Hum ... I don't think this is the proper fix. X$ accepts null, whereas X.type does not. These types should not be equal.

The proper fix, IMO, is for Alias to be inferred to have type X.type, instead of X$.

[retronym]

Not sure if this is the relevant or not, but I fixed a problem in scalac related to transitity of <:< and =:= being broken for:

    val tp1 = TypeRef(ThisType(EmptyPackageClass), moduleClass, Nil)
    val tp2 = SingleType(ThisType(EmptyPackageClass), module)
    val tp3 = ThisType(moduleClass)

Here's the test:

https://github.com/scala/scala/blob/b8e4d1f692c5712990b45f50625627015112df32/test/junit/scala/reflect/internal/TypesTest.scala#L38

[smarter]

@sjrd What you're suggesting might be better in principle but note that module classes are not nullable in dotty, so the difference might not be observable: https://github.com/lampepfl/dotty/blob/5a5f9d7ed37ca6449ef61ee5e0f6fbf9731df795/src/dotty/tools/dotc/core/SymDenotations.scala#L616-L618