@alpha has no effect over double definition error

[soronpo]

minimized code

import scala.annotation.alpha
@alpha("fooString") def foo(ps: String*) : Unit = ???
@alpha("fooInt") def foo(ps: Int*) : Unit = ???
@alpha("fooAny") def foo(ps: Any*) : Unit = ???

Compilation output

Double definition:
def foo(ps: String*): Unit in package object main$package at line 4 and
def foo(ps: Int*): Unit in package object main$package at line 5
have the same type after erasure.
@alpha("fooAny") def foo(ps: Any*) : Unit = ???

Double definition:
def foo(ps: Int*): Unit in package object main$package at line 5 and
def foo(ps: Any*): Unit in package object main$package at line 6
have the same type after erasure.

see scastie: https://scastie.scala-lang.org/owQEIEShQayiRjUJ6Esk2w

expectation

Currently DummyImplicit is used as a workaround to create unique signatures after erasure.
@odersky mentioned that @alpha annotation could be used to avoid double definition error, however it does not seem to affect the compiler when it checks for double definitions.

[odersky]

I tried to just remove the error condition but then we run into more trouble:

-- Error: i7942.scala:2:0 ------------------------------------------------------
2 |@alpha("fooString") def foo(ps: String*) : Unit = ???
  |^
  |cannot merge
  |  method foo of type (ps: Seq[Any]): Unit  and
  |  method foo of type (ps: Seq[Int]): Unit
  |they are both defined in package <empty> but have matching signatures
  |  (ps: Seq[Any]): Unit and
  |  (ps: Seq[Int]): Unit
  |as members of package object i7942$package
  |       
3 |@alpha("fooInt") def foo(ps: Int*) : Unit = ???
4 |@alpha("fooAny") def foo(ps: Any*) : Unit = ???

To fix this we need to change our way how we treat signatures. Since signatures are used for many different things this will require a lot of thought.