Ostensible inconsistencies in singleton types

Question

I have a couple of questions about singleton types, but since they're both very closely related, I am posting them under the same thread.

Q1. Why does #1 does not compile but #2 does?

def id(x: Any): x.type = x      // #1
def id(x: AnyRef): x.type = x   // #2

Q2. The type is correctly inferred in case of String but not in case of other reference types I tried. Why is that so?

scala> id("hello")
res3: String = hello

scala> id(BigInt(9))
res4: AnyRef = 9

scala> class Foo
defined class Foo

scala> id(new Foo)
res5: AnyRef = Foo@7c5c5601

Answer 1

Singleton types can only refer to AnyRef descendants. See Why do String literals conform to Scala Singleton for more details.

The argument the application id(BigInt(9)) can't be referred to via a stable path, so consequently doesn't have an interesting singleton type.

scala> id(new {})
res4: AnyRef = $anon$1@7440d1b0

scala> var o = new {}; id(o)
o: Object = $anon$1@68207d99
res5: AnyRef = $anon$1@68207d99

scala> def o = new {}; id(o)
o: Object
res6: AnyRef = $anon$1@2d76343e

scala> val o = new {}; id(o) // Third time's the charm!
o: Object = $anon$1@3806846c
res7: o.type = $anon$1@3806846c