Are path-dependent types type projections?

Question

I'm reading Scala in depth now. Here is an excerpt from the book:

All path-dependent types are type projections. A path-dependent type foo.Bar is rewritten as foo.type#Bar by the compiler...

In Scala, all type references can be written as projects against named entities. The type scala.String is shorthand for scala.type#String where the name scala refers to the package scala and the type String is defined by the String class on the scala package.

Obviously, there isn't scala.String class, but I failed to reproduce this with Null.

scala> type N = scala.type#Null
<console>:7: error: type mismatch;
 found   : type
 required: AnyRef
       type N = scala.type#Null

So, my questions are as follows. Are path-dependent types type projections? Is it just inner compiler representation or can be expressed in scala code?

Answer 1

Here's a quick REPL session which confirms what Josh wrote,

scala> class Foo { type T = String }
defined class Foo

scala> val foo = new Foo
foo: Foo = Foo@10babe8

scala> implicitly[foo.type#T =:= foo.T]
res0: =:=[foo.T,foo.T] = <function1>

The problem with your scala.type#Null example is that the prefix scala is a package prefix rather than being a stable identifier of a value. Arguably it ought to be the latter, but unfortunately it's not ... that's a lingering mismatch between the semantics of Scala packages and Scala objects (in the sense of modules).