Singletons as Synthetic classes in Scala?

Question

I am reading Programming in Scala, and I don\'t understand the following sentence (pdf p.112):

Each singleton object is implemented as an instance of

Answer 1

The chapter 31 of the same "Programming in Scala" is more precise:

Java has no exact equivalent to a singleton object, but it does have static methods.

The Scala translation of singleton objects uses a combination of static and instance methods. For every Scala singleton object, the compiler will create a Java class for the object with a dollar sign added to the end.
For a singleton object named App, the compiler produces a Java class named App$.
This class has all the methods and fields of the Scala singleton object.
The Java class also has a single static field named MODULE$ to hold the one instance of the class that is created at run time.
As a full example, suppose you compile the following singleton object:

object App {
  def main(args: Array[String]) {
    println("Hello, world!")
  }
}

Scala will generate a Java App$ class with the following fields and methods:

$ javap App$
public final class App$ extends java.lang.Object
    implements scala.ScalaObject{
  public static final App$ MODULE$;
  public static {};
  public App$();
  public void main(java.lang.String[]);
  public int $tag();
}

That’s the translation for the general case.