Changing default values in MGrammar

Question

I have a syntax something like this:

syntax Foo 
     =   b:Bar z:Baz?
     => Foo { Bar => b, Baz => z }

But if Baz doesn't match then the graph projects to be:

Foo { Bar => Bar { ... }, Baz => null }

What I'd really like is for Baz to not project to null but something else instead (such as Baz { }). The only way I could get it to work so far is to completely duplicate the syntax one with Baz required and one with Baz totally missing and change the greater projection.

Here is a more complete example

Given the input text "bar", modify this language:

module test
{
    language test
    {
        syntax Main = Foo;
        
        syntax Foo 
            =  b:Bar z:Baz?
            => Foo { Bar => b, Baz => z };
        
        token Bar = "bar" => true;
        token Baz = "baz" => true;
    }
}

To produce the graph:

Main[
  Foo{
    Bar => true,
    Baz => false
  }
]

Answer 1

Rocky Lhotka helped me solve this perfectly by pointing out the "empty" keyword.

b : (b : Bar => b | empty => false)
z : (b : Baz => b | empty => false)