Does that mean we can get a computer to form sentences through programming grammar?

Yes, you can use these kinds of grammars to parse sentences and generate them. The actual grammars are way more complicated than my little toy snippet was. There's a whole field of study called computational linguistics that works on this very thing. There are also statistical grammars and n-grams and all kinds of cool stuff. A decent university library should have some books on it. Or I can give you some pointers if you wish.

Ceci n'est pas un seing.