To make it less ugly, and assuming you are using PostgreSQL you could make the code a little more appealing rewriting it like that. (If you are not using postgres WITH will probably not work but VALUES instead of UNION should still work). Please also notice that "binary" is quoted because it's a reserved postgresql word.
But this is a stand alone query, SQL really become useful IMHO if data is stored inside the DB or gathered automatically by the db. For the inheritance I'm really clueless, it depend on what you try to achieve and i'm just a DB guy.
As for the comment about stored data, that's actually the reason why I haven't considered SQL an option at first. The use case doesn't involve any stored data, so SQL intuitively doesn't sound like the right tool for the job.
In the end, I think the cartesian paradigm can be expressed using SQL, but you have to twist your traditional SQL mindset to do that. You have to forget about tables etc.
But this is a stand alone query, SQL really become useful IMHO if data is stored inside the DB or gathered automatically by the db. For the inheritance I'm really clueless, it depend on what you try to achieve and i'm just a DB guy.