Fair enough but it wouldn't surprise me if you just get the exact same problems you get with type systems except phrased differently. You already hinted at this

Fair enough but it wouldn't surprise me if you just get the exact same problems you get with type systems except phrased differently. You already hinted at this somewhat with your "num = num + num" example, surely that's just a type system in disguise? And well, personally I view types more like a way to denote pre- and post-conditions (with varying degrees of strictness). And a grammar just tells you what you are allowed to write, it doesn't dictate semantics. This becomes a problem when you get stuff like "daily_revenue + temperature", which grammatically makes perfect sense, but semantically does not. With types this can be fixed (admittedly in this case it might not be worth fixing), in a grammar this seem very hard to forbid.