That's an interesting question, but one that doesn't seem to have a really well defined answer. The best I can come up with is that if you want to talk about t

That's an interesting question, but one that doesn't seem to have a really well defined answer. The best I can come up with is that if you want to talk about the product of function types (A -> X) x (B -> X) then a sum type allows you to summarize this a single function type (A+B -> X). With just a product you could already do something similar for the type (X -> A) x (X -> B) which is equivalent to (X -> AxB), but with a sum type you have the dual variant as well. And I suppose that with sum and product types together you can kind of express BNF like rules directly in the type system. Which makes things like expressing syntax trees a hell of a lot cleaner. That said ultimately a type system is just a part of the language you can use to express certain rules, you can usually still decide on your own rules you'll just have to enforce them manually.