Another example of a language with limited dependent typing is Sail. It has "lightweight" dependent types for integers and array lengths (pretty similar to Ada from what it sounds like).
It's very good in my experience - it lets you do a lot of powerful stuff without having to have a PhD in formal verification (again, sounds similar to Ada).
> An example of something you can do in a dependently typed language is write a sorting function in such a way that the type checker proves that the output will always be in sorted order.
Yeah you can't do that but you can have the type checker say things like "n^m is positive if n is positive or even" or "foo(x) -> (bits(n), bits(m)) with m+n=x" (not the actual syntax). I'm pretty sure you can't do that stuff in a type system without dependent types right?