I think we're saying the same thing. If f(T) can return U or throw A or B or C, there needs to be a way to declare that Stream<T>#map takes a Function<T, U, A|B

I think we're saying the same thing. If f(T) can return U or throw A or B or C, there needs to be a way to declare that Stream<T>#map takes a Function<T, U, A|B|C> and returns a Stream<U> or throws A or B or C. But that sum type A|B|C doesn't exist in Java if there's no common base class.