Is 'polymorphism' possible when trait has dependent types?

pub trait A<'a> {
    type R: R + 'a;
    type S: S + 'a;

Suppose I want to create a struct that holds something that implements the A trait:

pub struct B<'a> {
    a: &dyn A<'a>,

but I want B::new(u8 type) to dynamically decide which object it's gonna hold in the a field, based on the value of type. Since A has these custom types R and S, I couldn't find a way to make this thing compile. Is it possible to do what I want? If there was no dependent types, I guess yes, but with dependent types, I don't know.

No, trait objects must specify the value of all associated types.

error[E0191]: the value of the associated types `R` (from trait `A`), `S` (from trait `A`) must be specified
 --> src/
5 |     type R: R + 'a;
  |     --------------- `R` defined here
6 |     type S: S + 'a;
  |     --------------- `S` defined here
9 |     a: &'a dyn A<'a>,
  |                ^^^^^ help: specify the associated types: `A<'a, R = Type, S = Type>`

You could perhaps simulate it by not using associated types and having the A trait contain a new_r method that produces a dyn R.


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