Closure returning borrowed value

[LorenzSelv]

fn stateful<ProduceOutputClj>(clj: ProduceOutputClj)
    where
        ProduceOutputClj: FnMut(Box<dyn FnMut() -> Option<&usize>>)
{
    let next_update =  {
        let mut x = 1_usize;
        move || {
            if x < 5 { x += 1; Some(&x) }
            else { None }
        }
    };
    
    clj(Box::new(next_update));
}

fn main() {
    stateful(|next_update| { 
        while let Some(x) = next_update() {
            println!("next update is {:?}", x);
        }
    });
}

(Playground)

Errors:

   Compiling playground v0.0.1 (/playground)
error[E0106]: missing lifetime specifier
 --> src/main.rs:4:59
  |
4 |         ProduceOutputClj: FnMut(Box<dyn FnMut() -> Option<&usize>>)
  |                                                           ^ help: consider giving it a 'static lifetime: `&'static`
  |
  = help: this function's return type contains a borrowed value, but there is no value for it to be borrowed from

error: aborting due to previous error

For more information about this error, try `rustc --explain E0106`.
error: could not compile `playground`.

To learn more, run the command again with --verbose.

I'm having some trouble getting this code to compile due to lifetime issues.

What I would like to do is to provide the caller of the stateful function with a closure (next_update) that, when invoked multiple times, returns references to some data owned by the stateful function (x: usize in this example).

I tried to use explicit lifetimes but none of the my attemps worked out.

Thanks in advance.

[alice]

You can't return references into the closure itself due to the signature of call_mut, which doesn't allow the Self::Output type to depend on the lifetime on the &mut self.