@seekstar I meet this similar issue and use comapre::natural::<str>().borrowing() to implement. This should work for you also :D

Thank you for the suggestion. But in fact I'm using compare to constrain the argument type of an interface, where Q is the type of key to search in a tree of T, and therefore T and Q is not necessarily String and str. I think in my case impl compare<T, Q> for Natural<T> where T: Borrow<Q> is more suitable.