This "list of trees of increasing size" data structure is not new. You can find plenty of these structures in Okasaki's Purely Functional Data Structures (look

This "list of trees of increasing size" data structure is not new. You can find plenty of these structures in Okasaki's Purely Functional Data Structures (look in the chapter about numerical representations). His random access lists have O(1) adding an element compared to this O(log n).