0. no moves. This is very often needed for FFI callbacks, among others.
1. trivial copies. This is similar to 2, but means you do not have to do `swap`-like things in cases for non-destructive moves (which are, in fact, also important, they just shouldn't be the only kind of move. Note that supporting destructive moves likely implies supporting destructuring).
2. trivial moves. You can just use `memcpy`, `realloc`, etc. This is the only kind of move supported by Rust. C++ can introspect for it but with severe limitations. Note that "trivial" does NOT mean "cheap"; memory can be large.
3. moves with retroactive fixup (old address considered dead). What you do here is call `realloc` or whatever, then pass the old address (or the delta?) to a fixup function so that it (possibly with offset) can be replaced with the new address. Great caution is required to avoid UB by C's rules (the delta approach may be safer?). The compiler needs to be able to optimize this into the preceding when the fixup turns out to be empty (since generic wrapper classes may not know if their fields are trivially-movable or not).
4. full moves (both old and new address ranges are valid at the same time). C++ is the only language I know that supports this (though it is limited to non-destructive moves). One major use for this is maintaining "peer pointers" without forcing an extra allocation. Note that this can be simulated on top of "no moves" with some extra verbosity (C++98 anyone?).
Related to this, it really is essential for allocators to provide a "reallocate in place if possible, else fail" function, to avoid unnecessary move-constructor calls. Unfortunately, real-world allocators do not actually avoid copies if you use `malloc_usable_size` + `realloc`. If emitting C, note that you must avoid `__attribute__((malloc))` etc. to avoid setting off the bug-laden-piece-of-crap that is `__builtin_dynamic_object_size`.
Random reminder that "conditionally insert and move my object(s) into a container (usually a map), but keep my object alive if an equal one was already there" is important, and most languages do it pretty badly.
What are they?