There is a straight-forward mapping of the IPv4 address space into IPv6 (you can do ping6 "::ffff:127.0.0.1"), and for new development that is also by far the easiest way to support both protocols: the application does everything in IPv6, and without writing a single line of code, the OS takes care of transparently using IPv4 when needed.

There is no mapping back from IPv6 to IPv4 (so IPv6 is backwards compatible, but not forwards compatible), but it can't be because the whole point is to have a larger address space.