Apple DOS was the first disk operating systems for the Apple II computer range. It was written in 1978 by Paul Laughton of Shepardson Microsystems.
Paul Laughton was originally contracted to write a Basic interpreter before he switched to writing Apple DOS. As this was due to limited resources inside Apple (Woz was busy with the disk hardware and couldn't do the DOS at the same time, which was why Laughton was moved from writing Basic to writing Apple DOS), the question is if Apple originally planned a replacement for Applesoft BASIC which had been released the year before.
Laughton incremented a revision counter whenever he recompiled the code during development, which had become 3.0 for the first beta, and that is why the first release of Apple DOS was version 3.1 (although Laughton's internal revision counter had continued to increment before the release happened).