It would be criminal to list sets of operating systems that provide real innovations without including the "granddaddy" of modern operating systems, Multics.
The Multics development project provided, many years ago, a rich set of OS innovations many of which are still being integrated into the mainstream including such things as:
Separating the command shell from the operating system kernel, as discussed here.
Hierarchical file systems
Lots of developments in management of virtual memory.
If you think that segmented memory is fundamentally evil, that's probably because you think that segments must be 64K in size. That was true with early Intel CPUs, which meant that it became a hard-coded assumption in Microsoft OSes, and that invokes a whole mouthful of evils. The fact that certain hardware and software vendors have worked together to create monstrously flawed implementations of memory segmentation does not ipso facto imply that the notion of segmentation is itself flawed.
Many developments in the area of secure computer systems.
One version of Multics was rated "B3" by the NCSC. A subsequent system (based on the Multics experience) built by Honeywell was the first computer system ever rated "A1."
Mapping of logical disk volumes onto physical volumes ("volume" ~= "partition")
Multics Relational Data Store (MRDS) - The first commercial relational database management system
Management of shared memory
Spreadsheets were developed on the Multics platform.
The book The Multics System; An Examination of Its Structure may be found at Amazon.com. It is long out of print, and they may not be able to get the book...
A would-be Multics emulation
The results [of a 1974 Air Force audit of Multics] are still interesting today, because many of the concepts of UNIX and other modern operating systems came directly from Multics. This paper revisits those results and relates them to the widespread security problems that the computer industry is suffering today. The unpleasant conclusion is that although few, if any, fundamentally new vulnerabilities are evident today, today's products generally do not even include many of the Multics security techniques, let alone the enhancements identified as 'essential.'
Concealment of...penetrations does nothing to deter a sophisticated penetrator and can in fact impede technical interchange and delay the development of a proper solution. A system which contains vulnerabilities cannot be protected by keeping those vulnerabilities secret.
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