Thank you. This helps. But does that mean a POSIX shell, or any other UNIX utility, must implement these operators. Using them in shell scripts makes the scripts non-portable, e.g., Almquist sh, NetBSD Almquist sh or Debian Almquist sh do not support them. Maybe the author of the "Pure POSIX Sh Bible" always runs Bash in --posix mode. Hence "Pure POSIX sh".
This just means that you're going to have to find a better way to describe the level of backwards compatibility you're going for other than "POSIX compliance", because these do seem to be required in the standards.
Seems like there are different interpretations by authors/maintainers of what is required versus what is optional.
As an ordinary user, I am most interested, perhaps mistakenly, in POSIX for a single reason: portability. (Whether portability is a goal of POSIX I am not sure. I have not done much research. Maybe it isn't.) As a user, I want to be able to write scripts on Linux than run on BSD and vice versa. Perhaps I have conflated portability with "POSIX compliance". However, as a practical matter, I would not use these operators in scripts that I wanted to be portable. When I have the motivation, I am working on a unenhanced port of NetBSD sh to Linux, i.e., without the Herbert Xu changes. Being lazy, so far I just added tab completion to dash so it feels more like NetBSD sh.
The "Bible" I would be interested in reading, if it exists. is the "Portable Sh Bible". (I am not a Bash user.) When I have a question I usually consult https://www.in-ulm.de/~mascheck/
