Following McQuaid's suggestion, I chose a practical target: installing Homebrew on Alpine Linux. I understood each step and the current issues faced, then I wrote an article describing the installation process.

According to the current tier policy, Alpine Linux should be considered Tier 2. Since Homebrew doesn't appear to be interested in migrating its images to Alpine, I didn't add CI tests running on Alpine Linux.

The current issues of installing and running Homebrew on Alpine Linux are:

• It needs to patch ldd for installation.
  • This is unavoidable, Apline Linux is based on musl libc.
• It needs long options of grep and sort for installation, but busybox do not support them.
  • This would be unneeded after this PR merged.
• It needs /usr/bin/stat existing for installation, but Alpine Linux only has /bin/stat.
  • This should be resolved after the /usr-merge work.
• brew shellenv needs ps to support -p option, but busybox do not support it.
  • -p is POSIX-required, that should be fixed by busybox.
  • This can be bypassed by explicitly providing the second argument, such as brew shellenv sh.
• brew list needs ls to support -q option, but busybox do not support it.
  • -q is POSIX-required, that should be fixed by busybox.
  • We can use a stub script to patch the ls command.
• The uninstallation script need find to support -lname option, but busybox do not support it.
  • The uninstallation script is not used often. It would be easy to edit it before executing it.

In summary, the changes involved in this PR are all the required changes.