Homebrew claims cairo depends on Python - homebrew

Question

When uninstalling the python#3.9 package, Homebrew complains that the cairo package depends on it. This is unlikely to be true:
brew uses python#3.9
lists several packages but not cairo, and
brew deps --tree cairo
shows a tree without any python#*.* in it. On the other hand,
brew uses --installed python#3.9
does list the cairo package, and commands like brew missing and brew doctor create a warning about the missing dependency python#3.9.
I don't know whether the cairo package (see its formula here) somehow depends on python#3.9, but I guess it does not, and the behavior is weird. What's going on and how can it be fixed?

Answer 1

I think I've found what causes the problem, inspired by a comment on an old issue on Homebrew's Github repository:
brew uses --installed uses the dependency resolution information from your installed formulae whereas brew uses alone does not.
Indeed, whereas the formula doesn't contain a dependency on python#3.9, the installed package does: on my system, the file /opt/homebrew/Cellar/cairo/1.16.0_5/INSTALL_RECEIPT.json has a key runtime_dependencies that includes this element:
{
"full_name": "python#3.9",
"version": "3.9.9",
"declared_directly": false
}
In a further comment, the developer explains:
When built from source some things pick up dependencies opportunistically i.e. they link against stuff without us trying to make them do so. The other thing where this kicks in is if you've built a formula with a particular, non-default option. We now store these links in the formula itself and use it for certain commands so you get a result that's correct for your system (i.e. brew uses --installed doesn't miss results that will break things if uninstalled).
This may not be a complete explanation (I'm pretty sure I installed cairo from a binary 'bottle' without any non-standard options), but it does suggest the general area where the issue may have arisen.
The next thing to find out is how to resolve the issue. I don't know whether there's an official workaround, but the options seem to be
Manually remove that part from INSTALL_RECEIPT.json
Uninstall the cairo package while suppressing warnings and removal of dependent packages, and then reinstall it.
I chose 1. and it seems (so far) to work.