Dependency with additional headers fails to install

[ossimoi]

• I have searched the issue tracker and believe that this is not a duplicate.

Steps to reproduce

Include greenlet in project dependencies. Run pdm install.

`Traceback (most recent call last):
  File "/home/user/project/.venv/bin/pdm", line 8, in <module>
    sys.exit(main())
             ^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/core.py", line 288, in main
    return Core().main(args or sys.argv[1:])
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/core.py", line 208, in main
    raise cast(Exception, err).with_traceback(traceback) from None
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/core.py", line 203, in main
    self.handle(project, options)
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/core.py", line 157, in handle
    command.handle(project, options)
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/cli/commands/install.py", line 100, in handle
    actions.do_sync(
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/cli/actions.py", line 237, in do_sync
    synchronizer.synchronize()
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 386, in synchronize
    to_add, to_update, to_remove = self.compare_with_working_set()
                                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 217, in compare_with_working_set
    candidates = self.candidates.copy()
                 ^^^^^^^^^^^^^^^
  File "/usr/lib/python3.11/functools.py", line 1001, in __get__
    val = self.func(instance)
          ^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 152, in candidates
    if self.should_install_editables():
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 170, in should_install_editables
    metadata = self.self_candidate.prepare(self.environment).metadata
               ^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.11/functools.py", line 1001, in __get__
    val = self.func(instance)
          ^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 140, in self_candidate
    return self.environment.project.make_self_candidate(not self.no_editable)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/project/core.py", line 505, in make_self_candidate
    can.prepare(self.environment).metadata
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/models/candidates.py", line 605, in metadata
    result = self.prepare_metadata()
             ^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/models/candidates.py", line 512, in prepare_metadata
    return self._get_metadata_from_build(self._unpacked_dir, metadata_parent)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/models/candidates.py", line 587, in _get_metadata_from_build
    self._metadata_dir = builder(source_dir, self.environment).prepare_metadata(metadata_parent)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/builders/editable.py", line 21, in prepare_metadata
    self.install(self._requires, shared=True)
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/builders/base.py", line 298, in install
    install_requirements(missing, env)
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/core.py", line 30, in install_requirements
    syncer.synchronize()
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/synchronizers.py", line 256, in synchronize
    manager.install(can)
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/manager.py", line 34, in install
    dist_info = installer(str(prepared.build()), self.environment, prepared.direct_url())
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/installers.py", line 199, in install_wheel
    return _install_wheel(wheel=wheel, destination=destination, additional_metadata=additional_metadata)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/installers.py", line 312, in _install_wheel
    install(source, destination, additional_metadata=additional_metadata or {})
  File "/home/user/project/.venv/lib/python3.11/site-packages/installer/_core.py", line 109, in install
    record = destination.write_file(
             ^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/installer/destinations.py", line 207, in write_file
    return self.write_to_fs(scheme, path_, stream, is_executable)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/pdm/installers/installers.py", line 167, in write_to_fs
    return super().write_to_fs(scheme, path, stream, is_executable)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/user/project/.venv/lib/python3.11/site-packages/installer/destinations.py", line 173, in write_to_fs
    with open(target_path, "wb") as f:
         ^^^^^^^^^^^^^^^^^^^^^^^
PermissionError: [Errno 13] Permission denied: '/usr/include/python3.11/greenlet.h'

# Paste the output of `pdm info && pdm info --env` below:
PDM version:
  2.12.1
Python Interpreter:
  /home/user/project/.venv/bin/python (3.11)
Project Root:
  /home/user/project

Happens when pdm is installed in either system or venv. pip install greenlet works.

[frostming]

What's the output of /home/user/project/.venv/bin/python -m sysconfig?

[ossimoi]

What's the output of /home/user/project/.venv/bin/python -m sysconfig?

Platform: "linux-x86_64"
Python version: "3.11"
Current installation scheme: "venv"

Paths:
        data = "/home/user/project/.venv"
        include = "/usr/include/python3.11"
        platinclude = "/usr/include/python3.11"
        platlib = "/home/user/project/.venv/lib/python3.11/site-packages"
        platstdlib = "/home/user/project/.venv/lib/python3.11"
        purelib = "/home/user/project/.venv/lib/python3.11/site-packages"
        scripts = "/home/user/project/.venv/bin"
        stdlib = "/usr/lib/python3.11"

I assume include dir is wrong? If you need the full list of vars provided by sysconfig I'll pastebin it.