As of today 3.11-dev requires Programs/_freeze_module to compile Python code to byte code. The dependency on an extra and special tool makes cross building more complicated. The _freeze_module is trivial and can be easily implemented in pure Python code. The re-introduction of _bootstrap_python helper would allow us to use a pure Python freeze_module for all modules except two importlib bootstrap modules. I have a proof of concept implementation that works for me.

Proposal for standard builds:
- Use Programs/_freeze_module to create Python/frozen_modules/importlib._bootstrap.h and Python/frozen_modules/importlib._bootstrap_external.h
- build _bootstrap_python
- use new tool "./_bootstrap_python Tools/scripts/freezemodule.py" to create remaining Python/frozen_modules/*.h

Proposal for cross builds:
- use user-provider Python interpreter (./configure --with-build-python) to generate all Python/frozen_modules/*.h with new freezemodule.py tool.

When cross building the user must already provide a Python interpreter with same version and bytecode version as the build target. Users would no longer need to provide a _freeze_module binary with ./configure --with-freeze-module.

IIRC, Programs/_freeze_module.c was originally a C implementation of the basic functionality in Tools/freeze/freeze.py.

Ideally we would not have two scripts that do the same thing.

Eric, could you review my PR, please? It simplifies cross building to other platforms.

I took a look at Tools/freeze/freeze.py. The freeze tool creates different output than Program/_freeze_module.c.

In his code review Eric made a point that the relationship of variables and their impact on normal and cross builds are not obvious. I'm going to introduce new variables for freezing and freezing dependencies. Bonus: Cross builds no longer build non-functional _bootstrap_python and Programs/_freeze_module.

Normal build:

PYTHON_FOR_FREEZE=./_bootstrap_python
FREEZE_MODULE_BOOTSTRAP=./Programs/_freeze_module
FREEZE_MODULE_BOOTSTRAP_DEPS=Programs/_freeze_module
FREEZE_MODULE=$(PYTHON_FOR_FREEZE) $(srcdir)/Programs/_freeze_module.py
FREEZE_MODULE_DEPS=_bootstrap_python $(srcdir)/Programs/_freeze_module.py


Cross build:

PYTHON_FOR_FREEZE=/path/to/build/python
FREEZE_MODULE_BOOTSTRAP=$(PYTHON_FOR_FREEZE) $(srcdir)/Programs/_freeze_module.py
FREEZE_MODULE_BOOTSTRAP_DEPS=$(srcdir)/Programs/_freeze_module.py
FREEZE_MODULE=$(FREEZE_MODULE_BOOTSTRAP)
FREEZE_MODULE_DEPS=$(FREEZE_MODULE_BOOTSTRAP_DEPS)

New changeset eb483c46d62707bdf705491f76cf1fa9642fb47e by Christian Heimes in branch 'main':
bpo-45949: Pure Python freeze module for cross builds (GH-29899)
https://github.com/python/cpython/commit/eb483c46d62707bdf705491f76cf1fa9642fb47e

Thanks for your review, Eric!

You're welcome!  Thanks for doing the work!