Improve the test infrastructure

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While working on #23, I have run into some challenges because of our messy testing setup. The property-based testing approach seems to work well but there are a few things that need to be improved:

Make adding a new property to a test significantly simpler, with less boilerplate.
#159
#158
#150
#56
#96
#97
Document the testing architecture (see #94)
#59
#61

It might be worthwhile to use an existing testing framework like GoogleTest, but I do not yet know enough about those to make an informed decision.

Start by reading issue #23 and the remaining unchecked items, especially #159, #158, and #150. Compare the current property-based testing approach with the GoogleTest option mentioned here, then define a focused testing-infrastructure scope and a concrete completion criterion before making changes.

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