Comment by tpoacher

Unit tests are programmatic specification. I'm assuming it is in this manner that the article is referring to them as documentation, rather than as "explanations" per se.

Obviously unit tests cannot enumerate all inputs, but as a form of programmatic specification, neither do they have to.

For the case you mention where a broad relation should hold, this is a special kind of unit test strategy, which is property testing. Though admittedly other aspects of design-by-contract are also better suited here; nobody's claiming that tests are the best or only programmatic documentation strategy.

Finally, there's another kind of unit testing, which is more appropriately called characterisation testing, as per M. Feathers book on legacy code. The difference being, unit tests are for developing a feature and ensuring adherence to a spec, whereas characterisation tests are for exploring the actual behaviour of existing code (which may or may not be behaving according to the intended spec). These are definitely then tests as programmatic documentation.