>the purpose of testing is to explain to other other developers what the code under test assumes and what should be expected of it under various conditions
No, the point of automated testing is to verify that what is under test behaves correctly and to be able to scale this verification cheaper than having humans do it. Documenting what it verifies and under what conditions is just a side effect.
That is a common falsehood. Testing does not verify that the code under test behaves correctly. It only verifies that the what the documentation asserts correctly matches what the code does. Indeed, enabling the machine to verify that the documentation is true is cheaper than having humans do it. Also less error prone. Humans are notoriously bad at keeping documentation properly up to date.
