It is not possible to prove that a program is correct by testing. On the contrary, it has been formally proven that it is impossible to prove programs in general by testing. Theoretical program proofs or plain examination of code can be viable options for those wishing to certify that a program is correct. The test server, as it is based on testing, cannot be used for certification. Its intended use is instead to (cost effectively) find bugs. A successful test suite is one that reveals a bug. If a test suite results in OK, then we know very little that we did not know before.
There are many kinds of test suites. Some concentrate on calling every function or command (in the documented way) in a certain interface. Some others do the same, but use all kinds of illegal parameters, and verify that the server stays alive and rejects the requests with reasonable error codes. Some test suites simulate an application (typically consisting of a few modules of an application), some try to do tricky requests in general, and some test suites even test internal functions with help of special Load Modules on target.
Another interesting category of test suites is the one checking that fixed bugs do not reoccur. When a bugfix is introduced, a test case that checks for that specific bug is written and submitted to the affected test suites.
Aim for finding bugs. Write whatever test that has the highest probability of finding a bug, now or in the future. Concentrate more on the critical parts. Bugs in critical subsystems are much more expensive than others.
Aim for functionality testing rather than implementation details. Implementation details change quite often, and the test suites are to be long lived. Implementation details often differ on different platforms and versions. If implementation details must be tested, try to factor them out into separate test cases. These test cases can later be rewritten or skipped.
Also, aim for testing everything once, no less, no more. It is not effective having every test case fail only because one function in the interface changed.
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