Prove correct unit test

Question

I am creating a graph structure for training purposes. I use the TDD approach, so I write a lot of unit tests. However, I am still figuring out how to prove the correctness of my unit tests.

For example, I have this class (not including the implementation, and I simplified it)

public class SimpleGraph(){
 //Returns true on success
 public boolean addEdge(Vertex v1, Vertex v2) { ... }

 //Returns true on sucess
 public boolean addVertex(Vertex v1) { ... }
}

I also created these unit tests.

@Test
public void SimpleGraph_addVertex_noSelfLoopsAllowed(){
 SimpleGraph g = new SimpleGraph();
 Vertex v1 = new Vertex('Vertex 1');
 actual = g.addVertex(v1);
 boolean expected = false;
 boolean actual = g.addEdge(v1,v1);
 Assert.assertEquals(expected,actual);
}

Ok, this is awesome. There is only one question here, I proved that functions only work for this case. However, in my courses on graph theory, everything I do theoretically proves theorems (induction, contradiction, etc.).

So, I was wondering if there is a way to prove my unit tests mathematically for correctness? So there is good practice for this. Therefore, we test the block for correctness, instead of testing it for a specific result.

Answer 1

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int add(int a, int b) {
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    return a + b;
}

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If you are familiar with JML (it's not difficult to learn, mostly Java with a bit of logic), you can try this approach. For the really important parts of your systems, validation can really be something to think about; for other parts of the code, testing some possible unit traces with unit testing may already be sufficient, for example, to avoid regression problems.