Understanding correctness of code really comes down to proving that the code does the right thing. What tools do we have as programmers for proving the correctness of our code?
 Tests prove that the code is correct for specific inputs.
 Type systems prove the absence of (certain kinds of) incorrectness.
 Theorem provers prove sophisticated claims about our code for us.
 Monitoring tools prove that incorrect behavior hasn’t occurred yet, or provide us with a concrete counter example when it happens.^{1}
 Program authors can prove the correctness of their code (i.e., with a traditional penandpaper proof).
The first three are exciting because they involve a computer doing most of the work for us! The fourth might seem not helpful, but is often better than nothing, and in many situations can be leveraged into making powerful claims. None of the above are as universally applicable as the last: doing the proof ourself, but it’s also usually the most error prone.
Note the double negation in (2). Type systems themselves don’t prove correctness, they prove that there aren’t certain kinds of incorrectness, namely: type errors. Meanwhile, tests are rarely (if ever) exhaustive, and frequently allow bugs to pass through to production. This is why testing, types, and monitoring are complementary—one is not a substitute for another.
The hardest part of writing highquality software is ensuring that it runs without bugs. The more tools we have in our arsenal to combat incorrectness, the easier it is to write code for the long term.

Recall that raising an exception is logically the same as throwing a value to a continuation and carrying out a proof by contradiction!↩